A framework for grand scale parallelization of the combined finite discrete element method in 2d
Lei, Z.; Rougier, E.; Knight, E. E.; Munjiza, A.
2014-09-01
Within the context of rock mechanics, the Combined Finite-Discrete Element Method (FDEM) has been applied to many complex industrial problems such as block caving, deep mining techniques (tunneling, pillar strength, etc.), rock blasting, seismic wave propagation, packing problems, dam stability, rock slope stability, rock mass strength characterization problems, etc. The reality is that most of these were accomplished in a 2D and/or single processor realm. In this work a hardware independent FDEM parallelization framework has been developed using the Virtual Parallel Machine for FDEM, (V-FDEM). With V-FDEM, a parallel FDEM software can be adapted to different parallel architecture systems ranging from just a few to thousands of cores.
Synchronization Techniques in Parallel Discrete Event Simulation
Lindén, Jonatan
2018-01-01
Discrete event simulation is an important tool for evaluating system models in many fields of science and engineering. To improve the performance of large-scale discrete event simulations, several techniques to parallelize discrete event simulation have been developed. In parallel discrete event simulation, the work of a single discrete event simulation is distributed over multiple processing elements. A key challenge in parallel discrete event simulation is to ensure that causally dependent ...
Directory of Open Access Journals (Sweden)
Spyridon Liakas
2017-08-01
Full Text Available The particulate discrete element method (DEM can be employed to capture the response of rock, provided that appropriate bonding models are used to cement the particles to each other. Simulations of laboratory tests are important to establish the extent to which those models can capture realistic rock behaviors. Hitherto the focus in such comparison studies has either been on homogeneous specimens or use of two-dimensional (2D models. In situ rock formations are often heterogeneous, thus exploring the ability of this type of models to capture heterogeneous material behavior is important to facilitate their use in design analysis. In situ stress states are basically three-dimensional (3D, and therefore it is important to develop 3D models for this purpose. This paper revisits an earlier experimental study on heterogeneous specimens, of which the relative proportions of weaker material (siltstone and stronger, harder material (sandstone were varied in a controlled manner. Using a 3D DEM model with the parallel bond model, virtual heterogeneous specimens were created. The overall responses in terms of variations in strength and stiffness with different percentages of weaker material (siltstone were shown to agree with the experimental observations. There was also a good qualitative agreement in the failure patterns observed in the experiments and the simulations, suggesting that the DEM data enabled analysis of the initiation of localizations and micro fractures in the specimens.
Chen, Jian; Matuttis, Hans-Georg
2013-02-01
We report our experiences with the optimization and parallelization of a discrete element code for convex polyhedra on multi-core machines and introduce a novel variant of the sort-and-sweep neighborhood algorithm. While in theory the whole code in itself parallelizes ideally, in practice the results on different architectures with different compilers and performance measurement tools depend very much on the particle number and optimization of the code. After difficulties with the interpretation of the data for speedup and efficiency are overcome, respectable parallelization speedups could be obtained.
A parallel Discrete Element Method to model collisions between non-convex particles
Directory of Open Access Journals (Sweden)
Rakotonirina Andriarimina Daniel
2017-01-01
Full Text Available In many dry granular and suspension flow configurations, particles can be highly non-spherical. It is now well established in the literature that particle shape affects the flow dynamics or the microstructure of the particles assembly in assorted ways as e.g. compacity of packed bed or heap, dilation under shear, resistance to shear, momentum transfer between translational and angular motions, ability to form arches and block the flow. In this talk, we suggest an accurate and efficient way to model collisions between particles of (almost arbitrary shape. For that purpose, we develop a Discrete Element Method (DEM combined with a soft particle contact model. The collision detection algorithm handles contacts between bodies of various shape and size. For nonconvex bodies, our strategy is based on decomposing a non-convex body into a set of convex ones. Therefore, our novel method can be called “glued-convex method” (in the sense clumping convex bodies together, as an extension of the popular “glued-spheres” method, and is implemented in our own granular dynamics code Grains3D. Since the whole problem is solved explicitly, our fully-MPI parallelized code Grains3D exhibits a very high scalability when dynamic load balancing is not required. In particular, simulations on up to a few thousands cores in configurations involving up to a few tens of millions of particles can readily be performed. We apply our enhanced numerical model to (i the collapse of a granular column made of convex particles and (i the microstructure of a heap of non-convex particles in a cylindrical reactor.
Arteaga, Santiago Egido
1998-12-01
The steady-state Navier-Stokes equations are of considerable interest because they are used to model numerous common physical phenomena. The applications encountered in practice often involve small viscosities and complicated domain geometries, and they result in challenging problems in spite of the vast attention that has been dedicated to them. In this thesis we examine methods for computing the numerical solution of the primitive variable formulation of the incompressible equations on distributed memory parallel computers. We use the Galerkin method to discretize the differential equations, although most results are stated so that they apply also to stabilized methods. We also reformulate some classical results in a single framework and discuss some issues frequently dismissed in the literature, such as the implementation of pressure space basis and non- homogeneous boundary values. We consider three nonlinear methods: Newton's method, Oseen's (or Picard) iteration, and sequences of Stokes problems. All these iterative nonlinear methods require solving a linear system at every step. Newton's method has quadratic convergence while that of the others is only linear; however, we obtain theoretical bounds showing that Oseen's iteration is more robust, and we confirm it experimentally. In addition, although Oseen's iteration usually requires more iterations than Newton's method, the linear systems it generates tend to be simpler and its overall costs (in CPU time) are lower. The Stokes problems result in linear systems which are easier to solve, but its convergence is much slower, so that it is competitive only for large viscosities. Inexact versions of these methods are studied, and we explain why the best timings are obtained using relatively modest error tolerances in solving the corresponding linear systems. We also present a new damping optimization strategy based on the quadratic nature of the Navier-Stokes equations, which improves the robustness of all the
Energy Technology Data Exchange (ETDEWEB)
Morris, J; Johnson, S
2007-12-03
The Distinct Element Method (also frequently referred to as the Discrete Element Method) (DEM) is a Lagrangian numerical technique where the computational domain consists of discrete solid elements which interact via compliant contacts. This can be contrasted with Finite Element Methods where the computational domain is assumed to represent a continuum (although many modern implementations of the FEM can accommodate some Distinct Element capabilities). Often the terms Discrete Element Method and Distinct Element Method are used interchangeably in the literature, although Cundall and Hart (1992) suggested that Discrete Element Methods should be a more inclusive term covering Distinct Element Methods, Displacement Discontinuity Analysis and Modal Methods. In this work, DEM specifically refers to the Distinct Element Method, where the discrete elements interact via compliant contacts, in contrast with Displacement Discontinuity Analysis where the contacts are rigid and all compliance is taken up by the adjacent intact material.
Parallel discrete event simulation
Overeinder, B.J.; Hertzberger, L.O.; Sloot, P.M.A.; Withagen, W.J.
1991-01-01
In simulating applications for execution on specific computing systems, the simulation performance figures must be known in a short period of time. One basic approach to the problem of reducing the required simulation time is the exploitation of parallelism. However, in parallelizing the simulation
Synchronization Of Parallel Discrete Event Simulations
Steinman, Jeffrey S.
1992-01-01
Adaptive, parallel, discrete-event-simulation-synchronization algorithm, Breathing Time Buckets, developed in Synchronous Parallel Environment for Emulation and Discrete Event Simulation (SPEEDES) operating system. Algorithm allows parallel simulations to process events optimistically in fluctuating time cycles that naturally adapt while simulation in progress. Combines best of optimistic and conservative synchronization strategies while avoiding major disadvantages. Algorithm processes events optimistically in time cycles adapting while simulation in progress. Well suited for modeling communication networks, for large-scale war games, for simulated flights of aircraft, for simulations of computer equipment, for mathematical modeling, for interactive engineering simulations, and for depictions of flows of information.
A curvature theory for discrete surfaces based on mesh parallelity
Bobenko, Alexander Ivanovich
2009-12-18
We consider a general theory of curvatures of discrete surfaces equipped with edgewise parallel Gauss images, and where mean and Gaussian curvatures of faces are derived from the faces\\' areas and mixed areas. Remarkably these notions are capable of unifying notable previously defined classes of surfaces, such as discrete isothermic minimal surfaces and surfaces of constant mean curvature. We discuss various types of natural Gauss images, the existence of principal curvatures, constant curvature surfaces, Christoffel duality, Koenigs nets, contact element nets, s-isothermic nets, and interesting special cases such as discrete Delaunay surfaces derived from elliptic billiards. © 2009 Springer-Verlag.
Program For Parallel Discrete-Event Simulation
Beckman, Brian C.; Blume, Leo R.; Geiselman, John S.; Presley, Matthew T.; Wedel, John J., Jr.; Bellenot, Steven F.; Diloreto, Michael; Hontalas, Philip J.; Reiher, Peter L.; Weiland, Frederick P.
1991-01-01
User does not have to add any special logic to aid in synchronization. Time Warp Operating System (TWOS) computer program is special-purpose operating system designed to support parallel discrete-event simulation. Complete implementation of Time Warp mechanism. Supports only simulations and other computations designed for virtual time. Time Warp Simulator (TWSIM) subdirectory contains sequential simulation engine interface-compatible with TWOS. TWOS and TWSIM written in, and support simulations in, C programming language.
Massively Parallel Finite Element Programming
Heister, Timo
2010-01-01
Today\\'s large finite element simulations require parallel algorithms to scale on clusters with thousands or tens of thousands of processor cores. We present data structures and algorithms to take advantage of the power of high performance computers in generic finite element codes. Existing generic finite element libraries often restrict the parallelization to parallel linear algebra routines. This is a limiting factor when solving on more than a few hundreds of cores. We describe routines for distributed storage of all major components coupled with efficient, scalable algorithms. We give an overview of our effort to enable the modern and generic finite element library deal.II to take advantage of the power of large clusters. In particular, we describe the construction of a distributed mesh and develop algorithms to fully parallelize the finite element calculation. Numerical results demonstrate good scalability. © 2010 Springer-Verlag.
Massively Parallel Finite Element Programming
Heister, Timo; Kronbichler, Martin; Bangerth, Wolfgang
2010-01-01
Today's large finite element simulations require parallel algorithms to scale on clusters with thousands or tens of thousands of processor cores. We present data structures and algorithms to take advantage of the power of high performance computers in generic finite element codes. Existing generic finite element libraries often restrict the parallelization to parallel linear algebra routines. This is a limiting factor when solving on more than a few hundreds of cores. We describe routines for distributed storage of all major components coupled with efficient, scalable algorithms. We give an overview of our effort to enable the modern and generic finite element library deal.II to take advantage of the power of large clusters. In particular, we describe the construction of a distributed mesh and develop algorithms to fully parallelize the finite element calculation. Numerical results demonstrate good scalability. © 2010 Springer-Verlag.
Discrete elements method of neutron transport
International Nuclear Information System (INIS)
Mathews, K.A.
1988-01-01
In this paper a new neutron transport method, called discrete elements (L N ) is derived and compared to discrete ordinates methods, theoretically and by numerical experimentation. The discrete elements method is based on discretizing the Boltzmann equation over a set of elements of angle. The discrete elements method is shown to be more cost-effective than discrete ordinates, in terms of accuracy versus execution time and storage, for the cases tested. In a two-dimensional test case, a vacuum duct in a shield, the L N method is more consistently convergent toward a Monte Carlo benchmark solution
Parallel discrete event simulation using shared memory
Reed, Daniel A.; Malony, Allen D.; Mccredie, Bradley D.
1988-01-01
With traditional event-list techniques, evaluating a detailed discrete-event simulation-model can often require hours or even days of computation time. By eliminating the event list and maintaining only sufficient synchronization to ensure causality, parallel simulation can potentially provide speedups that are linear in the numbers of processors. A set of shared-memory experiments, using the Chandy-Misra distributed-simulation algorithm, to simulate networks of queues is presented. Parameters of the study include queueing network topology and routing probabilities, number of processors, and assignment of network nodes to processors. These experiments show that Chandy-Misra distributed simulation is a questionable alternative to sequential-simulation of most queueing network models.
An inherently parallel method for solving discretized diffusion equations
International Nuclear Information System (INIS)
Eccleston, B.R.; Palmer, T.S.
1999-01-01
A Monte Carlo approach to solving linear systems of equations is being investigated in the context of the solution of discretized diffusion equations. While the technique was originally devised decades ago, changes in computer architectures (namely, massively parallel machines) have driven the authors to revisit this technique. There are a number of potential advantages to this approach: (1) Analog Monte Carlo techniques are inherently parallel; this is not necessarily true to today's more advanced linear equation solvers (multigrid, conjugate gradient, etc.); (2) Some forms of this technique are adaptive in that they allow the user to specify locations in the problem where resolution is of particular importance and to concentrate the work at those locations; and (3) These techniques permit the solution of very large systems of equations in that matrix elements need not be stored. The user could trade calculational speed for storage if elements of the matrix are calculated on the fly. The goal of this study is to compare the parallel performance of Monte Carlo linear solvers to that of a more traditional parallelized linear solver. The authors observe the linear speedup that they expect from the Monte Carlo algorithm, given that there is no domain decomposition to cause significant communication overhead. Overall, PETSc outperforms the Monte Carlo solver for the test problem. The PETSc parallel performance improves with larger numbers of unknowns for a given number of processors. Parallel performance of the Monte Carlo technique is independent of the size of the matrix and the number of processes. They are investigating modifications to the scheme to accommodate matrix problems with positive off-diagonal elements. They are also currently coding an on-the-fly version of the algorithm to investigate the solution of very large linear systems
Discrete elements method of neutral particle transport
International Nuclear Information System (INIS)
Mathews, K.A.
1983-01-01
A new discrete elements (L/sub N/) transport method is derived and compared to the discrete ordinates S/sub N/ method, theoretically and by numerical experimentation. The discrete elements method is more accurate than discrete ordinates and strongly ameliorates ray effects for the practical problems studied. The discrete elements method is shown to be more cost effective, in terms of execution time with comparable storage to attain the same accuracy, for a one-dimensional test case using linear characteristic spatial quadrature. In a two-dimensional test case, a vacuum duct in a shield, L/sub N/ is more consistently convergent toward a Monte Carlo benchmark solution than S/sub N/, using step characteristic spatial quadrature. An analysis of the interaction of angular and spatial quadrature in xy-geometry indicates the desirability of using linear characteristic spatial quadrature with the L/sub N/ method
Running Parallel Discrete Event Simulators on Sierra
Energy Technology Data Exchange (ETDEWEB)
Barnes, P. D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Jefferson, D. R. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2015-12-03
In this proposal we consider porting the ROSS/Charm++ simulator and the discrete event models that run under its control so that they run on the Sierra architecture and make efficient use of the Volta GPUs.
Parallel image encryption algorithm based on discretized chaotic map
International Nuclear Information System (INIS)
Zhou Qing; Wong Kwokwo; Liao Xiaofeng; Xiang Tao; Hu Yue
2008-01-01
Recently, a variety of chaos-based algorithms were proposed for image encryption. Nevertheless, none of them works efficiently in parallel computing environment. In this paper, we propose a framework for parallel image encryption. Based on this framework, a new algorithm is designed using the discretized Kolmogorov flow map. It fulfills all the requirements for a parallel image encryption algorithm. Moreover, it is secure and fast. These properties make it a good choice for image encryption on parallel computing platforms
A curvature theory for discrete surfaces based on mesh parallelity
Bobenko, Alexander Ivanovich; Pottmann, Helmut; Wallner, Johannes
2009-01-01
We consider a general theory of curvatures of discrete surfaces equipped with edgewise parallel Gauss images, and where mean and Gaussian curvatures of faces are derived from the faces' areas and mixed areas. Remarkably these notions are capable
Discrete Hadamard transformation algorithm's parallelism analysis and achievement
Hu, Hui
2009-07-01
With respect to Discrete Hadamard Transformation (DHT) wide application in real-time signal processing while limitation in operation speed of DSP. The article makes DHT parallel research and its parallel performance analysis. Based on multiprocessor platform-TMS320C80 programming structure, the research is carried out to achieve two kinds of parallel DHT algorithms. Several experiments demonstrated the effectiveness of the proposed algorithms.
Yan, Beichuan; Regueiro, Richard A.
2018-02-01
A three-dimensional (3D) DEM code for simulating complex-shaped granular particles is parallelized using message-passing interface (MPI). The concepts of link-block, ghost/border layer, and migration layer are put forward for design of the parallel algorithm, and theoretical scalability function of 3-D DEM scalability and memory usage is derived. Many performance-critical implementation details are managed optimally to achieve high performance and scalability, such as: minimizing communication overhead, maintaining dynamic load balance, handling particle migrations across block borders, transmitting C++ dynamic objects of particles between MPI processes efficiently, eliminating redundant contact information between adjacent MPI processes. The code executes on multiple US Department of Defense (DoD) supercomputers and tests up to 2048 compute nodes for simulating 10 million three-axis ellipsoidal particles. Performance analyses of the code including speedup, efficiency, scalability, and granularity across five orders of magnitude of simulation scale (number of particles) are provided, and they demonstrate high speedup and excellent scalability. It is also discovered that communication time is a decreasing function of the number of compute nodes in strong scaling measurements. The code's capability of simulating a large number of complex-shaped particles on modern supercomputers will be of value in both laboratory studies on micromechanical properties of granular materials and many realistic engineering applications involving granular materials.
Parallel ray tracing for one-dimensional discrete ordinate computations
International Nuclear Information System (INIS)
Jarvis, R.D.; Nelson, P.
1996-01-01
The ray-tracing sweep in discrete-ordinates, spatially discrete numerical approximation methods applied to the linear, steady-state, plane-parallel, mono-energetic, azimuthally symmetric, neutral-particle transport equation can be reduced to a parallel prefix computation. In so doing, the often severe penalty in convergence rate of the source iteration, suffered by most current parallel algorithms using spatial domain decomposition, can be avoided while attaining parallelism in the spatial domain to whatever extent desired. In addition, the reduction implies parallel algorithm complexity limits for the ray-tracing sweep. The reduction applies to all closed, linear, one-cell functional (CLOF) spatial approximation methods, which encompasses most in current popular use. Scalability test results of an implementation of the algorithm on a 64-node nCube-2S hypercube-connected, message-passing, multi-computer are described. (author)
Parallel Element Agglomeration Algebraic Multigrid and Upscaling Library
Energy Technology Data Exchange (ETDEWEB)
2017-10-24
ParELAG is a parallel C++ library for numerical upscaling of finite element discretizations and element-based algebraic multigrid solvers. It provides optimal complexity algorithms to build multilevel hierarchies and solvers that can be used for solving a wide class of partial differential equations (elliptic, hyperbolic, saddle point problems) on general unstructured meshes. Additionally, a novel multilevel solver for saddle point problems with divergence constraint is implemented.
Scalable parallel prefix solvers for discrete ordinates transport
International Nuclear Information System (INIS)
Pautz, S.; Pandya, T.; Adams, M.
2009-01-01
The well-known 'sweep' algorithm for inverting the streaming-plus-collision term in first-order deterministic radiation transport calculations has some desirable numerical properties. However, it suffers from parallel scaling issues caused by a lack of concurrency. The maximum degree of concurrency, and thus the maximum parallelism, grows more slowly than the problem size for sweeps-based solvers. We investigate a new class of parallel algorithms that involves recasting the streaming-plus-collision problem in prefix form and solving via cyclic reduction. This method, although computationally more expensive at low levels of parallelism than the sweep algorithm, offers better theoretical scalability properties. Previous work has demonstrated this approach for one-dimensional calculations; we show how to extend it to multidimensional calculations. Notably, for multiple dimensions it appears that this approach is limited to long-characteristics discretizations; other discretizations cannot be cast in prefix form. We implement two variants of the algorithm within the radlib/SCEPTRE transport code library at Sandia National Laboratories and show results on two different massively parallel systems. Both the 'forward' and 'symmetric' solvers behave similarly, scaling well to larger degrees of parallelism then sweeps-based solvers. We do observe some issues at the highest levels of parallelism (relative to the system size) and discuss possible causes. We conclude that this approach shows good potential for future parallel systems, but the parallel scalability will depend heavily on the architecture of the communication networks of these systems. (authors)
Discrete element modeling of subglacial sediment deformation
DEFF Research Database (Denmark)
Damsgaard, Anders; Egholm, David L.; Piotrowski, Jan A.
2013-01-01
The Discrete Element Method (DEM) is used in this study to explore the highly nonlinear dynamics of a granular bed when exposed to stress conditions comparable to those at the bed of warm-based glaciers. Complementary to analog experiments, the numerical approach allows a detailed analysis...
Discrete element modeling of subglacial sediment deformation
DEFF Research Database (Denmark)
Damsgaard, Anders; Egholm, David L.; Piotrowski, Jan A.
The Discrete Element Method (DEM) is used to explore the highly nonlinear dynamics of a granular bed when exposed to stress conditions comparable to those at the bed of warm-based glaciers. In the DEM, the material is simulated on a grain-by-grain basis, and defining the micromechanical properties...
New formulation of the discrete element method
Rojek, Jerzy; Zubelewicz, Aleksander; Madan, Nikhil; Nosewicz, Szymon
2018-01-01
A new original formulation of the discrete element method based on the soft contact approach is presented in this work. The standard DEM has heen enhanced by the introduction of the additional (global) deformation mode caused by the stresses in the particles induced by the contact forces. Uniform stresses and strains are assumed for each particle. The stresses are calculated from the contact forces. The strains are obtained using an inverse constitutive relationship. The strains allow us to obtain deformed particle shapes. The deformed shapes (ellipses) are taken into account in contact detection and evaluation of the contact forces. A simple example of a uniaxial compression of a rectangular specimen, discreti.zed with equal sized particles is simulated to verify the DDEM algorithm. The numerical example shows that a particle deformation changes the particle interaction and the distribution of forces in the discrete element assembly. A quantitative study of micro-macro elastic properties proves the enhanced capabilities of the DDEM as compared to standard DEM.
Element-topology-independent preconditioners for parallel finite element computations
Park, K. C.; Alexander, Scott
1992-01-01
A family of preconditioners for the solution of finite element equations are presented, which are element-topology independent and thus can be applicable to element order-free parallel computations. A key feature of the present preconditioners is the repeated use of element connectivity matrices and their left and right inverses. The properties and performance of the present preconditioners are demonstrated via beam and two-dimensional finite element matrices for implicit time integration computations.
A discrete ordinate response matrix method for massively parallel computers
International Nuclear Information System (INIS)
Hanebutte, U.R.; Lewis, E.E.
1991-01-01
A discrete ordinate response matrix method is formulated for the solution of neutron transport problems on massively parallel computers. The response matrix formulation eliminates iteration on the scattering source. The nodal matrices which result from the diamond-differenced equations are utilized in a factored form which minimizes memory requirements and significantly reduces the required number of algorithm utilizes massive parallelism by assigning each spatial node to a processor. The algorithm is accelerated effectively by a synthetic method in which the low-order diffusion equations are also solved by massively parallel red/black iterations. The method has been implemented on a 16k Connection Machine-2, and S 8 and S 16 solutions have been obtained for fixed-source benchmark problems in X--Y geometry
Parallel discrete-event simulation of FCFS stochastic queueing networks
Nicol, David M.
1988-01-01
Physical systems are inherently parallel. Intuition suggests that simulations of these systems may be amenable to parallel execution. The parallel execution of a discrete-event simulation requires careful synchronization of processes in order to ensure the execution's correctness; this synchronization can degrade performance. Largely negative results were recently reported in a study which used a well-known synchronization method on queueing network simulations. Discussed here is a synchronization method (appointments), which has proven itself to be effective on simulations of FCFS queueing networks. The key concept behind appointments is the provision of lookahead. Lookahead is a prediction on a processor's future behavior, based on an analysis of the processor's simulation state. It is shown how lookahead can be computed for FCFS queueing network simulations, give performance data that demonstrates the method's effectiveness under moderate to heavy loads, and discuss performance tradeoffs between the quality of lookahead, and the cost of computing lookahead.
Parallel Stochastic discrete event simulation of calcium dynamics in neuron.
Ishlam Patoary, Mohammad Nazrul; Tropper, Carl; McDougal, Robert A; Zhongwei, Lin; Lytton, William W
2017-09-26
The intra-cellular calcium signaling pathways of a neuron depends on both biochemical reactions and diffusions. Some quasi-isolated compartments (e.g. spines) are so small and calcium concentrations are so low that one extra molecule diffusing in by chance can make a nontrivial difference in its concentration (percentage-wise). These rare events can affect dynamics discretely in such way that they cannot be evaluated by a deterministic simulation. Stochastic models of such a system provide a more detailed understanding of these systems than existing deterministic models because they capture their behavior at a molecular level. Our research focuses on the development of a high performance parallel discrete event simulation environment, Neuron Time Warp (NTW), which is intended for use in the parallel simulation of stochastic reaction-diffusion systems such as intra-calcium signaling. NTW is integrated with NEURON, a simulator which is widely used within the neuroscience community. We simulate two models, a calcium buffer and a calcium wave model. The calcium buffer model is employed in order to verify the correctness and performance of NTW by comparing it to a serial deterministic simulation in NEURON. We also derived a discrete event calcium wave model from a deterministic model using the stochastic IP3R structure.
Parallel discrete event simulation: A shared memory approach
Reed, Daniel A.; Malony, Allen D.; Mccredie, Bradley D.
1987-01-01
With traditional event list techniques, evaluating a detailed discrete event simulation model can often require hours or even days of computation time. Parallel simulation mimics the interacting servers and queues of a real system by assigning each simulated entity to a processor. By eliminating the event list and maintaining only sufficient synchronization to insure causality, parallel simulation can potentially provide speedups that are linear in the number of processors. A set of shared memory experiments is presented using the Chandy-Misra distributed simulation algorithm to simulate networks of queues. Parameters include queueing network topology and routing probabilities, number of processors, and assignment of network nodes to processors. These experiments show that Chandy-Misra distributed simulation is a questionable alternative to sequential simulation of most queueing network models.
The parallel algorithm for the 2D discrete wavelet transform
Barina, David; Najman, Pavel; Kleparnik, Petr; Kula, Michal; Zemcik, Pavel
2018-04-01
The discrete wavelet transform can be found at the heart of many image-processing algorithms. Until now, the transform on general-purpose processors (CPUs) was mostly computed using a separable lifting scheme. As the lifting scheme consists of a small number of operations, it is preferred for processing using single-core CPUs. However, considering a parallel processing using multi-core processors, this scheme is inappropriate due to a large number of steps. On such architectures, the number of steps corresponds to the number of points that represent the exchange of data. Consequently, these points often form a performance bottleneck. Our approach appropriately rearranges calculations inside the transform, and thereby reduces the number of steps. In other words, we propose a new scheme that is friendly to parallel environments. When evaluating on multi-core CPUs, we consistently overcome the original lifting scheme. The evaluation was performed on 61-core Intel Xeon Phi and 8-core Intel Xeon processors.
Discrete element modeling of microstructure of nacre
Chandler, Mei Qiang; Cheng, Jing-Ru C.
2018-04-01
The microstructure of nacre consists of polygon-shaped aragonite mineral tablets bonded by very thin layers of organic materials and is organized in a brick-mortar morphology. In this research, the discrete element method was utilized to model this structure. The aragonite mineral tablets were modeled with three-dimensional polygon particles generated by the Voronoi tessellation method to represent the Voronoi-like patterns of mineral tablets assembly observed in experiments. The organic matrix was modeled with a group of spring elements. The constitutive relations of the spring elements were inspired from the experimental results of organic molecules from the literature. The mineral bridges were modeled with simple elastic bonds with the parameters based on experimental data from the literature. The bulk stress-strain responses from the models agreed well with experimental results. The model results show that the mineral bridges play important roles in providing the stiffness and yield strength for the nacre, while the organic matrix in providing the ductility for the nacre. This work demonstrated the suitability of particle methods for modeling microstructures of nacre.
The cost of conservative synchronization in parallel discrete event simulations
Nicol, David M.
1990-01-01
The performance of a synchronous conservative parallel discrete-event simulation protocol is analyzed. The class of simulation models considered is oriented around a physical domain and possesses a limited ability to predict future behavior. A stochastic model is used to show that as the volume of simulation activity in the model increases relative to a fixed architecture, the complexity of the average per-event overhead due to synchronization, event list manipulation, lookahead calculations, and processor idle time approach the complexity of the average per-event overhead of a serial simulation. The method is therefore within a constant factor of optimal. The analysis demonstrates that on large problems--those for which parallel processing is ideally suited--there is often enough parallel workload so that processors are not usually idle. The viability of the method is also demonstrated empirically, showing how good performance is achieved on large problems using a thirty-two node Intel iPSC/2 distributed memory multiprocessor.
Discrete element simulation of crushable rockfill materials
Directory of Open Access Journals (Sweden)
Lei Shao
2013-04-01
Full Text Available A discrete element method was used to study the evolution of particle crushing in a rockfill sample subjected to triaxial shear. A simple procedure was developed to generate clusters with arbitrary shapes, which resembled real rockfill particles. A theoretical method was developed to define the failure criterion for an individual particle subjected to an arbitrary set of contact forces. Then, a series of numerical tests of large-scale drained triaxial tests were conducted to simulate the behaviors of the rockfill sample. Finally, we examined the development of micro-characteristics such as particle crushing, contact characteristics, porosity, deformation, movement, and energy dissipation. The simulation results were partially compared with the laboratory experiments, and good agreement was achieved, demonstrating that the particle crushing model proposed can be used to simulate the drained triaxial test of rockfill materials. Based on a comparison of macro behaviors of the rockfill sample and micro structures of the particles, the microscopic mechanism of the rockfill materials subjected to triaxial shear was determined qualitatively. It is shown that the crushing rate, rather than the number of crushed particles, can be used to reflect the relationship between macro- and micro-mechanical characteristics of rockfill materials. These research results further develop our understanding of the deformation mechanism of rockfill materials.
Calibration of discrete element model parameters: soybeans
Ghodki, Bhupendra M.; Patel, Manish; Namdeo, Rohit; Carpenter, Gopal
2018-05-01
Discrete element method (DEM) simulations are broadly used to get an insight of flow characteristics of granular materials in complex particulate systems. DEM input parameters for a model are the critical prerequisite for an efficient simulation. Thus, the present investigation aims to determine DEM input parameters for Hertz-Mindlin model using soybeans as a granular material. To achieve this aim, widely acceptable calibration approach was used having standard box-type apparatus. Further, qualitative and quantitative findings such as particle profile, height of kernels retaining the acrylic wall, and angle of repose of experiments and numerical simulations were compared to get the parameters. The calibrated set of DEM input parameters includes the following (a) material properties: particle geometric mean diameter (6.24 mm); spherical shape; particle density (1220 kg m^{-3} ), and (b) interaction parameters such as particle-particle: coefficient of restitution (0.17); coefficient of static friction (0.26); coefficient of rolling friction (0.08), and particle-wall: coefficient of restitution (0.35); coefficient of static friction (0.30); coefficient of rolling friction (0.08). The results may adequately be used to simulate particle scale mechanics (grain commingling, flow/motion, forces, etc) of soybeans in post-harvest machinery and devices.
Synchronous Parallel System for Emulation and Discrete Event Simulation
Steinman, Jeffrey S. (Inventor)
2001-01-01
A synchronous parallel system for emulation and discrete event simulation having parallel nodes responds to received messages at each node by generating event objects having individual time stamps, stores only the changes to the state variables of the simulation object attributable to the event object and produces corresponding messages. The system refrains from transmitting the messages and changing the state variables while it determines whether the changes are superseded, and then stores the unchanged state variables in the event object for later restoral to the simulation object if called for. This determination preferably includes sensing the time stamp of each new event object and determining which new event object has the earliest time stamp as the local event horizon, determining the earliest local event horizon of the nodes as the global event horizon, and ignoring events whose time stamps are less than the global event horizon. Host processing between the system and external terminals enables such a terminal to query, monitor, command or participate with a simulation object during the simulation process.
Predicting the behavior of microfluidic circuits made from discrete elements
Bhargava, Krisna C.; Thompson, Bryant; Iqbal, Danish; Malmstadt, Noah
2015-10-01
Microfluidic devices can be used to execute a variety of continuous flow analytical and synthetic chemistry protocols with a great degree of precision. The growing availability of additive manufacturing has enabled the design of microfluidic devices with new functionality and complexity. However, these devices are prone to larger manufacturing variation than is typical of those made with micromachining or soft lithography. In this report, we demonstrate a design-for-manufacturing workflow that addresses performance variation at the microfluidic element and circuit level, in context of mass-manufacturing and additive manufacturing. Our approach relies on discrete microfluidic elements that are characterized by their terminal hydraulic resistance and associated tolerance. Network analysis is employed to construct simple analytical design rules for model microfluidic circuits. Monte Carlo analysis is employed at both the individual element and circuit level to establish expected performance metrics for several specific circuit configurations. A protocol based on osmometry is used to experimentally probe mixing behavior in circuits in order to validate these approaches. The overall workflow is applied to two application circuits with immediate use at on the bench-top: series and parallel mixing circuits that are modularly programmable, virtually predictable, highly precise, and operable by hand.
Predicting the behavior of microfluidic circuits made from discrete elements.
Bhargava, Krisna C; Thompson, Bryant; Iqbal, Danish; Malmstadt, Noah
2015-10-30
Microfluidic devices can be used to execute a variety of continuous flow analytical and synthetic chemistry protocols with a great degree of precision. The growing availability of additive manufacturing has enabled the design of microfluidic devices with new functionality and complexity. However, these devices are prone to larger manufacturing variation than is typical of those made with micromachining or soft lithography. In this report, we demonstrate a design-for-manufacturing workflow that addresses performance variation at the microfluidic element and circuit level, in context of mass-manufacturing and additive manufacturing. Our approach relies on discrete microfluidic elements that are characterized by their terminal hydraulic resistance and associated tolerance. Network analysis is employed to construct simple analytical design rules for model microfluidic circuits. Monte Carlo analysis is employed at both the individual element and circuit level to establish expected performance metrics for several specific circuit configurations. A protocol based on osmometry is used to experimentally probe mixing behavior in circuits in order to validate these approaches. The overall workflow is applied to two application circuits with immediate use at on the bench-top: series and parallel mixing circuits that are modularly programmable, virtually predictable, highly precise, and operable by hand.
Discrete element modelling of bedload transport
Loyer, A.; Frey, P.
2011-12-01
Discrete element modelling (DEM) has been widely used in solid mechanics and in granular physics. In this type of modelling, each individual particle is taken into account and intergranular interactions are modelled with simple laws (e.g. Coulomb friction). Gravity and contact forces permit to solve the dynamical behaviour of the system. DEM is interesting to model configurations and access to parameters not directly available in laboratory experimentation, hence the term "numerical experimentations" sometimes used to describe DEM. DEM was used to model bedload transport experiments performed at the particle scale with spherical glass beads in a steep and narrow flume. Bedload is the larger material that is transported on the bed on stream channels. It has a great geomorphic impact. Physical processes ruling bedload transport and more generally coarse-particle/fluid systems are poorly known, arguably because granular interactions have been somewhat neglected. An existing DEM code (PFC3D) already computing granular interactions was used. We implemented basic hydrodynamic forces to model the fluid interactions (buoyancy, drag, lift). The idea was to use the minimum number of ingredients to match the experimental results. Experiments were performed with one-size and two-size mixtures of coarse spherical glass beads entrained by a shallow turbulent and supercritical water flow down a steep channel with a mobile bed. The particle diameters were 4 and 6mm, the channel width 6.5mm (about the same width as the coarser particles) and the channel inclination was typically 10%. The water flow rate and the particle rate were kept constant at the upstream entrance and adjusted to obtain bedload transport equilibrium. Flows were filmed from the side by a high-speed camera. Using image processing algorithms made it possible to determine the position, velocity and trajectory of both smaller and coarser particles. Modelled and experimental particle velocity and concentration depth
Finite element discretization of Darcy's equations with pressure dependent porosity
Girault, Vivette; Murat, Franç ois; Salgado, Abner
2010-01-01
We consider the flow of a viscous incompressible fluid through a rigid homogeneous porous medium. The permeability of the medium depends on the pressure, so that the model is nonlinear. We propose a finite element discretization of this problem and
Parallel discrete ordinates algorithms on distributed and common memory systems
International Nuclear Information System (INIS)
Wienke, B.R.; Hiromoto, R.E.; Brickner, R.G.
1987-01-01
The S/sub n/ algorithm employs iterative techniques in solving the linear Boltzmann equation. These methods, both ordered and chaotic, were compared on both the Denelcor HEP and the Intel hypercube. Strategies are linked to the organization and accessibility of memory (common memory versus distributed memory architectures), with common concern for acquisition of global information. Apart from this, the inherent parallelism of the algorithm maps directly onto the two architectures. Results comparing execution times, speedup, and efficiency are based on a representative 16-group (full upscatter and downscatter) sample problem. Calculations were performed on both the Los Alamos National Laboratory (LANL) Denelcor HEP and the LANL Intel hypercube. The Denelcor HEP is a 64-bit multi-instruction, multidate MIMD machine consisting of up to 16 process execution modules (PEMs), each capable of executing 64 processes concurrently. Each PEM can cooperate on a job, or run several unrelated jobs, and share a common global memory through a crossbar switch. The Intel hypercube, on the other hand, is a distributed memory system composed of 128 processing elements, each with its own local memory. Processing elements are connected in a nearest-neighbor hypercube configuration and sharing of data among processors requires execution of explicit message-passing constructs
Directory of Open Access Journals (Sweden)
Pablo Soto-Quiros
2015-01-01
Full Text Available This paper presents a parallel implementation of a kind of discrete Fourier transform (DFT: the vector-valued DFT. The vector-valued DFT is a novel tool to analyze the spectra of vector-valued discrete-time signals. This parallel implementation is developed in terms of a mathematical framework with a set of block matrix operations. These block matrix operations contribute to analysis, design, and implementation of parallel algorithms in multicore processors. In this work, an implementation and experimental investigation of the mathematical framework are performed using MATLAB with the Parallel Computing Toolbox. We found that there is advantage to use multicore processors and a parallel computing environment to minimize the high execution time. Additionally, speedup increases when the number of logical processors and length of the signal increase.
Out-of-order parallel discrete event simulation for electronic system-level design
Chen, Weiwei
2014-01-01
This book offers readers a set of new approaches and tools a set of tools and techniques for facing challenges in parallelization with design of embedded systems.? It provides an advanced parallel simulation infrastructure for efficient and effective system-level model validation and development so as to build better products in less time.? Since parallel discrete event simulation (PDES) has the potential to exploit the underlying parallel computational capability in today's multi-core simulation hosts, the author begins by reviewing the parallelization of discrete event simulation, identifyin
Finite element bending behaviour of discretely delaminated ...
African Journals Online (AJOL)
user
due to their light weight, high specific strength and stiffness properties. ... cylindrical shell roofs respectively using finite element method with centrally located .... where { }ε and { }γ are the direct and shear strains in midplane and { }κ denotes ...
Optimized Parallel Discrete Event Simulation (PDES) for High Performance Computing (HPC) Clusters
National Research Council Canada - National Science Library
Abu-Ghazaleh, Nael
2005-01-01
The aim of this project was to study the communication subsystem performance of state of the art optimistic simulator Synchronous Parallel Environment for Emulation and Discrete-Event Simulation (SPEEDES...
Discrete element modeling of deformable particles in YADE
Directory of Open Access Journals (Sweden)
Martin Haustein
2017-01-01
Full Text Available In this paper we describe the open-source discrete element framework YADE and the implementation of a new deformation engine. YADE is a highly expandable software package that allows the simulation of current industrial problems in the field of granular materials using particle-based numerical methods. The description of the compaction of powders and granular material like metal pellets is now possible with a pure and simple discrete element approach in a modern DEM-framework. The deformation is realized by expanding the radius of the spherical particles, depending on their overlap, so that the volume of the material is kept constant.
An Advanced Simulation Framework for Parallel Discrete-Event Simulation
Li, P. P.; Tyrrell, R. Yeung D.; Adhami, N.; Li, T.; Henry, H.
1994-01-01
Discrete-event simulation (DEVS) users have long been faced with a three-way trade-off of balancing execution time, model fidelity, and number of objects simulated. Because of the limits of computer processing power the analyst is often forced to settle for less than desired performances in one or more of these areas.
Modelling of Granular Materials Using the Discrete Element Method
DEFF Research Database (Denmark)
Ullidtz, Per
1997-01-01
With the Discrete Element Method it is possible to model materials that consists of individual particles where a particle may role or slide on other particles. This is interesting because most of the deformation in granular materials is due to rolling or sliding rather that compression of the gra...
GPU-based discrete element rigid body transport
CSIR Research Space (South Africa)
Govender, Nicolin
2013-08-01
Full Text Available . For applications in coastal engineering and also in pavement engineering, the capture of particle shapes as polyhedra rather than clumped spheres is particularly important. The development of a Discrete Element Model applicable to both fields, and to industrial...
Fast parallel approach for 2-D DHT-based real-valued discrete Gabor transform.
Tao, Liang; Kwan, Hon Keung
2009-12-01
Two-dimensional fast Gabor transform algorithms are useful for real-time applications due to the high computational complexity of the traditional 2-D complex-valued discrete Gabor transform (CDGT). This paper presents two block time-recursive algorithms for 2-D DHT-based real-valued discrete Gabor transform (RDGT) and its inverse transform and develops a fast parallel approach for the implementation of the two algorithms. The computational complexity of the proposed parallel approach is analyzed and compared with that of the existing 2-D CDGT algorithms. The results indicate that the proposed parallel approach is attractive for real time image processing.
Shared memory parallelism for 3D cartesian discrete ordinates solver
International Nuclear Information System (INIS)
Moustafa, S.; Dutka-Malen, I.; Plagne, L.; Poncot, A.; Ramet, P.
2013-01-01
This paper describes the design and the performance of DOMINO, a 3D Cartesian SN solver that implements two nested levels of parallelism (multi-core + SIMD - Single Instruction on Multiple Data) on shared memory computation nodes. DOMINO is written in C++, a multi-paradigm programming language that enables the use of powerful and generic parallel programming tools such as Intel TBB and Eigen. These two libraries allow us to combine multi-thread parallelism with vector operations in an efficient and yet portable way. As a result, DOMINO can exploit the full power of modern multi-core processors and is able to tackle very large simulations, that usually require large HPC clusters, using a single computing node. For example, DOMINO solves a 3D full core PWR eigenvalue problem involving 26 energy groups, 288 angular directions (S16), 46*10 6 spatial cells and 1*10 12 DoFs within 11 hours on a single 32-core SMP node. This represents a sustained performance of 235 GFlops and 40.74% of the SMP node peak performance for the DOMINO sweep implementation. The very high Flops/Watt ratio of DOMINO makes it a very interesting building block for a future many-nodes nuclear simulation tool. (authors)
Symplectic discretization for spectral element solution of Maxwell's equations
International Nuclear Information System (INIS)
Zhao Yanmin; Dai Guidong; Tang Yifa; Liu Qinghuo
2009-01-01
Applying the spectral element method (SEM) based on the Gauss-Lobatto-Legendre (GLL) polynomial to discretize Maxwell's equations, we obtain a Poisson system or a Poisson system with at most a perturbation. For the system, we prove that any symplectic partitioned Runge-Kutta (PRK) method preserves the Poisson structure and its implied symplectic structure. Numerical examples show the high accuracy of SEM and the benefit of conserving energy due to the use of symplectic methods.
Implementation of a high performance parallel finite element micromagnetics package
International Nuclear Information System (INIS)
Scholz, W.; Suess, D.; Dittrich, R.; Schrefl, T.; Tsiantos, V.; Forster, H.; Fidler, J.
2004-01-01
A new high performance scalable parallel finite element micromagnetics package has been implemented. It includes solvers for static energy minimization, time integration of the Landau-Lifshitz-Gilbert equation, and the nudged elastic band method
Parallel and Serial Grouping of Image Elements in Visual Perception
Houtkamp, Roos; Roelfsema, Pieter R.
2010-01-01
The visual system groups image elements that belong to an object and segregates them from other objects and the background. Important cues for this grouping process are the Gestalt criteria, and most theories propose that these are applied in parallel across the visual scene. Here, we find that Gestalt grouping can indeed occur in parallel in some…
A finite element solution method for quadrics parallel computer
International Nuclear Information System (INIS)
Zucchini, A.
1996-08-01
A distributed preconditioned conjugate gradient method for finite element analysis has been developed and implemented on a parallel SIMD Quadrics computer. The main characteristic of the method is that it does not require any actual assembling of all element equations in a global system. The physical domain of the problem is partitioned in cells of n p finite elements and each cell element is assigned to a different node of an n p -processors machine. Element stiffness matrices are stored in the data memory of the assigned processing node and the solution process is completely executed in parallel at element level. Inter-element and therefore inter-processor communications are required once per iteration to perform local sums of vector quantities between neighbouring elements. A prototype implementation has been tested on an 8-nodes Quadrics machine in a simple 2D benchmark problem
Directory of Open Access Journals (Sweden)
José Miguel Vargas-Félix
2012-11-01
Full Text Available The Finite Element Method (FEM is used to solve problems like solid deformation and heat diffusion in domains with complex geometries. This kind of geometries requires discretization with millions of elements; this is equivalent to solve systems of equations with sparse matrices and tens or hundreds of millions of variables. The aim is to use computer clusters to solve these systems. The solution method used is Schur substructuration. Using it is possible to divide a large system of equations into many small ones to solve them more efficiently. This method allows parallelization. MPI (Message Passing Interface is used to distribute the systems of equations to solve each one in a computer of a cluster. Each system of equations is solved using a solver implemented to use OpenMP as a local parallelization method.The Finite Element Method (FEM is used to solve problems like solid deformation and heat diffusion in domains with complex geometries. This kind of geometries requires discretization with millions of elements; this is equivalent to solve systems of equations with sparse matrices and tens or hundreds of millions of variables. The aim is to use computer clusters to solve these systems. The solution method used is Schur substructuration. Using it is possible to divide a large system of equations into many small ones to solve them more efficiently. This method allows parallelization. MPI (Message Passing Interface is used to distribute the systems of equations to solve each one in a computer of a cluster. Each system of equations is solved using a solver implemented to use OpenMP as a local parallelization method.
Finite element discretization of Darcy's equations with pressure dependent porosity
Girault, Vivette
2010-02-23
We consider the flow of a viscous incompressible fluid through a rigid homogeneous porous medium. The permeability of the medium depends on the pressure, so that the model is nonlinear. We propose a finite element discretization of this problem and, in the case where the dependence on the pressure is bounded from above and below, we prove its convergence to the solution and propose an algorithm to solve the discrete system. In the case where the dependence on the pressure is exponential, we propose a splitting scheme which involves solving two linear systems, but parts of the analysis of this method are still heuristic. Numerical tests are presented, which illustrate the introduced methods. © 2010 EDP Sciences, SMAI.
Discrete Element Modeling (DEM) of Triboelectrically Charged Particles: Revised Experiments
Hogue, Michael D.; Calle, Carlos I.; Curry, D. R.; Weitzman, P. S.
2008-01-01
In a previous work, the addition of basic screened Coulombic electrostatic forces to an existing commercial discrete element modeling (DEM) software was reported. Triboelectric experiments were performed to charge glass spheres rolling on inclined planes of various materials. Charge generation constants and the Q/m ratios for the test materials were calculated from the experimental data and compared to the simulation output of the DEM software. In this paper, we will discuss new values of the charge generation constants calculated from improved experimental procedures and data. Also, planned work to include dielectrophoretic, Van der Waals forces, and advanced mechanical forces into the software will be discussed.
Granulation of snow: From tumbler experiments to discrete element simulations
Steinkogler, Walter; Gaume, Johan; Löwe, Henning; Sovilla, Betty; Lehning, Michael
2015-06-01
It is well known that snow avalanches exhibit granulation phenomena, i.e., the formation of large and apparently stable snow granules during the flow. The size distribution of the granules has an influence on flow behavior which, in turn, affects runout distances and avalanche velocities. The underlying mechanisms of granule formation are notoriously difficult to investigate within large-scale field experiments, due to limitations in the scope for measuring temperatures, velocities, and size distributions. To address this issue we present experiments with a concrete tumbler, which provide an appropriate means to investigate granule formation of snow. In a set of experiments at constant rotation velocity with varying temperatures and water content, we demonstrate that temperature has a major impact on the formation of granules. The experiments showed that granules only formed when the snow temperature exceeded -1∘C. No evolution in the granule size was observed at colder temperatures. Depending on the conditions, different granulation regimes are obtained, which are qualitatively classified according to their persistence and size distribution. The potential of granulation of snow in a tumbler is further demonstrated by showing that generic features of the experiments can be reproduced by cohesive discrete element simulations. The proposed discrete element model mimics the competition between cohesive forces, which promote aggregation, and impact forces, which induce fragmentation, and supports the interpretation of the granule regime classification obtained from the tumbler experiments. Generalizations, implications for flow dynamics, and experimental and model limitations as well as suggestions for future work are discussed.
Zerr, Robert Joseph
2011-12-01
The integral transport matrix method (ITMM) has been used as the kernel of new parallel solution methods for the discrete ordinates approximation of the within-group neutron transport equation. The ITMM abandons the repetitive mesh sweeps of the traditional source iterations (SI) scheme in favor of constructing stored operators that account for the direct coupling factors among all the cells and between the cells and boundary surfaces. The main goals of this work were to develop the algorithms that construct these operators and employ them in the solution process, determine the most suitable way to parallelize the entire procedure, and evaluate the behavior and performance of the developed methods for increasing number of processes. This project compares the effectiveness of the ITMM with the SI scheme parallelized with the Koch-Baker-Alcouffe (KBA) method. The primary parallel solution method involves a decomposition of the domain into smaller spatial sub-domains, each with their own transport matrices, and coupled together via interface boundary angular fluxes. Each sub-domain has its own set of ITMM operators and represents an independent transport problem. Multiple iterative parallel solution methods have investigated, including parallel block Jacobi (PBJ), parallel red/black Gauss-Seidel (PGS), and parallel GMRES (PGMRES). The fastest observed parallel solution method, PGS, was used in a weak scaling comparison with the PARTISN code. Compared to the state-of-the-art SI-KBA with diffusion synthetic acceleration (DSA), this new method without acceleration/preconditioning is not competitive for any problem parameters considered. The best comparisons occur for problems that are difficult for SI DSA, namely highly scattering and optically thick. SI DSA execution time curves are generally steeper than the PGS ones. However, until further testing is performed it cannot be concluded that SI DSA does not outperform the ITMM with PGS even on several thousand or tens of
An implicit finite element method for discrete dynamic fracture
Energy Technology Data Exchange (ETDEWEB)
Gerken, Jobie M. [Colorado State Univ., Fort Collins, CO (United States)
1999-12-01
A method for modeling the discrete fracture of two-dimensional linear elastic structures with a distribution of small cracks subject to dynamic conditions has been developed. The foundation for this numerical model is a plane element formulated from the Hu-Washizu energy principle. The distribution of small cracks is incorporated into the numerical model by including a small crack at each element interface. The additional strain field in an element adjacent to this crack is treated as an externally applied strain field in the Hu-Washizu energy principle. The resulting stiffness matrix is that of a standard plane element. The resulting load vector is that of a standard plane element with an additional term that includes the externally applied strain field. Except for the crack strain field equations, all terms of the stiffness matrix and load vector are integrated symbolically in Maple V so that fully integrated plane stress and plane strain elements are constructed. The crack strain field equations are integrated numerically. The modeling of dynamic behavior of simple structures was demonstrated within acceptable engineering accuracy. In the model of axial and transverse vibration of a beam and the breathing mode of vibration of a thin ring, the dynamic characteristics were shown to be within expected limits. The models dominated by tensile forces (the axially loaded beam and the pressurized ring) were within 0.5% of the theoretical values while the shear dominated model (the transversely loaded beam) is within 5% of the calculated theoretical value. The constant strain field of the tensile problems can be modeled exactly by the numerical model. The numerical results should therefore, be exact. The discrepancies can be accounted for by errors in the calculation of frequency from the numerical results. The linear strain field of the transverse model must be modeled by a series of constant strain elements. This is an approximation to the true strain field, so some
Parallel and serial grouping of image elements in visual perception
Houtkamp, R.; Roelfsema, P.R.
2010-01-01
The visual system groups image elements that belong to an object and segregates them from other objects and the background. Important cues for this grouping process are the Gestalt criteria, and most theories propose that these are applied in parallel across the visual scene. Here, we find that
International Nuclear Information System (INIS)
Fischer, J.W.; Azmy, Y.Y.
2003-01-01
A previously reported parallel performance model for Angular Domain Decomposition (ADD) of the Discrete Ordinates method for solving multidimensional neutron transport problems is revisited for further validation. Three communication schemes: native MPI, the bucket algorithm, and the distributed bucket algorithm, are included in the validation exercise that is successfully conducted on a Beowulf cluster. The parallel performance model is comprised of three components: serial, parallel, and communication. The serial component is largely independent of the number of participating processors, P, while the parallel component decreases like 1/P. These two components are independent of the communication scheme, in contrast with the communication component that typically increases with P in a manner highly dependent on the global reduced algorithm. Correct trends for each component and each communication scheme were measured for the Arbitrarily High Order Transport (AHOT) code, thus validating the performance models. Furthermore, extensive experiments illustrate the superiority of the bucket algorithm. The primary question addressed in this research is: for a given problem size, which domain decomposition method, angular or spatial, is best suited to parallelize Discrete Ordinates methods on a specific computational platform? We address this question for three-dimensional applications via parallel performance models that include parameters specifying the problem size and system performance: the above-mentioned ADD, and a previously constructed and validated Spatial Domain Decomposition (SDD) model. We conclude that for large problems the parallel component dwarfs the communication component even on moderately large numbers of processors. The main advantages of SDD are: (a) scalability to higher numbers of processors of the order of the number of computational cells; (b) smaller memory requirement; (c) better performance than ADD on high-end platforms and large number of
Determining Trajectory of Triboelectrically Charged Particles, Using Discrete Element Modeling
2008-01-01
The Kennedy Space Center (KSC) Electrostatics and Surface Physics Laboratory is participating in an Innovative Partnership Program (IPP) project with an industry partner to modify a commercial off-the-shelf simulation software product to treat the electrodynamics of particulate systems. Discrete element modeling (DEM) is a numerical technique that can track the dynamics of particle systems. This technique, which was introduced in 1979 for analysis of rock mechanics, was recently refined to include the contact force interaction of particles with arbitrary surfaces and moving machinery. In our work, we endeavor to incorporate electrostatic forces into the DEM calculations to enhance the fidelity of the software and its applicability to (1) particle processes, such as electrophotography, that are greatly affected by electrostatic forces, (2) grain and dust transport, and (3) the study of lunar and Martian regoliths.
Discrete element modeling of calcium-silicate-hydrate
International Nuclear Information System (INIS)
Chandler, Mei Qiang; Peters, John F; Pelessone, Daniele
2013-01-01
The discrete element method (DEM) was used to model calcium-silicate-hydrate (C-S-H) at the nanoscale. The C-S-H nanoparticles were modeled as spherical particles with diameters of approximately 5 nm. Interparticle forces included traditional mechanical contact forces, van der Waals forces and ionic correlation forces due to negatively charged C-S-H nanoparticles and ion species in the nanopores. Previous work by the authors demonstrated the DEM method was feasible in studying the properties of the C-S-H nanostructures. In this work, the simulations were performed to look into the effects of nanoparticle packing, nanoparticle morphology, interparticle forces and nanoparticle properties on the deformation mechanisms and mechanical properties of the C-S-H matrix. This work will provide insights into possible ways to improve the properties of the C-S-H matrix. (paper)
Visual Data-Analytics of Large-Scale Parallel Discrete-Event Simulations
Energy Technology Data Exchange (ETDEWEB)
Ross, Caitlin; Carothers, Christopher D.; Mubarak, Misbah; Carns, Philip; Ross, Robert; Li, Jianping Kelvin; Ma, Kwan-Liu
2016-11-13
Parallel discrete-event simulation (PDES) is an important tool in the codesign of extreme-scale systems because PDES provides a cost-effective way to evaluate designs of highperformance computing systems. Optimistic synchronization algorithms for PDES, such as Time Warp, allow events to be processed without global synchronization among the processing elements. A rollback mechanism is provided when events are processed out of timestamp order. Although optimistic synchronization protocols enable the scalability of large-scale PDES, the performance of the simulations must be tuned to reduce the number of rollbacks and provide an improved simulation runtime. To enable efficient large-scale optimistic simulations, one has to gain insight into the factors that affect the rollback behavior and simulation performance. We developed a tool for ROSS model developers that gives them detailed metrics on the performance of their large-scale optimistic simulations at varying levels of simulation granularity. Model developers can use this information for parameter tuning of optimistic simulations in order to achieve better runtime and fewer rollbacks. In this work, we instrument the ROSS optimistic PDES framework to gather detailed statistics about the simulation engine. We have also developed an interactive visualization interface that uses the data collected by the ROSS instrumentation to understand the underlying behavior of the simulation engine. The interface connects real time to virtual time in the simulation and provides the ability to view simulation data at different granularities. We demonstrate the usefulness of our framework by performing a visual analysis of the dragonfly network topology model provided by the CODES simulation framework built on top of ROSS. The instrumentation needs to minimize overhead in order to accurately collect data about the simulation performance. To ensure that the instrumentation does not introduce unnecessary overhead, we perform a
Development of parallel 3D discrete ordinates transport program on JASMIN framework
International Nuclear Information System (INIS)
Cheng, T.; Wei, J.; Shen, H.; Zhong, B.; Deng, L.
2015-01-01
A parallel 3D discrete ordinates radiation transport code JSNT-S is developed, aiming at simulating real-world radiation shielding and reactor physics applications in a reasonable time. Through the patch-based domain partition algorithm, the memory requirement is shared among processors and a space-angle parallel sweeping algorithm is developed based on data-driven algorithm. Acceleration methods such as partial current rebalance are implemented. The correctness is proved through the VENUS-3 and other benchmark models. In the radiation shielding calculation of the Qinshan-II reactor pressure vessel model with 24.3 billion DoF, only 88 seconds is required and the overall parallel efficiency of 44% is achieved on 1536 CPU cores. (author)
A massively parallel discrete ordinates response matrix method for neutron transport
International Nuclear Information System (INIS)
Hanebutte, U.R.; Lewis, E.E.
1992-01-01
In this paper a discrete ordinates response matrix method is formulated with anisotropic scattering for the solution of neutron transport problems on massively parallel computers. The response matrix formulation eliminates iteration on the scattering source. The nodal matrices that result from the diamond-differenced equations are utilized in a factored form that minimizes memory requirements and significantly reduces the number of arithmetic operations required per node. The red-black solution algorithm utilizes massive parallelism by assigning each spatial node to one or more processors. The algorithm is accelerated by a synthetic method in which the low-order diffusion equations are also solved by massively parallel red-black iterations. The method is implemented on a 16K Connection Machine-2, and S 8 and S 16 solutions are obtained for fixed-source benchmark problems in x-y geometry
A parallel algorithm for solving the integral form of the discrete ordinates equations
International Nuclear Information System (INIS)
Zerr, R. J.; Azmy, Y. Y.
2009-01-01
The integral form of the discrete ordinates equations involves a system of equations that has a large, dense coefficient matrix. The serial construction methodology is presented and properties that affect the execution times to construct and solve the system are evaluated. Two approaches for massively parallel implementation of the solution algorithm are proposed and the current results of one of these are presented. The system of equations May be solved using two parallel solvers-block Jacobi and conjugate gradient. Results indicate that both methods can reduce overall wall-clock time for execution. The conjugate gradient solver exhibits better performance to compete with the traditional source iteration technique in terms of execution time and scalability. The parallel conjugate gradient method is synchronous, hence it does not increase the number of iterations for convergence compared to serial execution, and the efficiency of the algorithm demonstrates an apparent asymptotic decline. (authors)
A modified discrete element model for sea ice dynamics
Institute of Scientific and Technical Information of China (English)
LI Baohui; LI Hai; LIU Yu; WANG Anliang; JI Shunying
2014-01-01
Considering the discontinuous characteristics of sea ice on various scales, a modified discrete element mod-el (DEM) for sea ice dynamics is developed based on the granular material rheology. In this modified DEM, a soft sea ice particle element is introduced as a self-adjustive particle size function. Each ice particle can be treated as an assembly of ice floes, with its concentration and thickness changing to variable sizes un-der the conservation of mass. In this model, the contact forces among ice particles are calculated using a viscous-elastic-plastic model, while the maximum shear forces are described with the Mohr-Coulomb fric-tion law. With this modified DEM, the ice flow dynamics is simulated under the drags of wind and current in a channel of various widths. The thicknesses, concentrations and velocities of ice particles are obtained, and then reasonable dynamic process is analyzed. The sea ice dynamic process is also simulated in a vortex wind field. Taking the influence of thermodynamics into account, this modified DEM will be improved in the future work.
Element-by-element parallel spectral-element methods for 3-D teleseismic wave modeling
Liu, Shaolin
2017-09-28
The development of an efficient algorithm for teleseismic wave field modeling is valuable for calculating the gradients of the misfit function (termed misfit gradients) or Fréchet derivatives when the teleseismic waveform is used for adjoint tomography. Here, we introduce an element-by-element parallel spectral-element method (EBE-SEM) for the efficient modeling of teleseismic wave field propagation in a reduced geology model. Under the plane-wave assumption, the frequency-wavenumber (FK) technique is implemented to compute the boundary wave field used to construct the boundary condition of the teleseismic wave incidence. To reduce the memory required for the storage of the boundary wave field for the incidence boundary condition, a strategy is introduced to efficiently store the boundary wave field on the model boundary. The perfectly matched layers absorbing boundary condition (PML ABC) is formulated using the EBE-SEM to absorb the scattered wave field from the model interior. The misfit gradient can easily be constructed in each time step during the calculation of the adjoint wave field. Three synthetic examples demonstrate the validity of the EBE-SEM for use in teleseismic wave field modeling and the misfit gradient calculation.
SPEEDES - A multiple-synchronization environment for parallel discrete-event simulation
Steinman, Jeff S.
1992-01-01
Synchronous Parallel Environment for Emulation and Discrete-Event Simulation (SPEEDES) is a unified parallel simulation environment. It supports multiple-synchronization protocols without requiring users to recompile their code. When a SPEEDES simulation runs on one node, all the extra parallel overhead is removed automatically at run time. When the same executable runs in parallel, the user preselects the synchronization algorithm from a list of options. SPEEDES currently runs on UNIX networks and on the California Institute of Technology/Jet Propulsion Laboratory Mark III Hypercube. SPEEDES also supports interactive simulations. Featured in the SPEEDES environment is a new parallel synchronization approach called Breathing Time Buckets. This algorithm uses some of the conservative techniques found in Time Bucket synchronization, along with the optimism that characterizes the Time Warp approach. A mathematical model derived from first principles predicts the performance of Breathing Time Buckets. Along with the Breathing Time Buckets algorithm, this paper discusses the rules for processing events in SPEEDES, describes the implementation of various other synchronization protocols supported by SPEEDES, describes some new ones for the future, discusses interactive simulations, and then gives some performance results.
Sistaninia, M.; Phillion, A. B.; Drezet, J.-M.; Rappaz, M.
2011-01-01
As a necessary step toward the quantitative prediction of hot tearing defects, a three-dimensional stress-strain simulation based on a combined finite element (FE)/discrete element method (DEM) has been developed that is capable of predicting the mechanical behavior of semisolid metallic alloys during solidification. The solidification model used for generating the initial solid-liquid structure is based on a Voronoi tessellation of randomly distributed nucleation centers and a solute diffusion model for each element of this tessellation. At a given fraction of solid, the deformation is then simulated with the solid grains being modeled using an elastoviscoplastic constitutive law, whereas the remaining liquid layers at grain boundaries are approximated by flexible connectors, each consisting of a spring element and a damper element acting in parallel. The model predictions have been validated against Al-Cu alloy experimental data from the literature. The results show that a combined FE/DEM approach is able to express the overall mechanical behavior of semisolid alloys at the macroscale based on the morphology of the grain structure. For the first time, the localization of strain in the intergranular regions is taken into account. Thus, this approach constitutes an indispensible step towards the development of a comprehensive model of hot tearing.
Directory of Open Access Journals (Sweden)
T. Stefański
2014-12-01
Full Text Available Parallel implementation of the discrete Green's function formulation of the finite-difference time-domain (DGF-FDTD method was developed on a multicore central processing unit. DGF-FDTD avoids computations of the electromagnetic field in free-space cells and does not require domain termination by absorbing boundary conditions. Computed DGF-FDTD solutions are compatible with the FDTD grid enabling the perfect hybridization of FDTD with the use of time-domain integral equation methods. The developed implementation can be applied to simulations of antenna characteristics. For the sake of example, arrays of Yagi-Uda antennas were simulated with the use of parallel DGF-FDTD. The efficiency of parallel computations was investigated as a function of the number of current elements in the FDTD grid. Although the developed method does not apply the fast Fourier transform for convolution computations, advantages stemming from the application of DGF-FDTD instead of FDTD can be demonstrated for one-dimensional wire antennas when simulation results are post-processed by the near-to-far-field transformation.
Simulation of hemp fibre bundle and cores using discrete element method
Energy Technology Data Exchange (ETDEWEB)
Al-Amin Sadek, M.; Chen, Y. [Manitoba Univ., Winnipeg, MB (Canada). Dept. of Biosystems Engineering; Lague, C. [Ottawa Univ., Ottawa, ON (Canada). Faculty of Engineering; Landry, H. [Prairie Agricultural Machinery Inst., Humboldt, SK (Canada); Peng, Q. [Manitoba Univ., Winnipeg, MB (Canada). Dept. of Mechanical and Manufacturing Engineering; Zhong, W. [Manitoba Univ., Winnipeg, MB (Canada). Dept. of Textile Sciences
2010-07-01
The mechanical behaviour of hemp fibre and core must be well understood in order to obtain high-grade hemp fibre that is currently in high demand for various industrial applications. Modelling by discrete element method can simulate the mechanical behaviour of such materials. A commercial discrete element software called Particle Flow Code was used in this study. In particular, the 3-dimension (PFC3D) was used to simulate hemp fibre and core. Since the basic PFC3D particles are spherical, the individual virtual hemp fibres were defined as strings of balls held together by PFC3D parallel bonds. The study showed that the virtual fibre is flexible and can bend and break by forces. This reflects the characteristics of hemp fibre. Using the clump logic of PFC3D, the virtual hemp core was defined as a rigid and unbreakable body, which reflect the characteristics of the core. The virtual fibre and core were defined with several microproperties, some of which were previously calibrated. The PFC3D bond properties were calibrated in this study. They included normal and shear stiffness; pb{sub k}n and pb{sub k}s; normal and shear strength; and bond disk radius, R of the virtual fibre. The calibration started with developing a PFC3D model to simulate fibre tensile test. The microproperties of virtual fibre and core were calibrated by running the PFC3D model. Literature data from fibre tensile tests was compared with simulation results.
Three-dimensional discrete element method simulation of core disking
Wu, Shunchuan; Wu, Haoyan; Kemeny, John
2018-04-01
The phenomenon of core disking is commonly seen in deep drilling of highly stressed regions in the Earth's crust. Given its close relationship with the in situ stress state, the presence and features of core disking can be used to interpret the stresses when traditional in situ stress measuring techniques are not available. The core disking process was simulated in this paper using the three-dimensional discrete element method software PFC3D (particle flow code). In particular, PFC3D is used to examine the evolution of fracture initiation, propagation and coalescence associated with core disking under various stress states. In this paper, four unresolved problems concerning core disking are investigated with a series of numerical simulations. These simulations also provide some verification of existing results by other researchers: (1) Core disking occurs when the maximum principal stress is about 6.5 times the tensile strength. (2) For most stress situations, core disking occurs from the outer surface, except for the thrust faulting stress regime, where the fractures were found to initiate from the inner part. (3) The anisotropy of the two horizontal principal stresses has an effect on the core disking morphology. (4) The thickness of core disk has a positive relationship with radial stress and a negative relationship with axial stresses.
Applications of the discrete element method in mechanical engineering
International Nuclear Information System (INIS)
Fleissner, Florian; Gaugele, Timo; Eberhard, Peter
2007-01-01
Compared to other fields of engineering, in mechanical engineering, the Discrete Element Method (DEM) is not yet a well known method. Nevertheless, there is a variety of simulation problems where the method has obvious advantages due to its meshless nature. For problems where several free bodies can collide and break after having been largely deformed, the DEM is the method of choice. Neighborhood search and collision detection between bodies as well as the separation of large solids into smaller particles are naturally incorporated in the method. The main DEM algorithm consists of a relatively simple loop that basically contains the three substeps contact detection, force computation and integration. However, there exists a large variety of different algorithms to choose the substeps to compose the optimal method for a given problem. In this contribution, we describe the dynamics of particle systems together with appropriate numerical integration schemes and give an overview over different types of particle interactions that can be composed to adapt the method to fit to a given simulation problem. Surface triangulations are used to model complicated, non-convex bodies in contact with particle systems. The capabilities of the method are finally demonstrated by means of application examples
Mechanics of a crushable pebble assembly using discrete element method
International Nuclear Information System (INIS)
Annabattula, R.K.; Gan, Y.; Zhao, S.; Kamlah, M.
2012-01-01
The influence of crushing of individual pebbles on the overall strength of a pebble assembly is investigated using discrete element method. An assembly comprising of 5000 spherical pebbles is assigned with random critical failure energies with a Weibull distribution in accordance with the experimental observation. Then, the pebble assembly is subjected to uni-axial compression (ε 33 =1.5%) with periodic boundary conditions. The crushable pebble assembly shows a significant difference in stress–strain response in comparison to a non-crushable pebble assembly. The analysis shows that a ideal plasticity like behaviour (constant stress with increase in strain) is the characteristic of a crushable pebble assembly with sudden damage. The damage accumulation law plays a critical role in determining the critical stress while the critical number of completely failed pebbles at the onset of critical stress is independent of such a damage law. Furthermore, a loosely packed pebble assembly shows a higher crush resistance while the critical stress is insensitive to the packing factor (η) of the assembly.
Numerical simulations of granular dynamics: I. Hard-sphere discrete element method and tests
Richardson, Derek C.; Walsh, Kevin J.; Murdoch, Naomi; Michel, Patrick
2011-03-01
We present a new particle-based (discrete element) numerical method for the simulation of granular dynamics, with application to motions of particles on small solar system body and planetary surfaces. The method employs the parallel N-body tree code pkdgrav to search for collisions and compute particle trajectories. Collisions are treated as instantaneous point-contact events between rigid spheres. Particle confinement is achieved by combining arbitrary combinations of four provided wall primitives, namely infinite plane, finite disk, infinite cylinder, and finite cylinder, and degenerate cases of these. Various wall movements, including translation, oscillation, and rotation, are supported. We provide full derivations of collision prediction and resolution equations for all geometries and motions. Several tests of the method are described, including a model granular “atmosphere” that achieves correct energy equipartition, and a series of tumbler simulations that show the expected transition from tumbling to centrifuging as a function of rotation rate.
Experiences in the parallelization of the discrete ordinates method using OpenMP and MPI
Energy Technology Data Exchange (ETDEWEB)
Pautz, A. [TUV Hannover/Sachsen-Anhalt e.V. (Germany); Langenbuch, S. [Gesellschaft fur Anlagen- und Reaktorsicherheit (GRS) mbH (Germany)
2003-07-01
The method of Discrete Ordinates is in principle parallelizable to a high degree, since the transport 'mesh sweeps' are mutually independent for all angular directions. However, in the well-known production code Dort such a type of angular domain decomposition has to be done on a spatial line-byline basis, causing the parallelism in the code to be very fine-grained. The construction of scalar fluxes and moments requires a large effort for inter-thread or inter-process communication. We have implemented two different parallelization approaches in Dort: firstly, we have used a shared-memory model suitable for SMP (Symmetric Multiprocessor) machines based on the standard OpenMP. The second approach uses the well-known Message Passing Interface (MPI) to establish communication between parallel processes running in a distributed-memory environment. We investigate the benefits and drawbacks of both models and show first results on performance and scaling behaviour of the parallel Dort code. (authors)
Experiences in the parallelization of the discrete ordinates method using OpenMP and MPI
International Nuclear Information System (INIS)
Pautz, A.; Langenbuch, S.
2003-01-01
The method of Discrete Ordinates is in principle parallelizable to a high degree, since the transport 'mesh sweeps' are mutually independent for all angular directions. However, in the well-known production code Dort such a type of angular domain decomposition has to be done on a spatial line-byline basis, causing the parallelism in the code to be very fine-grained. The construction of scalar fluxes and moments requires a large effort for inter-thread or inter-process communication. We have implemented two different parallelization approaches in Dort: firstly, we have used a shared-memory model suitable for SMP (Symmetric Multiprocessor) machines based on the standard OpenMP. The second approach uses the well-known Message Passing Interface (MPI) to establish communication between parallel processes running in a distributed-memory environment. We investigate the benefits and drawbacks of both models and show first results on performance and scaling behaviour of the parallel Dort code. (authors)
Ruiz-Baier, Ricardo; Lunati, Ivan
2016-10-01
We present a novel discretization scheme tailored to a class of multiphase models that regard the physical system as consisting of multiple interacting continua. In the framework of mixture theory, we consider a general mathematical model that entails solving a system of mass and momentum equations for both the mixture and one of the phases. The model results in a strongly coupled and nonlinear system of partial differential equations that are written in terms of phase and mixture (barycentric) velocities, phase pressure, and saturation. We construct an accurate, robust and reliable hybrid method that combines a mixed finite element discretization of the momentum equations with a primal discontinuous finite volume-element discretization of the mass (or transport) equations. The scheme is devised for unstructured meshes and relies on mixed Brezzi-Douglas-Marini approximations of phase and total velocities, on piecewise constant elements for the approximation of phase or total pressures, as well as on a primal formulation that employs discontinuous finite volume elements defined on a dual diamond mesh to approximate scalar fields of interest (such as volume fraction, total density, saturation, etc.). As the discretization scheme is derived for a general formulation of multicontinuum physical systems, it can be readily applied to a large class of simplified multiphase models; on the other, the approach can be seen as a generalization of these models that are commonly encountered in the literature and employed when the latter are not sufficiently accurate. An extensive set of numerical test cases involving two- and three-dimensional porous media are presented to demonstrate the accuracy of the method (displaying an optimal convergence rate), the physics-preserving properties of the mixed-primal scheme, as well as the robustness of the method (which is successfully used to simulate diverse physical phenomena such as density fingering, Terzaghi's consolidation
Hybrid Discrete Element - Finite Element Simulation for Railway Bridge-Track Interaction
Kaewunruen, S.; Mirza, O.
2017-10-01
At the transition zone or sometimes called ‘bridge end’ or ‘bridge approach’, the stiffness difference between plain track and track over bridge often causes aggravated impact loading due to uneven train movement onto the area. The differential track settlement over the transition has been a classical problem in railway networks, especially for the aging rail infrastructures around the world. This problem is also additionally worsened by the fact that the construction practice over the area is difficult, resulting in a poor compaction of formation and subgrade. This paper presents an advanced hybrid simulation using coupled discrete elements and finite elements to investigate dynamic interaction at the transition zone. The goal is to evaluate the dynamic stresses and to better understand the impact dynamics redistribution at the bridge end. An existing bridge ‘Salt Pan Creek Railway Bridge’, located between Revesby and Kingsgrove, has been chosen for detailed investigation. The Salt Pan Bridge currently demonstrates crushing of the ballast causing significant deformation and damage. Thus, it’s imperative to assess the behaviours of the ballast under dynamic loads. This can be achieved by modelling the nonlinear interactions between the steel rail and sleeper, and sleeper to ballast. The continuum solid elements of track components have been modelled using finite element approach, while the granular media (i.e. ballast) have been simulated by discrete element method. The hybrid DE/FE model demonstrates that ballast experiences significant stresses at the contacts between the sleeper and concrete section. These overburden stress exists in the regions below the outer rails, identify fouling and permanent deformation of the ballast.
Collective Robotic Assembly of Discrete Lattice Elements (CRADLE)
National Aeronautics and Space Administration — CRADLE seeks to address this need through a novel application of an integrated robot-structure-material system based on discrete lattice construction using task...
Varma, Sashank; Karl, Stacy R
2013-05-01
Much of the research on mathematical cognition has focused on the numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9, with considerably less attention paid to more abstract number classes. The current research investigated how people understand decimal proportions--rational numbers between 0 and 1 expressed in the place-value symbol system. The results demonstrate that proportions are represented as discrete structures and processed in parallel. There was a semantic interference effect: When understanding a proportion expression (e.g., "0.29"), both the correct proportion referent (e.g., 0.29) and the incorrect natural number referent (e.g., 29) corresponding to the visually similar natural number expression (e.g., "29") are accessed in parallel, and when these referents lead to conflicting judgments, performance slows. There was also a syntactic interference effect, generalizing the unit-decade compatibility effect for natural numbers: When comparing two proportions, their tenths and hundredths components are processed in parallel, and when the different components lead to conflicting judgments, performance slows. The results also reveal that zero decimals--proportions ending in zero--serve multiple cognitive functions, including eliminating semantic interference and speeding processing. The current research also extends the distance, semantic congruence, and SNARC effects from natural numbers to decimal proportions. These findings inform how people understand the place-value symbol system, and the mental implementation of mathematical symbol systems more generally. Copyright © 2013 Elsevier Inc. All rights reserved.
Nakashima, Hiroshi; Takatsu, Yuzuru
The goal of this study is to develop a practical and fast simulation tool for soil-tire interaction analysis, where finite element method (FEM) and discrete element method (DEM) are coupled together, and which can be realized on a desktop PC. We have extended our formerly proposed dynamic FE-DE method (FE-DEM) to include practical soil-tire system interaction, where not only the vertical sinkage of a tire, but also the travel of a driven tire was considered. Numerical simulation by FE-DEM is stable, and the relationships between variables, such as load-sinkage and sinkage-travel distance, and the gross tractive effort and running resistance characteristics, are obtained. Moreover, the simulation result is accurate enough to predict the maximum drawbar pull for a given tire, once the appropriate parameter values are provided. Therefore, the developed FE-DEM program can be applied with sufficient accuracy to interaction problems in soil-tire systems.
A Dual Super-Element Domain Decomposition Approach for Parallel Nonlinear Finite Element Analysis
Jokhio, G. A.; Izzuddin, B. A.
2015-05-01
This article presents a new domain decomposition method for nonlinear finite element analysis introducing the concept of dual partition super-elements. The method extends ideas from the displacement frame method and is ideally suited for parallel nonlinear static/dynamic analysis of structural systems. In the new method, domain decomposition is realized by replacing one or more subdomains in a "parent system," each with a placeholder super-element, where the subdomains are processed separately as "child partitions," each wrapped by a dual super-element along the partition boundary. The analysis of the overall system, including the satisfaction of equilibrium and compatibility at all partition boundaries, is realized through direct communication between all pairs of placeholder and dual super-elements. The proposed method has particular advantages for matrix solution methods based on the frontal scheme, and can be readily implemented for existing finite element analysis programs to achieve parallelization on distributed memory systems with minimal intervention, thus overcoming memory bottlenecks typically faced in the analysis of large-scale problems. Several examples are presented in this article which demonstrate the computational benefits of the proposed parallel domain decomposition approach and its applicability to the nonlinear structural analysis of realistic structural systems.
Hegde, Ganapathi; Vaya, Pukhraj
2013-10-01
This article presents a parallel architecture for 3-D discrete wavelet transform (3-DDWT). The proposed design is based on the 1-D pipelined lifting scheme. The architecture is fully scalable beyond the present coherent Daubechies filter bank (9, 7). This 3-DDWT architecture has advantages such as no group of pictures restriction and reduced memory referencing. It offers low power consumption, low latency and high throughput. The computing technique is based on the concept that lifting scheme minimises the storage requirement. The application specific integrated circuit implementation of the proposed architecture is done by synthesising it using 65 nm Taiwan Semiconductor Manufacturing Company standard cell library. It offers a speed of 486 MHz with a power consumption of 2.56 mW. This architecture is suitable for real-time video compression even with large frame dimensions.
Discrete ordinates cross-section generation in parallel plane geometry -- 2: Computational results
International Nuclear Information System (INIS)
Yavuz, M.
1998-01-01
In Ref. 1, the author presented inverse discrete ordinates (S N ) methods for cross-section generation with an arbitrary scattering anisotropy of order L (L ≤ N - 1) in parallel plane geometry. The solution techniques depend on the S N eigensolutions. The eigensolutions are determined by the inverse simplified S N method (ISS N ), which uses the surface Green's function matrices (T and R). Inverse problems are generally designed so that experimentally measured physical quantities can be used in the formulations. In the formulations, although T and R (TR matrices) are measurable quantities, the author does not have such data to check the adequacy and accuracy of the methods. However, it is possible to compute TR matrices by S N methods. The author presents computational results and computationally observed properties
Parallel 3D Mortar Element Method for Adaptive Nonconforming Meshes
Feng, Huiyu; Mavriplis, Catherine; VanderWijngaart, Rob; Biswas, Rupak
2004-01-01
High order methods are frequently used in computational simulation for their high accuracy. An efficient way to avoid unnecessary computation in smooth regions of the solution is to use adaptive meshes which employ fine grids only in areas where they are needed. Nonconforming spectral elements allow the grid to be flexibly adjusted to satisfy the computational accuracy requirements. The method is suitable for computational simulations of unsteady problems with very disparate length scales or unsteady moving features, such as heat transfer, fluid dynamics or flame combustion. In this work, we select the Mark Element Method (MEM) to handle the non-conforming interfaces between elements. A new technique is introduced to efficiently implement MEM in 3-D nonconforming meshes. By introducing an "intermediate mortar", the proposed method decomposes the projection between 3-D elements and mortars into two steps. In each step, projection matrices derived in 2-D are used. The two-step method avoids explicitly forming/deriving large projection matrices for 3-D meshes, and also helps to simplify the implementation. This new technique can be used for both h- and p-type adaptation. This method is applied to an unsteady 3-D moving heat source problem. With our new MEM implementation, mesh adaptation is able to efficiently refine the grid near the heat source and coarsen the grid once the heat source passes. The savings in computational work resulting from the dynamic mesh adaptation is demonstrated by the reduction of the the number of elements used and CPU time spent. MEM and mesh adaptation, respectively, bring irregularity and dynamics to the computer memory access pattern. Hence, they provide a good way to gauge the performance of computer systems when running scientific applications whose memory access patterns are irregular and unpredictable. We select a 3-D moving heat source problem as the Unstructured Adaptive (UA) grid benchmark, a new component of the NAS Parallel
Algorithms and data structures for massively parallel generic adaptive finite element codes
Bangerth, Wolfgang
2011-12-01
Today\\'s largest supercomputers have 100,000s of processor cores and offer the potential to solve partial differential equations discretized by billions of unknowns. However, the complexity of scaling to such large machines and problem sizes has so far prevented the emergence of generic software libraries that support such computations, although these would lower the threshold of entry and enable many more applications to benefit from large-scale computing. We are concerned with providing this functionality for mesh-adaptive finite element computations. We assume the existence of an "oracle" that implements the generation and modification of an adaptive mesh distributed across many processors, and that responds to queries about its structure. Based on querying the oracle, we develop scalable algorithms and data structures for generic finite element methods. Specifically, we consider the parallel distribution of mesh data, global enumeration of degrees of freedom, constraints, and postprocessing. Our algorithms remove the bottlenecks that typically limit large-scale adaptive finite element analyses. We demonstrate scalability of complete finite element workflows on up to 16,384 processors. An implementation of the proposed algorithms, based on the open source software p4est as mesh oracle, is provided under an open source license through the widely used deal.II finite element software library. © 2011 ACM 0098-3500/2011/12-ART10 $10.00.
Radu, F.A.; Pop, I.S.; Knabner, P.; Bermúdez de Castro, A.; Gómez, D.; Quintela, P.; Salgado, P.
2006-01-01
In this paper we discuss some iterative approaches for solving the nonlinear algebraic systems encountered as fully discrete counterparts of some degenerate (fast diffusion) parabolic problems. After regularization, we combine a mixed finite element discretization with the Euler implicit scheme. For
Evaluating the performance of the particle finite element method in parallel architectures
Gimenez, Juan M.; Nigro, Norberto M.; Idelsohn, Sergio R.
2014-05-01
This paper presents a high performance implementation for the particle-mesh based method called particle finite element method two (PFEM-2). It consists of a material derivative based formulation of the equations with a hybrid spatial discretization which uses an Eulerian mesh and Lagrangian particles. The main aim of PFEM-2 is to solve transport equations as fast as possible keeping some level of accuracy. The method was found to be competitive with classical Eulerian alternatives for these targets, even in their range of optimal application. To evaluate the goodness of the method with large simulations, it is imperative to use of parallel environments. Parallel strategies for Finite Element Method have been widely studied and many libraries can be used to solve Eulerian stages of PFEM-2. However, Lagrangian stages, such as streamline integration, must be developed considering the parallel strategy selected. The main drawback of PFEM-2 is the large amount of memory needed, which limits its application to large problems with only one computer. Therefore, a distributed-memory implementation is urgently needed. Unlike a shared-memory approach, using domain decomposition the memory is automatically isolated, thus avoiding race conditions; however new issues appear due to data distribution over the processes. Thus, a domain decomposition strategy for both particle and mesh is adopted, which minimizes the communication between processes. Finally, performance analysis running over multicore and multinode architectures are presented. The Courant-Friedrichs-Lewy number used influences the efficiency of the parallelization and, in some cases, a weighted partitioning can be used to improve the speed-up. However the total cputime for cases presented is lower than that obtained when using classical Eulerian strategies.
A discrete finite element modelling and measurements for powder compaction
International Nuclear Information System (INIS)
Choi, J L; Gethin, D T
2009-01-01
An experimental investigation into friction between powder and a target surface together with numerical modelling of compaction and friction processes at a micro-scale are presented in this paper. The experimental work explores friction mechanisms by using an extended sliding plate apparatus operating at low load while sliding over a long distance. Tests were conducted for copper and 316 steel with variation in loads, surface finish and its orientation. The behaviours of the static and dynamic friction were identified highlighting the important influence of particle size, particle shape, material response and surface topography. The results also highlighted that under light loading the friction coefficient remains at a level lower than that derived from experiments on equipment having a wider dynamic range and this is attributed to the enhanced sensitivity of the measurement equipment. The results also suggest that friction variation with sliding distance is a consequence of damage, rather than presentation of an uncontaminated target sliding surface. The complete experimental cycle was modelled numerically using a combined discrete and finite element scheme enabling exploration of mechanisms that are defined at the particle level. Using compaction as the starting point, a number of simulation factors and process parameters were investigated. Comparisons were made with previously published work, showing reasonable agreement and the simulations were then used to explore the process response to the range of particle scale factors. Models comprising regular packing of round particles exhibited stiff response with high initial density. Models with random packing were explored and were found to reflect trends that are more closely aligned with experimental observation, including rearrangement, followed by compaction under a regime of elastic then plastic deformation. Numerical modelling of the compaction stage was extended to account for the shearing stage of the
A discrete element based simulation framework to investigate particulate spray deposition processes
Mukherjee, Debanjan; Zohdi, Tarek I.
2015-01-01
© 2015 Elsevier Inc. This work presents a computer simulation framework based on discrete element method to analyze manufacturing processes that comprise a loosely flowing stream of particles in a carrier fluid being deposited on a target surface
The Full—Discrete Mixed Finite Element Methods for Nonlinear Hyperbolic Equations
Institute of Scientific and Technical Information of China (English)
YanpingCHEN; YunqingHUANG
1998-01-01
This article treats mixed finite element methods for second order nonlinear hyperbolic equations.A fully discrete scheme is presented and improved L2-error estimates are established.The convergence of both the function value andthe flux is demonstrated.
Multirate-based fast parallel algorithms for 2-D DHT-based real-valued discrete Gabor transform.
Tao, Liang; Kwan, Hon Keung
2012-07-01
Novel algorithms for the multirate and fast parallel implementation of the 2-D discrete Hartley transform (DHT)-based real-valued discrete Gabor transform (RDGT) and its inverse transform are presented in this paper. A 2-D multirate-based analysis convolver bank is designed for the 2-D RDGT, and a 2-D multirate-based synthesis convolver bank is designed for the 2-D inverse RDGT. The parallel channels in each of the two convolver banks have a unified structure and can apply the 2-D fast DHT algorithm to speed up their computations. The computational complexity of each parallel channel is low and is independent of the Gabor oversampling rate. All the 2-D RDGT coefficients of an image are computed in parallel during the analysis process and can be reconstructed in parallel during the synthesis process. The computational complexity and time of the proposed parallel algorithms are analyzed and compared with those of the existing fastest algorithms for 2-D discrete Gabor transforms. The results indicate that the proposed algorithms are the fastest, which make them attractive for real-time image processing.
International Nuclear Information System (INIS)
Bailey, Teresa S.; Warsa, James S.; Chang, Jae H.; Adams, Marvin L.
2011-01-01
We present a new spatial discretization of the discrete-ordinates transport equation in two dimensional Cartesian (X-Y) geometry for arbitrary polygonal meshes. The discretization is a discontinuous finite element method (DFEM) that utilizes piecewise bi-linear (PWBL) basis functions, which are formally introduced in this paper. We also present a series of numerical results on quadrilateral and polygonal grids and compare these results to a variety of other spatial discretization that have been shown to be successful on these grid types. Finally, we note that the properties of the PWBL basis functions are such that the leading-order piecewise bi-linear discontinuous finite element (PWBLD) solution will satisfy a reasonably accurate diffusion discretization in the thick diffusion limit, making the PWBLD method a viable candidate for many different classes of transport problems. (author)
International Nuclear Information System (INIS)
Bailey, T.S.; Chang, J.H.; Warsa, J.S.; Adams, M.L.
2010-01-01
We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional Cartesian (X-Y) geometry for arbitrary polygonal meshes. The discretization is a discontinuous finite element method (DFEM) that utilizes piecewise bi-linear (PWBL) basis functions, which are formally introduced in this paper. We also present a series of numerical results on quadrilateral and polygonal grids and compare these results to a variety of other spatial discretizations that have been shown to be successful on these grid types. Finally, we note that the properties of the PWBL basis functions are such that the leading-order piecewise bi-linear discontinuous finite element (PWBLD) solution will satisfy a reasonably accurate diffusion discretization in the thick diffusion limit, making the PWBLD method a viable candidate for many different classes of transport problems.
Energy Technology Data Exchange (ETDEWEB)
Bailey, T S; Chang, J H; Warsa, J S; Adams, M L
2010-12-22
We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional Cartesian (X-Y) geometry for arbitrary polygonal meshes. The discretization is a discontinuous finite element method (DFEM) that utilizes piecewise bi-linear (PWBL) basis functions, which are formally introduced in this paper. We also present a series of numerical results on quadrilateral and polygonal grids and compare these results to a variety of other spatial discretizations that have been shown to be successful on these grid types. Finally, we note that the properties of the PWBL basis functions are such that the leading-order piecewise bi-linear discontinuous finite element (PWBLD) solution will satisfy a reasonably accurate diffusion discretization in the thick diffusion limit, making the PWBLD method a viable candidate for many different classes of transport problems.
Finite element electromagnetic field computation on the Sequent Symmetry 81 parallel computer
International Nuclear Information System (INIS)
Ratnajeevan, S.; Hoole, H.
1990-01-01
Finite element field analysis algorithms lend themselves to parallelization and this fact is exploited in this paper to implement a finite element analysis program for electromagnetic field computation on the Sequent Symmetry 81 parallel computer with three processors. In terms of waiting time, the maximum gains are to be made in matrix solution and therefore this paper concentrates on the gains in parallelizing the solution part of finite element analysis. An outline of how parallelization could be exploited in most finite element operations is given in this paper although the actual implemention of parallelism on the Sequent Symmetry 81 parallel computer was in sparsity computation, matrix assembly and the matrix solution areas. In all cases, the algorithms were modified suit the parallel programming application rather than allowing the compiler to parallelize on existing algorithms
Inversion of potential field data using the finite element method on parallel computers
Gross, L.; Altinay, C.; Shaw, S.
2015-11-01
In this paper we present a formulation of the joint inversion of potential field anomaly data as an optimization problem with partial differential equation (PDE) constraints. The problem is solved using the iterative Broyden-Fletcher-Goldfarb-Shanno (BFGS) method with the Hessian operator of the regularization and cross-gradient component of the cost function as preconditioner. We will show that each iterative step requires the solution of several PDEs namely for the potential fields, for the adjoint defects and for the application of the preconditioner. In extension to the traditional discrete formulation the BFGS method is applied to continuous descriptions of the unknown physical properties in combination with an appropriate integral form of the dot product. The PDEs can easily be solved using standard conforming finite element methods (FEMs) with potentially different resolutions. For two examples we demonstrate that the number of PDE solutions required to reach a given tolerance in the BFGS iteration is controlled by weighting regularization and cross-gradient but is independent of the resolution of PDE discretization and that as a consequence the method is weakly scalable with the number of cells on parallel computers. We also show a comparison with the UBC-GIF GRAV3D code.
Sarvari, S. M. Hosseini
2017-09-01
The traditional form of discrete ordinates method is applied to solve the radiative transfer equation in plane-parallel semi-transparent media with variable refractive index through using the variable discrete ordinate directions and the concept of refracted radiative intensity. The refractive index are taken as constant in each control volume, such that the direction cosines of radiative rays remain non-variant through each control volume, and then, the directions of discrete ordinates are changed locally by passing each control volume, according to the Snell's law of refraction. The results are compared by the previous studies in this field. Despite simplicity, the results show that the variable discrete ordinate method has a good accuracy in solving the radiative transfer equation in the semi-transparent media with arbitrary distribution of refractive index.
Parallel, but Dissociable, Processing in Discrete Corticostriatal Inputs Encodes Skill Learning.
Kupferschmidt, David A; Juczewski, Konrad; Cui, Guohong; Johnson, Kari A; Lovinger, David M
2017-10-11
Changes in cortical and striatal function underlie the transition from novel actions to refined motor skills. How discrete, anatomically defined corticostriatal projections function in vivo to encode skill learning remains unclear. Using novel fiber photometry approaches to assess real-time activity of associative inputs from medial prefrontal cortex to dorsomedial striatum and sensorimotor inputs from motor cortex to dorsolateral striatum, we show that associative and sensorimotor inputs co-engage early in action learning and disengage in a dissociable manner as actions are refined. Disengagement of associative, but not sensorimotor, inputs predicts individual differences in subsequent skill learning. Divergent somatic and presynaptic engagement in both projections during early action learning suggests potential learning-related in vivo modulation of presynaptic corticostriatal function. These findings reveal parallel processing within associative and sensorimotor circuits that challenges and refines existing views of corticostriatal function and expose neuronal projection- and compartment-specific activity dynamics that encode and predict action learning. Published by Elsevier Inc.
Toward the modeling of combustion reactions through discrete element method (DEM) simulations
Reis, Martina Costa; Alobaid, Falah; Wang, Yongqi
2018-03-01
In this work, the process of combustion of coal particles under turbulent regime in a high-temperature reaction chamber is modeled through 3D discrete element method (DEM) simulations. By assuming the occurrence of interfacial transport phenomena between the gas and solid phases, one investigates the influence of the physicochemical properties of particles on the rates of heterogeneous chemical reactions, as well as the influence of eddies present in the gas phase on the mass transport of reactants toward the coal particles surface. Moreover, by considering a simplistic chemical mechanism for the combustion process, thermochemical and kinetic parameters obtained from the simulations are employed to discuss some phenomenological aspects of the combustion process. In particular, the observed changes in the mass and volume of coal particles during the gasification and combustion steps are discussed by emphasizing the changes in the chemical structure of the coal. In addition to illustrate how DEM simulations can be used in the modeling of consecutive and parallel chemical reactions, this work also shows how heterogeneous and homogeneous chemical reactions become a source of mass and energy for the gas phase.
Directory of Open Access Journals (Sweden)
Qi Zhao
2014-12-01
Full Text Available Hydraulic fracturing (HF technique has been extensively used for the exploitation of unconventional oil and gas reservoirs. HF enhances the connectivity of less permeable oil and gas-bearing rock formations by fluid injection, which creates an interconnected fracture network and increases the hydrocarbon production. Meanwhile, microseismic (MS monitoring is one of the most effective approaches to evaluate such stimulation process. In this paper, the combined finite-discrete element method (FDEM is adopted to numerically simulate HF and associated MS. Several post-processing tools, including frequency-magnitude distribution (b-value, fractal dimension (D-value, and seismic events clustering, are utilized to interpret numerical results. A non-parametric clustering algorithm designed specifically for FDEM is used to reduce the mesh dependency and extract more realistic seismic information. Simulation results indicated that at the local scale, the HF process tends to propagate following the rock mass discontinuities; while at the reservoir scale, it tends to develop in the direction parallel to the maximum in-situ stress.
Discrete Maximum Principle for Higher-Order Finite Elements in 1D
Czech Academy of Sciences Publication Activity Database
Vejchodský, Tomáš; Šolín, Pavel
2007-01-01
Roč. 76, č. 260 (2007), s. 1833-1846 ISSN 0025-5718 R&D Projects: GA ČR GP201/04/P021 Institutional research plan: CEZ:AV0Z10190503; CEZ:AV0Z20760514 Keywords : discrete maximum principle * discrete Grren´s function * higher-order elements Subject RIV: BA - General Mathematics Impact factor: 1.230, year: 2007
Finite-element semi-discretization of linearized compressible and resistive MHD
International Nuclear Information System (INIS)
Kerner, W.; Jakoby, A.; Lerbinger, K.
1985-08-01
The full resistive MHD equations are linearized around an equilibrium with cylindrical symmetry and solved numerically as an initial-value problem. The semi-discretization using cubic and quadratic finite elements for the spatial discretization and a fully implicit time advance yields very accurate results even for small values of the resistivity. In the application different phenomena such as waves, resistive instabilities and overstable modes are addressed. (orig.)
International Nuclear Information System (INIS)
Godoy, William F.; Liu Xu
2012-01-01
The present study introduces a parallel Jacobian-free Newton Krylov (JFNK) general minimal residual (GMRES) solution for the discretized radiative transfer equation (RTE) in 3D, absorbing, emitting and scattering media. For the angular and spatial discretization of the RTE, the discrete ordinates method (DOM) and the finite volume method (FVM) including flux limiters are employed, respectively. Instead of forming and storing a large Jacobian matrix, JFNK methods allow for large memory savings as the required Jacobian-vector products are rather approximated by semiexact and numerical formulations, for which convergence and computational times are presented. Parallelization of the GMRES solution is introduced in a combined memory-shared/memory-distributed formulation that takes advantage of the fact that only large vector arrays remain in the JFNK process. Results are presented for 3D test cases including a simple homogeneous, isotropic medium and a more complex non-homogeneous, non-isothermal, absorbing–emitting and anisotropic scattering medium with collimated intensities. Additionally, convergence and stability of Gram–Schmidt and Householder orthogonalizations for the Arnoldi process in the parallel GMRES algorithms are discussed and analyzed. Overall, the introduction of JFNK methods results in a parallel, yet scalable to the tested 2048 processors, and memory affordable solution to 3D radiative transfer problems without compromising the accuracy and convergence of a Newton-like solution.
Entropy-stable summation-by-parts discretization of the Euler equations on general curved elements
Crean, Jared; Hicken, Jason E.; Del Rey Fernández, David C.; Zingg, David W.; Carpenter, Mark H.
2018-03-01
We present and analyze an entropy-stable semi-discretization of the Euler equations based on high-order summation-by-parts (SBP) operators. In particular, we consider general multidimensional SBP elements, building on and generalizing previous work with tensor-product discretizations. In the absence of dissipation, we prove that the semi-discrete scheme conserves entropy; significantly, this proof of nonlinear L2 stability does not rely on integral exactness. Furthermore, interior penalties can be incorporated into the discretization to ensure that the total (mathematical) entropy decreases monotonically, producing an entropy-stable scheme. SBP discretizations with curved elements remain accurate, conservative, and entropy stable provided the mapping Jacobian satisfies the discrete metric invariants; polynomial mappings at most one degree higher than the SBP operators automatically satisfy the metric invariants in two dimensions. In three-dimensions, we describe an elementwise optimization that leads to suitable Jacobians in the case of polynomial mappings. The properties of the semi-discrete scheme are verified and investigated using numerical experiments.
Discrete-ordinates finite-element method for atmospheric radiative transfer and remote sensing
International Nuclear Information System (INIS)
Gerstl, S.A.W.; Zardecki, A.
1985-01-01
Advantages and disadvantages of modern discrete-ordinates finite-element methods for the solution of radiative transfer problems in meteorology, climatology, and remote sensing applications are evaluated. After the common basis of the formulation of radiative transfer problems in the fields of neutron transport and atmospheric optics is established, the essential features of the discrete-ordinates finite-element method are described including the limitations of the method and their remedies. Numerical results are presented for 1-D and 2-D atmospheric radiative transfer problems where integral as well as angular dependent quantities are compared with published results from other calculations and with measured data. These comparisons provide a verification of the discrete-ordinates results for a wide spectrum of cases with varying degrees of absorption, scattering, and anisotropic phase functions. Accuracy and computational speed are also discussed. Since practically all discrete-ordinates codes offer a builtin adjoint capability, the general concept of the adjoint method is described and illustrated by sample problems. Our general conclusion is that the strengths of the discrete-ordinates finite-element method outweight its weaknesses. We demonstrate that existing general-purpose discrete-ordinates codes can provide a powerful tool to analyze radiative transfer problems through the atmosphere, especially when 2-D geometries must be considered
Discrete maximum principle for the P1 - P0 weak Galerkin finite element approximations
Wang, Junping; Ye, Xiu; Zhai, Qilong; Zhang, Ran
2018-06-01
This paper presents two discrete maximum principles (DMP) for the numerical solution of second order elliptic equations arising from the weak Galerkin finite element method. The results are established by assuming an h-acute angle condition for the underlying finite element triangulations. The mathematical theory is based on the well-known De Giorgi technique adapted in the finite element context. Some numerical results are reported to validate the theory of DMP.
International Nuclear Information System (INIS)
Rousseau, J.
2009-07-01
That study focuses on concrete structures submitted to impact loading and is aimed at predicting local damage in the vicinity of an impact zone as well as the global response of the structure. The Discrete Element Method (DEM) seems particularly well suited in this context for modeling fractures. An identification process of DEM material parameters from macroscopic data (Young's modulus, compressive and tensile strength, fracture energy, etc.) will first be presented for the purpose of enhancing reproducibility and reliability of the simulation results with DE samples of various sizes. Then, a particular interaction, between concrete and steel elements, was developed for the simulation of reinforced concrete. The discrete elements method was validated on quasi-static and dynamic tests carried out on small samples of concrete and reinforced concrete. Finally, discrete elements were used to simulate impacts on reinforced concrete slabs in order to confront the results with experimental tests. The modeling of a large structure by means of DEM may lead to prohibitive computation times. A refined discretization becomes required in the vicinity of the impact, while the structure may be modeled using a coarse FE mesh further from the impact area, where the material behaves elastically. A coupled discrete-finite element approach is thus proposed: the impact zone is modeled by means of DE and elastic FE are used on the rest of the structure. An existing method for 3D finite elements was extended to shells. This new method was then validated on many quasi-static and dynamic tests. The proposed approach is then applied to an impact on a concrete structure in order to validate the coupled method and compare computation times. (author)
Discrete-Roughness-Element-Enhanced Swept-Wing Natural Laminar Flow at High Reynolds Numbers
Malik, Mujeeb; Liao, Wei; Li, Fei; Choudhari, Meelan
2015-01-01
Nonlinear parabolized stability equations and secondary-instability analyses are used to provide a computational assessment of the potential use of the discrete-roughness-element technology for extending swept-wing natural laminar flow at chord Reynolds numbers relevant to transport aircraft. Computations performed for the boundary layer on a natural-laminar-flow airfoil with a leading-edge sweep angle of 34.6 deg, freestream Mach number of 0.75, and chord Reynolds numbers of 17 × 10(exp 6), 24 × 10(exp 6), and 30 × 10(exp 6) suggest that discrete roughness elements could delay laminar-turbulent transition by about 20% when transition is caused by stationary crossflow disturbances. Computations show that the introduction of small-wavelength stationary crossflow disturbances (i.e., discrete roughness element) also suppresses the growth of most amplified traveling crossflow disturbances.
Numerical Integration Techniques for Curved-Element Discretizations of Molecule–Solvent Interfaces
Bardhan, Jaydeep P.; Altman, Michael D.; Willis, David J.; Lippow, Shaun M.; Tidor, Bruce; White, Jacob K.
2012-01-01
Surface formulations of biophysical modeling problems offer attractive theoretical and computational properties. Numerical simulations based on these formulations usually begin with discretization of the surface under consideration; often, the surface is curved, possessing complicated structure and possibly singularities. Numerical simulations commonly are based on approximate, rather than exact, discretizations of these surfaces. To assess the strength of the dependence of simulation accuracy on the fidelity of surface representation, we have developed methods to model several important surface formulations using exact surface discretizations. Following and refining Zauhar’s work (J. Comp.-Aid. Mol. Des. 9:149-159, 1995), we define two classes of curved elements that can exactly discretize the van der Waals, solvent-accessible, and solvent-excluded (molecular) surfaces. We then present numerical integration techniques that can accurately evaluate nonsingular and singular integrals over these curved surfaces. After validating the exactness of the surface discretizations and demonstrating the correctness of the presented integration methods, we present a set of calculations that compare the accuracy of approximate, planar-triangle-based discretizations and exact, curved-element-based simulations of surface-generalized-Born (sGB), surface-continuum van der Waals (scvdW), and boundary-element method (BEM) electrostatics problems. Results demonstrate that continuum electrostatic calculations with BEM using curved elements, piecewise-constant basis functions, and centroid collocation are nearly ten times more accurate than planartriangle BEM for basis sets of comparable size. The sGB and scvdW calculations give exceptional accuracy even for the coarsest obtainable discretized surfaces. The extra accuracy is attributed to the exact representation of the solute–solvent interface; in contrast, commonly used planar-triangle discretizations can only offer improved
Discrete Element Method simulations of standing jumps in granular flows down inclines
Directory of Open Access Journals (Sweden)
Méjean Ségolène
2017-01-01
Full Text Available This paper describes a numerical set-up which uses Discrete Element Method to produce standing jumps in flows of dry granular materials down a slope in two dimensions. The grain-scale force interactions are modeled by a visco-elastic normal force and an elastic tangential force with a Coulomb threshold. We will show how it is possible to reproduce all the shapes of the jumps observed in a previous laboratory study: diffuse versus steep jumps and compressible versus incompressible jumps. Moreover, we will discuss the additional measurements that can be done thanks to discrete element modelling.
Discrete Element study of granular material - Bumpy wall interface behavior
El Cheikh, Khadija; Rémond, Sébastien; Pizette, Patrick; Vanhove, Yannick; Djelal, Chafika
2016-09-01
This paper presents a DEM study of a confined granular material sheared between two parallel bumpy walls. The granular material consists of packed dry spherical particles. The bumpiness is modeled by spheres of a given diameter glued on horizontal planes. Different bumpy surfaces are modeled by varying diameter or concentration of glued spheres. The material is sheared by moving the two bumpy walls at fixed velocity. During shear, the confining pressure applied on each bumpy wall is controlled. The effect of wall bumpiness on the effective friction coefficient and on the granular material behavior at the bumpy walls is reported for various shearing conditions. For given bumpiness and confining pressure that we have studied, it is found that the shear velocity does not affect the shear stress. However, the effective friction coefficient and the behavior of the granular material depend on the bumpiness. When the diameter of the glued spheres is larger than about the average grains diameter of the medium, the latter is uniformly sheared and the effective friction coefficient remains constant. For smaller diameters of the glued spheres, the effective friction coefficient increases with the diameter of glued spheres. The influence of glued spheres concentration is significant only for small glued spheres diameters, typically half of average particle diameter of the granular material. In this case, increasing the concentration of glued spheres leads to a decrease in effective friction coefficient and to shear localization at the interface. For different diameters and concentrations of glued spheres, we show that the effect of bumpiness on the effective friction coefficient can be characterized by the depth of interlocking.
2016-06-12
Particle Size in Discrete Element Method to Particle Gas Method (DEM_PGM) Coupling in Underbody Blast Simulations Venkatesh Babu, Kumar Kulkarni, Sanjay...buried in soil viz., (1) coupled discrete element & particle gas methods (DEM-PGM) and (2) Arbitrary Lagrangian-Eulerian (ALE), are investigated. The...DEM_PGM and identify the limitations/strengths compared to the ALE method. Discrete Element Method (DEM) can model individual particle directly, and
Dynamics of parallel robots from rigid bodies to flexible elements
Briot, Sébastien
2015-01-01
This book starts with a short recapitulation on basic concepts, common to any types of robots (serial, tree structure, parallel, etc.), that are also necessary for computation of the dynamic models of parallel robots. Then, as dynamics requires the use of geometry and kinematics, the general equations of geometric and kinematic models of parallel robots are given. After, it is explained that parallel robot dynamic models can be obtained by decomposing the real robot into two virtual systems: a tree-structure robot (equivalent to the robot legs for which all joints would be actuated) plus a free body corresponding to the platform. Thus, the dynamics of rigid tree-structure robots is analyzed and algorithms to obtain their dynamic models in the most compact form are given. The dynamic model of the real rigid parallel robot is obtained by closing the loops through the use of the Lagrange multipliers. The problem of the dynamic model degeneracy near singularities is treated and optimal trajectory planning for cro...
International Nuclear Information System (INIS)
Zerr, R.J.; Azmy, Y.Y.
2010-01-01
A spatial domain decomposition with a parallel block Jacobi solution algorithm has been developed based on the integral transport matrix formulation of the discrete ordinates approximation for solving the within-group transport equation. The new methodology abandons the typical source iteration scheme and solves directly for the fully converged scalar flux. Four matrix operators are constructed based upon the integral form of the discrete ordinates equations. A single differential mesh sweep is performed to construct these operators. The method is parallelized by decomposing the problem domain into several smaller sub-domains, each treated as an independent problem. The scalar flux of each sub-domain is solved exactly given incoming angular flux boundary conditions. Sub-domain boundary conditions are updated iteratively, and convergence is achieved when the scalar flux error in all cells meets a pre-specified convergence criterion. The method has been implemented in a computer code that was then employed for strong scaling studies of the algorithm's parallel performance via a fixed-size problem in tests ranging from one domain up to one cell per sub-domain. Results indicate that the best parallel performance compared to source iterations occurs for optically thick, highly scattering problems, the variety that is most difficult for the traditional SI scheme to solve. Moreover, the minimum execution time occurs when each sub-domain contains a total of four cells. (authors)
Cai, Yong; Cui, Xiangyang; Li, Guangyao; Liu, Wenyang
2018-04-01
The edge-smooth finite element method (ES-FEM) can improve the computational accuracy of triangular shell elements and the mesh partition efficiency of complex models. In this paper, an approach is developed to perform explicit finite element simulations of contact-impact problems with a graphical processing unit (GPU) using a special edge-smooth triangular shell element based on ES-FEM. Of critical importance for this problem is achieving finer-grained parallelism to enable efficient data loading and to minimize communication between the device and host. Four kinds of parallel strategies are then developed to efficiently solve these ES-FEM based shell element formulas, and various optimization methods are adopted to ensure aligned memory access. Special focus is dedicated to developing an approach for the parallel construction of edge systems. A parallel hierarchy-territory contact-searching algorithm (HITA) and a parallel penalty function calculation method are embedded in this parallel explicit algorithm. Finally, the program flow is well designed, and a GPU-based simulation system is developed, using Nvidia's CUDA. Several numerical examples are presented to illustrate the high quality of the results obtained with the proposed methods. In addition, the GPU-based parallel computation is shown to significantly reduce the computing time.
CSIR Research Space (South Africa)
Govender, Nicolin
2013-01-01
Full Text Available in nature and cannot be described by a closed form solution for more than a few particles. A popular and successful approach in simulating the underlying dynamics of GM is by using the Discrete Element Method (DEM). Computational viable simulations...
Particle models for discrete element modeling of bulk grain properties of wheat kernels
Recent research has shown the potential of discrete element method (DEM) in simulating grain flow in bulk handling systems. Research has also revealed that simulation of grain flow with DEM requires establishment of appropriate particle models for each grain type. This research completes the three-p...
Applications of discrete element method in modeling of grain postharvest operations
Grain kernels are finite and discrete materials. Although flowing grain can behave like a continuum fluid at times, the discontinuous behavior exhibited by grain kernels cannot be simulated solely with conventional continuum-based computer modeling such as finite-element or finite-difference methods...
Discrete element simulation of mill charge in 3D using the BLAZE-DEM GPU framework
CSIR Research Space (South Africa)
Govender, Nicolin
2015-08-01
Full Text Available The Discrete Element Method (DEM) simulation of charge motion in ball, semi autogenous (SAG) and autogenous mills has advanced to a stage where the effects of lifter design, power draft and product size can be evaluated with sufficient accuracy...
Sound propagation in dry granular materials : discrete element simulations, theory, and experiments
Mouraille, O.J.P.
2009-01-01
In this study sound wave propagation through different types of dry confined granular systems is studied. With three-dimensional discrete element simulations, theory and experiments, the influence of several micro-scale properties: friction, dissipation, particle rotation, and contact disorder, on
Imole, Olukayode Isaiah; Krijgsman, Dinant; Weinhart, Thomas; Magnanimo, Vanessa; Chavez Montes, Bruno E.; Ramaioli, Marco; Luding, Stefan
2016-01-01
We perform experiments and discrete element simulations on the dosing of cohesive granular materials in a simplified geometry. The setup is a canister box where the powder is dosed out through the action of a constant-pitch coil feeder connected to a motor. A dosing step consists of a rotation
Discrete element simulation of internal stress in SiCp/aluminum ...
African Journals Online (AJOL)
SiCp / Al-Mg-Si matrix composite was prepared by pressureless Infiltration Process. By discrete element method, microcosmic two-dimensional numerical model of SiCp / Al matrix composites was established and the simulation of the size and distribution of micro-contact pressure and tension was performed from small load ...
Parallel direct solver for finite element modeling of manufacturing processes
DEFF Research Database (Denmark)
Nielsen, Chris Valentin; Martins, P.A.F.
2017-01-01
The central processing unit (CPU) time is of paramount importance in finite element modeling of manufacturing processes. Because the most significant part of the CPU time is consumed in solving the main system of equations resulting from finite element assemblies, different approaches have been...
Parallelized Three-Dimensional Resistivity Inversion Using Finite Elements And Adjoint State Methods
Schaa, Ralf; Gross, Lutz; Du Plessis, Jaco
2015-04-01
The resistivity method is one of the oldest geophysical exploration methods, which employs one pair of electrodes to inject current into the ground and one or more pairs of electrodes to measure the electrical potential difference. The potential difference is a non-linear function of the subsurface resistivity distribution described by an elliptic partial differential equation (PDE) of the Poisson type. Inversion of measured potentials solves for the subsurface resistivity represented by PDE coefficients. With increasing advances in multichannel resistivity acquisition systems (systems with more than 60 channels and full waveform recording are now emerging), inversion software require efficient storage and solver algorithms. We developed the finite element solver Escript, which provides a user-friendly programming environment in Python to solve large-scale PDE-based problems (see https://launchpad.net/escript-finley). Using finite elements, highly irregular shaped geology and topography can readily be taken into account. For the 3D resistivity problem, we have implemented the secondary potential approach, where the PDE is decomposed into a primary potential caused by the source current and the secondary potential caused by changes in subsurface resistivity. The primary potential is calculated analytically, and the boundary value problem for the secondary potential is solved using nodal finite elements. This approach removes the singularity caused by the source currents and provides more accurate 3D resistivity models. To solve the inversion problem we apply a 'first optimize then discretize' approach using the quasi-Newton scheme in form of the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method (see Gross & Kemp 2013). The evaluation of the cost function requires the solution of the secondary potential PDE for each source current and the solution of the corresponding adjoint-state PDE for the cost function gradients with respect to the subsurface
Parallel Fast Multipole Boundary Element Method for crustal dynamics
International Nuclear Information System (INIS)
Quevedo, Leonardo; Morra, Gabriele; Mueller, R Dietmar
2010-01-01
Crustal faults and sharp material transitions in the crust are usually represented as triangulated surfaces in structural geological models. The complex range of volumes separating such surfaces is typically three-dimensionally meshed in order to solve equations that describe crustal deformation with the finite-difference (FD) or finite-element (FEM) methods. We show here how the Boundary Element Method, combined with the Multipole approach, can revolutionise the calculation of stress and strain, solving the problem of computational scalability from reservoir to basin scales. The Fast Multipole Boundary Element Method (Fast BEM) tackles the difficulty of handling the intricate volume meshes and high resolution of crustal data that has put classical Finite 3D approaches in a performance crisis. The two main performance enhancements of this method: the reduction of required mesh elements from cubic to quadratic with linear size and linear-logarithmic runtime; achieve a reduction of memory and runtime requirements allowing the treatment of a new scale of geodynamic models. This approach was recently tested and applied in a series of papers by [1, 2, 3] for regional and global geodynamics, using KD trees for fast identification of near and far-field interacting elements, and MPI parallelised code on distributed memory architectures, and is now in active development for crustal dynamics. As the method is based on a free-surface, it allows easy data transfer to geological visualisation tools where only changes in boundaries and material properties are required as input parameters. In addition, easy volume mesh sampling of physical quantities enables direct integration with existing FD/FEM code.
Modeling of asphalt by means of discrete element method – an initial study
DEFF Research Database (Denmark)
Feng, Huan; Hededal, Ole; Stang, Henrik
of conducting time-consuming and lab-costly procedures. The use of numerical models, capable of reducing greatly the testing cost, has shown great potential in characterizing asphalt-aggregate mixtures for both material evaluation and structural design purposes, [1],[2]. Discrete element method (DEM) is one...... – will be applied. The work presented here will focus on the discrete element method as a tool for modelling composite materials, i.e. determination of a representative volume; boundary conditions; characterisation of the components mastic (binder + filler) and aggregates; and establishment of virtual test samples....... Results from initial tests will be presented and the future development of the model towards characterising asphalt from its composition will be outlined....
Study of the Internal Mechanical response of an asphalt mixture by 3-D Discrete Element Modeling
DEFF Research Database (Denmark)
Feng, Huan; Pettinari, Matteo; Hofko, Bernhard
2015-01-01
and the reliability of which have been validated. The dynamic modulus of asphalt mixtures were predicted by conducting Discrete Element simulation under dynamic strain control loading. In order to reduce the calculation time, a method based on frequency–temperature superposition principle has been implemented......In this paper the viscoelastic behavior of asphalt mixture was investigated by employing a three-dimensional Discrete Element Method (DEM). The cylinder model was filled with cubic array of spheres with a specified radius, and was considered as a whole mixture with uniform contact properties....... The ball density effect on the internal stress distribution of the asphalt mixture model has been studied when using this method. Furthermore, the internal stresses under dynamic loading have been studied. The agreement between the predicted and the laboratory test results of the complex modulus shows...
Davletshin, I. A.; Dushina, O. A.; Mikheev, N. I.; Kolchin, S. A.
2017-11-01
The pulsating flow in a circular channel with semicircular annular ribs as discrete roughness elements has been studied experimentally. Air flow under atmospheric conditions at the channel inlet has been considered. Steady and pulsating air flow has been studied under different frequencies and amplitudes of forced pulsations generated by periodic blockage of the channel cross section by a rotating flap. Flow resistance in pulsating regimes has been estimated from the average static pressure drop. The resistance values attained twice the steady flow ones.
A Discrete Element Method Centrifuge Model of Monopile under Cyclic Lateral Loads
Nuo Duan; Yi Pik Cheng
2016-01-01
This paper presents the data of a series of two-dimensional Discrete Element Method (DEM) simulations of a large-diameter rigid monopile subjected to cyclic loading under a high gravitational force. At present, monopile foundations are widely used to support the tall and heavy wind turbines, which are also subjected to significant from wind and wave actions. A safe design must address issues such as rotations and changes in soil stiffness subject to these loadings conditions. Design guidance ...
Discrete/Finite Element Modelling of Rock Cutting with a TBM Disc Cutter
Labra, Carlos; Rojek, Jerzy; Oñate, Eugenio
2017-03-01
This paper presents advanced computer simulation of rock cutting process typical for excavation works in civil engineering. Theoretical formulation of the hybrid discrete/finite element model has been presented. The discrete and finite element methods have been used in different subdomains of a rock sample according to expected material behaviour, the part which is fractured and damaged during cutting is discretized with the discrete elements while the other part is treated as a continuous body and it is modelled using the finite element method. In this way, an optimum model is created, enabling a proper representation of the physical phenomena during cutting and efficient numerical computation. The model has been applied to simulation of the laboratory test of rock cutting with a single TBM (tunnel boring machine) disc cutter. The micromechanical parameters have been determined using the dimensionless relationships between micro- and macroscopic parameters. A number of numerical simulations of the LCM test in the unrelieved and relieved cutting modes have been performed. Numerical results have been compared with available data from in-situ measurements in a real TBM as well as with the theoretical predictions showing quite a good agreement. The numerical model has provided a new insight into the cutting mechanism enabling us to investigate the stress and pressure distribution at the tool-rock interaction. Sensitivity analysis of rock cutting performed for different parameters including disc geometry, cutting velocity, disc penetration and spacing has shown that the presented numerical model is a suitable tool for the design and optimization of rock cutting process.
Discrete element modeling of cemented sand and particle crushing at high pressures
de Bono, John Patrick
2013-01-01
This project aims to provide an insight into the behaviour of cemented sand under high pressures, and to further the understanding of the role of particle crushing. The discrete element method is used to investigate the micro mechanics of sand and cemented sand in high-pressure triaxial tests and one-dimensional normal compression. Using the software PFC3D, a new triaxial model has been developed, which features an effective flexible membrane that allows free deformation of the specimen ...
A discrete element model for the investigation of the geometrically nonlinear behaviour of solids
Ockelmann, Felix; Dinkler, Dieter
2018-07-01
A three-dimensional discrete element model for elastic solids with large deformations is presented. Therefore, an discontinuum approach is made for solids. The properties of elastic material are transferred analytically into the parameters of a discrete element model. A new and improved octahedron gap-filled face-centred cubic close packing of spheres is split into unit cells, to determine the parameters of the discrete element model. The symmetrical unit cells allow a model with equal shear components in each contact plane and fully isotropic behaviour for Poisson's ratio above 0. To validate and show the broad field of applications of the new model, the pin-pin Euler elastica is presented and investigated. The thin and sensitive structure tends to undergo large deformations and rotations with a highly geometrically nonlinear behaviour. This behaviour of the elastica can be modelled and is compared to reference solutions. Afterwards, an improved more realistic simulation of the elastica is presented which softens secondary buckling phenomena. The model is capable of simulating solids with small strains but large deformations and a strongly geometrically nonlinear behaviour, taking the shear stiffness of the material into account correctly.
Spiral waves are stable in discrete element models of two-dimensional homogeneous excitable media
Feldman, A. B.; Chernyak, Y. B.; Cohen, R. J.
1998-01-01
The spontaneous breakup of a single spiral wave of excitation into a turbulent wave pattern has been observed in both discrete element models and continuous reaction-diffusion models of spatially homogeneous 2D excitable media. These results have attracted considerable interest, since spiral breakup is thought to be an important mechanism of transition from the heart rhythm disturbance ventricular tachycardia to the fatal arrhythmia ventricular fibrillation. It is not known whether this process can occur in the absence of disease-induced spatial heterogeneity of the electrical properties of the ventricular tissue. Candidate mechanisms for spiral breakup in uniform 2D media have emerged, but the physical validity of the mechanisms and their applicability to myocardium require further scrutiny. In this letter, we examine the computer simulation results obtained in two discrete element models and show that the instability of each spiral is an artifact resulting from an unphysical dependence of wave speed on wave front curvature in the medium. We conclude that spiral breakup does not occur in these two models at the specified parameter values and that great care must be exercised in the representation of a continuous excitable medium via discrete elements.
Energy Technology Data Exchange (ETDEWEB)
Bailey, T S; Adams, M L [Texas A M Univ., Dept. of Nuclear Engineering, College Station, TX (United States); Yang, B; Zika, M R [Lawrence Livermore National Lab., Livermore, CA (United States)
2005-07-01
We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses piecewise linear weight and basis functions in the finite element approximation, and it can be applied on arbitrary polygonal (2-dimensional) or polyhedral (3-dimensional) grids. We show that this new PWL method gives solutions comparable to those from Palmer's finite-volume method. However, since the PWL method produces a symmetric positive definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids. (authors)
The Effect of Loading Rate on Hydraulic Fracturing in Synthetic Granite - a Discrete Element Study
Tomac, I.; Gutierrez, M.
2015-12-01
Hydraulic fracture initiation and propagation from a borehole in hard synthetic rock is modeled using the two dimensional Discrete Element Method (DEM). DEM uses previously established procedure for modeling the strength and deformation parameters of quasi-brittle rocks with the Bonded Particle Model (Itasca, 2004). A series of simulations of laboratory tests on granite in DEM serve as a reference for synthetic rock behavior. Fracturing is enabled by breaking parallel bonds between DEM particles as a result of the local stress state. Subsequent bond breakage induces fracture propagation during a time-stepping procedure. Hydraulic fracturing occurs when pressurized fluid induces hoop stresses around the wellbore which cause rock fracturing and serves for geo-reservoir permeability enhancement in oil, gas and geothermal industries. In DEM, a network of fluid pipes and reservoirs is used for mathematical calculation of fluid flow through narrow channels between DEM particles, where the hydro-mechanical coupling is fully enabled. The fluid flow calculation is superimposed with DEM stress-strain calculation at each time step. As a result, the fluid pressures during borehole pressurization in hydraulic fracturing, as well as, during the fracture propagation from the borehole, can be simulated. The objective of this study is to investigate numerically a hypothesis that fluid pressurization rate, or the fluid flow rate, influences upon character, shape and velocity of fracture propagation in rock. The second objective is to better understand and define constraints which are important for successful fracture propagation in quasi-brittle rock from the perspective of flow rate, fluid density, viscosity and compressibility relative to the rock physical properties. Results from this study indicate that not only too high fluid flow rates cause fracture arrest and multiple fracture branching from the borehole, but also that the relative compressibility of fracturing fluid and
Comparisons between a high resolution discrete element model and analogue model
LI, C. S.; Yin, H.; WU, C.; Zhang, J.
2017-12-01
A two-dimensional discrete element model (DEM) with high resolution is constructed to simulate the evolution of thrust wedge and an analogue model (AM) experiment is constructed to compare with the DEM results. This efficient parallel DEM program is written in the C language, and it is useful to solve the complex geological problems. More detailed about fold and thrust belts of DEM can be identified with the help of strain field. With non-rotating and non-tensile assumption, dynamic evolution of DEM is highly consistent with AM. Simulations in different scale can compare with each other by conversion formulas in DEM. Our results show that: (1) The overall evolution of DEM and AM is broadly similar. (2) Shortening is accommodated by in-sequence forward propagation of thrusts. The surface slope of the thrust wedge is within the stable field predicted by critical taper theory. (3) Details of thrust spacing, dip angle and number of thrusts vary between DEM and AM for the shortening experiment, but the characteristics of thrusts are similar on the whole. (4) Dip angles of the forward thrusts increased from foreland (ca. 30°) to the mobile wall (ca. 80°) (5) With shortening, both models had not the obvious volume loss. Instead, the volume basic remained unchanged in the whole extrusion processes. (6) Almost all high strain values are within fold-and-thrust belts in DEM, which allows a direct comparison between the fault zone identified on the DEM deformation field and that in the strain field. (7) The first fault initiates at deep depths and propagate down toward the surface. For the maximal volumetric strain focused on the décollement near the mobile wall, strengthening the material and making it for brittle. (8) With non-tensile particles for DEM, contraction is broadly distributed throughout the model and dilation is hardly any, which also leads to a higher efficient computation. (9) High resolution DEM can to first order successfully reproduce structures observed
A parallel neural network training algorithm for control of discrete dynamical systems.
Energy Technology Data Exchange (ETDEWEB)
Gordillo, J. L.; Hanebutte, U. R.; Vitela, J. E.
1998-01-20
In this work we present a parallel neural network controller training code, that uses MPI, a portable message passing environment. A comprehensive performance analysis is reported which compares results of a performance model with actual measurements. The analysis is made for three different load assignment schemes: block distribution, strip mining and a sliding average bin packing (best-fit) algorithm. Such analysis is crucial since optimal load balance can not be achieved because the work load information is not available a priori. The speedup results obtained with the above schemes are compared with those corresponding to the bin packing load balance scheme with perfect load prediction based on a priori knowledge of the computing effort. Two multiprocessor platforms: a SGI/Cray Origin 2000 and a IBM SP have been utilized for this study. It is shown that for the best load balance scheme a parallel efficiency of over 50% for the entire computation is achieved by 17 processors of either parallel computers.
Parallel finite elements with domain decomposition and its pre-processing
International Nuclear Information System (INIS)
Yoshida, A.; Yagawa, G.; Hamada, S.
1993-01-01
This paper describes a parallel finite element analysis using a domain decomposition method, and the pre-processing for the parallel calculation. Computer simulations are about to replace experiments in various fields, and the scale of model to be simulated tends to be extremely large. On the other hand, computational environment has drastically changed in these years. Especially, parallel processing on massively parallel computers or computer networks is considered to be promising techniques. In order to achieve high efficiency on such parallel computation environment, large granularity of tasks, a well-balanced workload distribution are key issues. It is also important to reduce the cost of pre-processing in such parallel FEM. From the point of view, the authors developed the domain decomposition FEM with the automatic and dynamic task-allocation mechanism and the automatic mesh generation/domain subdivision system for it. (author)
Finite Volume Element (FVE) discretization and multilevel solution of the axisymmetric heat equation
Litaker, Eric T.
1994-12-01
The axisymmetric heat equation, resulting from a point-source of heat applied to a metal block, is solved numerically; both iterative and multilevel solutions are computed in order to compare the two processes. The continuum problem is discretized in two stages: finite differences are used to discretize the time derivatives, resulting is a fully implicit backward time-stepping scheme, and the Finite Volume Element (FVE) method is used to discretize the spatial derivatives. The application of the FVE method to a problem in cylindrical coordinates is new, and results in stencils which are analyzed extensively. Several iteration schemes are considered, including both Jacobi and Gauss-Seidel; a thorough analysis of these schemes is done, using both the spectral radii of the iteration matrices and local mode analysis. Using this discretization, a Gauss-Seidel relaxation scheme is used to solve the heat equation iteratively. A multilevel solution process is then constructed, including the development of intergrid transfer and coarse grid operators. Local mode analysis is performed on the components of the amplification matrix, resulting in the two-level convergence factors for various combinations of the operators. A multilevel solution process is implemented by using multigrid V-cycles; the iterative and multilevel results are compared and discussed in detail. The computational savings resulting from the multilevel process are then discussed.
Failure analysis of pebble bed reactors during earthquake by discrete element method
International Nuclear Information System (INIS)
Keppler, Istvan
2013-01-01
Highlights: ► We evaluated the load acting on the central reflector beam of a pebble bed reactor. ► The load acting on the reflector beam highly depends on fuel element distribution. ► The contact force values do not show high dependence on fuel element distribution. ► Earthquake increases the load of the reflector, not the contact forces. -- Abstract: Pebble bed reactors (PBR) are graphite-moderated, gas-cooled nuclear reactors. PBR reactors use a large number of spherical fuel elements called pebbles. From mechanical point of view, the arrangement of “small” spherical fuel elements in a container poses the same problem, as the so-called silo problem in powder technology and agricultural engineering. To get more exact information about the contact forces arising between the fuel elements in static and dynamic case, we simulated the static case and the effects of an earthquake on a model reactor by using discrete element method. We determined the maximal contact forces acting between the individual fuel elements. We found that the value of the maximal bending moment in the central reflector beam has a high deviation from the average value even in static case, and it can significantly increase in case of an earthquake. Our results can help the engineers working on the design of such types of reactors to get information about the contact forces, to determine the dust production and the crush probability of fuel elements within the reactor, and to model different accident scenarios
Failure analysis of pebble bed reactors during earthquake by discrete element method
Energy Technology Data Exchange (ETDEWEB)
Keppler, Istvan, E-mail: keppler.istvan@gek.szie.hu [Department of Mechanics and Engineering Design, Szent István University, Páter K.u.1., Gödöllő H-2103 (Hungary)
2013-05-15
Highlights: ► We evaluated the load acting on the central reflector beam of a pebble bed reactor. ► The load acting on the reflector beam highly depends on fuel element distribution. ► The contact force values do not show high dependence on fuel element distribution. ► Earthquake increases the load of the reflector, not the contact forces. -- Abstract: Pebble bed reactors (PBR) are graphite-moderated, gas-cooled nuclear reactors. PBR reactors use a large number of spherical fuel elements called pebbles. From mechanical point of view, the arrangement of “small” spherical fuel elements in a container poses the same problem, as the so-called silo problem in powder technology and agricultural engineering. To get more exact information about the contact forces arising between the fuel elements in static and dynamic case, we simulated the static case and the effects of an earthquake on a model reactor by using discrete element method. We determined the maximal contact forces acting between the individual fuel elements. We found that the value of the maximal bending moment in the central reflector beam has a high deviation from the average value even in static case, and it can significantly increase in case of an earthquake. Our results can help the engineers working on the design of such types of reactors to get information about the contact forces, to determine the dust production and the crush probability of fuel elements within the reactor, and to model different accident scenarios.
DEFF Research Database (Denmark)
Rasmussen, Marie-Louise Højlund; Stolpe, Mathias
2008-01-01
the physics, and the cuts (Combinatorial Benders’ and projected Chvátal–Gomory) come from an understanding of the particular mathematical structure of the reformulation. The impact of a stronger representation is investigated on several truss topology optimization problems in two and three dimensions.......The subject of this article is solving discrete truss topology optimization problems with local stress and displacement constraints to global optimum. We consider a formulation based on the Simultaneous ANalysis and Design (SAND) approach. This intrinsically non-convex problem is reformulated...
Li, Kenli; Zou, Shuting; Xv, Jin
2008-01-01
Elliptic curve cryptographic algorithms convert input data to unrecognizable encryption and the unrecognizable data back again into its original decrypted form. The security of this form of encryption hinges on the enormous difficulty that is required to solve the elliptic curve discrete logarithm problem (ECDLP), especially over GF(2(n)), n in Z+. This paper describes an effective method to find solutions to the ECDLP by means of a molecular computer. We propose that this research accomplishment would represent a breakthrough for applied biological computation and this paper demonstrates that in principle this is possible. Three DNA-based algorithms: a parallel adder, a parallel multiplier, and a parallel inverse over GF(2(n)) are described. The biological operation time of all of these algorithms is polynomial with respect to n. Considering this analysis, cryptography using a public key might be less secure. In this respect, a principal contribution of this paper is to provide enhanced evidence of the potential of molecular computing to tackle such ambitious computations.
Parallel Implementation and Scaling of an Adaptive Mesh Discrete Ordinates Algorithm for Transport
International Nuclear Information System (INIS)
Howell, L H
2004-01-01
Block-structured adaptive mesh refinement (AMR) uses a mesh structure built up out of locally-uniform rectangular grids. In the BoxLib parallel framework used by the Raptor code, each processor operates on one or more of these grids at each refinement level. The decomposition of the mesh into grids and the distribution of these grids among processors may change every few timesteps as a calculation proceeds. Finer grids use smaller timesteps than coarser grids, requiring additional work to keep the system synchronized and ensure conservation between different refinement levels. In a paper for NECDC 2002 I presented preliminary results on implementation of parallel transport sweeps on the AMR mesh, conjugate gradient acceleration, accuracy of the AMR solution, and scalar speedup of the AMR algorithm compared to a uniform fully-refined mesh. This paper continues with a more in-depth examination of the parallel scaling properties of the scheme, both in single-level and multi-level calculations. Both sweeping and setup costs are considered. The algorithm scales with acceptable performance to several hundred processors. Trends suggest, however, that this is the limit for efficient calculations with traditional transport sweeps, and that modifications to the sweep algorithm will be increasingly needed as job sizes in the thousands of processors become common
Energy Technology Data Exchange (ETDEWEB)
Bailey, Teresa S. [Texas A and M University, Department of Nuclear Engineering, College Station, TX 77843-3133 (United States)], E-mail: baileyte@tamu.edu; Adams, Marvin L. [Texas A and M University, Department of Nuclear Engineering, College Station, TX 77843-3133 (United States)], E-mail: mladams@tamu.edu; Yang, Brian [Lawrence Livermore National Laboratory, Livermore, CA 94551 (United States); Zika, Michael R. [Lawrence Livermore National Laboratory, Livermore, CA 94551 (United States)], E-mail: zika@llnl.gov
2008-04-01
We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses recently introduced piecewise linear weight and basis functions in the finite element approximation and it can be applied on arbitrary polygonal (2D) or polyhedral (3D) grids. We first demonstrate some analytical properties of the PWL method and perform a simple mode analysis to compare the PWL method with Palmer's vertex-centered finite-volume method and with a bilinear continuous finite element method. We then show that this new PWL method gives solutions comparable to those from Palmer's. However, since the PWL method produces a symmetric positive-definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids.
International Nuclear Information System (INIS)
Bailey, Teresa S.; Adams, Marvin L.; Yang, Brian; Zika, Michael R.
2008-01-01
We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses recently introduced piecewise linear weight and basis functions in the finite element approximation and it can be applied on arbitrary polygonal (2D) or polyhedral (3D) grids. We first demonstrate some analytical properties of the PWL method and perform a simple mode analysis to compare the PWL method with Palmer's vertex-centered finite-volume method and with a bilinear continuous finite element method. We then show that this new PWL method gives solutions comparable to those from Palmer's. However, since the PWL method produces a symmetric positive-definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids
Imole, Olukayode Isaiah; Kumar, Nishant; Magnanimo, Vanessa; Luding, Stefan
2012-01-01
We compare element test experiments and simulations on the deformation of frictional, cohesive particles in a bi-axial box. We show that computer simulations with the Discrete Element Method qualitatively reproduce a uniaxial compression element test in the true bi-axial tester. We highlight the
Analysis of Massively Parallel Discrete-Ordinates Transport Sweep Algorithms with Collisions
International Nuclear Information System (INIS)
Bailey, T.S.; Falgout, R.D.
2008-01-01
We present theoretical scaling models for a variety of discrete-ordinates sweep algorithms. In these models, we pay particular attention to the way each algorithm handles collisions. A collision is defined as a processor having multiple angles with ready to be swept during one stage of the sweep. The models also take into account how subdomains are assigned to processors and how angles are grouped during the sweep. We describe a data driven algorithm that resolves collisions efficiently during the sweep as well as other algorithms that have been designed to avoid collisions completely. Our models are validated using the ARGES and AMTRAN transport codes. We then use the models to study and predict scaling trends in all of the sweep algorithms
Vescovi, Dalila; Berzi, Diego; Richard, Patrick; Brodu, Nicolas
2014-01-01
International audience; We use existing 3D Discrete Element simulations of simple shear flows of spheres to evaluate the radial distribution function at contact that enables kinetic theory to correctly predict the pressure and the shear stress, for different values of the collisional coefficient of restitution. Then, we perform 3D Discrete Element simulations of plane flows of frictionless, inelastic spheres, sheared between walls made bumpy by gluing particles in a regular array, at fixed av...
Prediction of Fracture Behavior in Rock and Rock-like Materials Using Discrete Element Models
Katsaga, T.; Young, P.
2009-05-01
The study of fracture initiation and propagation in heterogeneous materials such as rock and rock-like materials are of principal interest in the field of rock mechanics and rock engineering. It is crucial to study and investigate failure prediction and safety measures in civil and mining structures. Our work offers a practical approach to predict fracture behaviour using discrete element models. In this approach, the microstructures of materials are presented through the combination of clusters of bonded particles with different inter-cluster particle and bond properties, and intra-cluster bond properties. The geometry of clusters is transferred from information available from thin sections, computed tomography (CT) images and other visual presentation of the modeled material using customized AutoCAD built-in dialog- based Visual Basic Application. Exact microstructures of the tested sample, including fractures, faults, inclusions and void spaces can be duplicated in the discrete element models. Although the microstructural fabrics of rocks and rock-like structures may have different scale, fracture formation and propagation through these materials are alike and will follow similar mechanics. Synthetic material provides an excellent condition for validating the modelling approaches, as fracture behaviours are known with the well-defined composite's properties. Calibration of the macro-properties of matrix material and inclusions (aggregates), were followed with the overall mechanical material responses calibration by adjusting the interfacial properties. The discrete element model predicted similar fracture propagation features and path as that of the real sample material. The path of the fractures and matrix-inclusion interaction was compared using computed tomography images. Initiation and fracture formation in the model and real material were compared using Acoustic Emission data. Analysing the temporal and spatial evolution of AE events, collected during the
Parallel eigenanalysis of finite element models in a completely connected architecture
Akl, F. A.; Morel, M. R.
1989-01-01
A parallel algorithm is presented for the solution of the generalized eigenproblem in linear elastic finite element analysis, (K)(phi) = (M)(phi)(omega), where (K) and (M) are of order N, and (omega) is order of q. The concurrent solution of the eigenproblem is based on the multifrontal/modified subspace method and is achieved in a completely connected parallel architecture in which each processor is allowed to communicate with all other processors. The algorithm was successfully implemented on a tightly coupled multiple-instruction multiple-data parallel processing machine, Cray X-MP. A finite element model is divided into m domains each of which is assumed to process n elements. Each domain is then assigned to a processor or to a logical processor (task) if the number of domains exceeds the number of physical processors. The macrotasking library routines are used in mapping each domain to a user task. Computational speed-up and efficiency are used to determine the effectiveness of the algorithm. The effect of the number of domains, the number of degrees-of-freedom located along the global fronts and the dimension of the subspace on the performance of the algorithm are investigated. A parallel finite element dynamic analysis program, p-feda, is documented and the performance of its subroutines in parallel environment is analyzed.
Analysis of gamma irradiator dose rate using spent fuel elements with parallel configuration
International Nuclear Information System (INIS)
Setiyanto; Pudjijanto MS; Ardani
2006-01-01
To enhance the utilization of the RSG-GAS reactor spent fuel, the gamma irradiator using spent fuel elements as a gamma source is a suitable choice. This irradiator can be used for food sterilization and preservation. The first step before realization, it is necessary to determine the gamma dose rate theoretically. The assessment was realized for parallel configuration fuel elements with the irradiation space can be placed between fuel element series. This analysis of parallel model was choice to compare with the circle model and as long as possible to get more space for irradiation and to do manipulation of irradiation target. Dose rate calculation were done with MCNP, while the estimation of gamma activities of fuel element was realized by OREGEN code with 1 year of average delay time. The calculation result show that the gamma dose rate of parallel model decreased up to 50% relatively compared with the circle model, but the value still enough for sterilization and preservation. Especially for food preservation, this parallel model give more flexible, while the gamma dose rate can be adjusted to the irradiation needed. The conclusion of this assessment showed that the utilization of reactor spent fuels for gamma irradiator with parallel model give more advantage the circle model. (author)
Discrete Element Method Modeling of the Rheological Properties of Coke/Pitch Mixtures
Majidi, Behzad; Taghavi, Seyed Mohammad; Fafard, Mario; Ziegler, Donald P.; Alamdari, Houshang
2016-01-01
Rheological properties of pitch and pitch/coke mixtures at temperatures around 150 °C are of great interest for the carbon anode manufacturing process in the aluminum industry. In the present work, a cohesive viscoelastic contact model based on Burger’s model is developed using the discrete element method (DEM) on the YADE, the open-source DEM software. A dynamic shear rheometer (DSR) is used to measure the viscoelastic properties of pitch at 150 °C. The experimental data obtained is then use...
Discrete Element Method Simulation of a Boulder Extraction From an Asteroid
Kulchitsky, Anton K.; Johnson, Jerome B.; Reeves, David M.; Wilkinson, Allen
2014-01-01
The force required to pull 7t and 40t polyhedral boulders from the surface of an asteroid is simulated using the discrete element method considering the effects of microgravity, regolith cohesion and boulder acceleration. The connection between particle surface energy and regolith cohesion is estimated by simulating a cohesion sample tearing test. An optimal constant acceleration is found where the peak net force from inertia and cohesion is a minimum. Peak pulling forces can be further reduced by using linear and quadratic acceleration functions with up to a 40% reduction in force for quadratic acceleration.
The compaction of a random distribution of metal cylinders by the discrete element method
DEFF Research Database (Denmark)
Redanz, Pia; Fleck, N. A.
2001-01-01
-linear springs. The initial packing of the particles is generated by the ballistic deposition method. Salient micromechanical features of closed die and isostatic powder compaction are elucidated for both frictionless and sticking contacts. It is found that substantial rearrangement of frictionless particles......The cold compaction of a 2D random distribution of metal circular cylinders has been investigated numerically by the discrete element method. Each cylindrical particle is located by a node at its centre and the plastic indentation of the contacts between neighbouring particles is represented by non...
A discrete-element model for viscoelastic deformation and fracture of glacial ice
Riikilä, T. I.; Tallinen, T.; Åström, J.; Timonen, J.
2015-10-01
A discrete-element model was developed to study the behavior of viscoelastic materials that are allowed to fracture. Applicable to many materials, the main objective of this analysis was to develop a model specifically for ice dynamics. A realistic model of glacial ice must include elasticity, brittle fracture and slow viscous deformations. Here the model is described in detail and tested with several benchmark simulations. The model was used to simulate various ice-specific applications with resulting flow rates that were compatible with Glen's law, and produced under fragmentation fragment-size distributions that agreed with the known analytical and experimental results.
Steinman, Jeffrey S. (Inventor)
1998-01-01
The present invention is embodied in a method of performing object-oriented simulation and a system having inter-connected processor nodes operating in parallel to simulate mutual interactions of a set of discrete simulation objects distributed among the nodes as a sequence of discrete events changing state variables of respective simulation objects so as to generate new event-defining messages addressed to respective ones of the nodes. The object-oriented simulation is performed at each one of the nodes by assigning passive self-contained simulation objects to each one of the nodes, responding to messages received at one node by generating corresponding active event objects having user-defined inherent capabilities and individual time stamps and corresponding to respective events affecting one of the passive self-contained simulation objects of the one node, restricting the respective passive self-contained simulation objects to only providing and receiving information from die respective active event objects, requesting information and changing variables within a passive self-contained simulation object by the active event object, and producing corresponding messages specifying events resulting therefrom by the active event objects.
A 2D Electromechanical Model of Human Atrial Tissue Using the Discrete Element Method
Directory of Open Access Journals (Sweden)
Paul Brocklehurst
2015-01-01
Full Text Available Cardiac tissue is a syncytium of coupled cells with pronounced intrinsic discrete nature. Previous models of cardiac electromechanics often ignore such discrete properties and treat cardiac tissue as a continuous medium, which has fundamental limitations. In the present study, we introduce a 2D electromechanical model for human atrial tissue based on the discrete element method (DEM. In the model, single-cell dynamics are governed by strongly coupling the electrophysiological model of Courtemanche et al. to the myofilament model of Rice et al. with two-way feedbacks. Each cell is treated as a viscoelastic body, which is physically represented by a clump of nine particles. Cell aggregations are arranged so that the anisotropic nature of cardiac tissue due to fibre orientations can be modelled. Each cell is electrically coupled to neighbouring cells, allowing excitation waves to propagate through the tissue. Cell-to-cell mechanical interactions are modelled using a linear contact bond model in DEM. By coupling cardiac electrophysiology with mechanics via the intracellular Ca2+ concentration, the DEM model successfully simulates the conduction of cardiac electrical waves and the tissue’s corresponding mechanical contractions. The developed DEM model is numerically stable and provides a powerful method for studying the electromechanical coupling problem in the heart.
Modeling a Million-Node Slim Fly Network Using Parallel Discrete-Event Simulation
Energy Technology Data Exchange (ETDEWEB)
Wolfe, Noah; Carothers, Christopher; Mubarak, Misbah; Ross, Robert; Carns, Philip
2016-05-15
As supercomputers close in on exascale performance, the increased number of processors and processing power translates to an increased demand on the underlying network interconnect. The Slim Fly network topology, a new lowdiameter and low-latency interconnection network, is gaining interest as one possible solution for next-generation supercomputing interconnect systems. In this paper, we present a high-fidelity Slim Fly it-level model leveraging the Rensselaer Optimistic Simulation System (ROSS) and Co-Design of Exascale Storage (CODES) frameworks. We validate our Slim Fly model with the Kathareios et al. Slim Fly model results provided at moderately sized network scales. We further scale the model size up to n unprecedented 1 million compute nodes; and through visualization of network simulation metrics such as link bandwidth, packet latency, and port occupancy, we get an insight into the network behavior at the million-node scale. We also show linear strong scaling of the Slim Fly model on an Intel cluster achieving a peak event rate of 36 million events per second using 128 MPI tasks to process 7 billion events. Detailed analysis of the underlying discrete-event simulation performance shows that a million-node Slim Fly model simulation can execute in 198 seconds on the Intel cluster.
Node-based finite element method for large-scale adaptive fluid analysis in parallel environments
Energy Technology Data Exchange (ETDEWEB)
Toshimitsu, Fujisawa [Tokyo Univ., Collaborative Research Center of Frontier Simulation Software for Industrial Science, Institute of Industrial Science (Japan); Genki, Yagawa [Tokyo Univ., Department of Quantum Engineering and Systems Science (Japan)
2003-07-01
In this paper, a FEM-based (finite element method) mesh free method with a probabilistic node generation technique is presented. In the proposed method, all computational procedures, from the mesh generation to the solution of a system of equations, can be performed fluently in parallel in terms of nodes. Local finite element mesh is generated robustly around each node, even for harsh boundary shapes such as cracks. The algorithm and the data structure of finite element calculation are based on nodes, and parallel computing is realized by dividing a system of equations by the row of the global coefficient matrix. In addition, the node-based finite element method is accompanied by a probabilistic node generation technique, which generates good-natured points for nodes of finite element mesh. Furthermore, the probabilistic node generation technique can be performed in parallel environments. As a numerical example of the proposed method, we perform a compressible flow simulation containing strong shocks. Numerical simulations with frequent mesh refinement, which are required for such kind of analysis, can effectively be performed on parallel processors by using the proposed method. (authors)
Node-based finite element method for large-scale adaptive fluid analysis in parallel environments
International Nuclear Information System (INIS)
Toshimitsu, Fujisawa; Genki, Yagawa
2003-01-01
In this paper, a FEM-based (finite element method) mesh free method with a probabilistic node generation technique is presented. In the proposed method, all computational procedures, from the mesh generation to the solution of a system of equations, can be performed fluently in parallel in terms of nodes. Local finite element mesh is generated robustly around each node, even for harsh boundary shapes such as cracks. The algorithm and the data structure of finite element calculation are based on nodes, and parallel computing is realized by dividing a system of equations by the row of the global coefficient matrix. In addition, the node-based finite element method is accompanied by a probabilistic node generation technique, which generates good-natured points for nodes of finite element mesh. Furthermore, the probabilistic node generation technique can be performed in parallel environments. As a numerical example of the proposed method, we perform a compressible flow simulation containing strong shocks. Numerical simulations with frequent mesh refinement, which are required for such kind of analysis, can effectively be performed on parallel processors by using the proposed method. (authors)
Takizawa, Kenji; Tezduyar, Tayfun E.; Otoguro, Yuto
2018-04-01
Stabilized methods, which have been very common in flow computations for many years, typically involve stabilization parameters, and discontinuity-capturing (DC) parameters if the method is supplemented with a DC term. Various well-performing stabilization and DC parameters have been introduced for stabilized space-time (ST) computational methods in the context of the advection-diffusion equation and the Navier-Stokes equations of incompressible and compressible flows. These parameters were all originally intended for finite element discretization but quite often used also for isogeometric discretization. The stabilization and DC parameters we present here for ST computations are in the context of the advection-diffusion equation and the Navier-Stokes equations of incompressible flows, target isogeometric discretization, and are also applicable to finite element discretization. The parameters are based on a direction-dependent element length expression. The expression is outcome of an easy to understand derivation. The key components of the derivation are mapping the direction vector from the physical ST element to the parent ST element, accounting for the discretization spacing along each of the parametric coordinates, and mapping what we have in the parent element back to the physical element. The test computations we present for pure-advection cases show that the parameters proposed result in good solution profiles.
Energy Technology Data Exchange (ETDEWEB)
Bailey, T.S.; Adams, M.L. [Texas A M Univ., Dept. of Nuclear Engineering, College Station, TX (United States); Yang, B.; Zika, M.R. [Lawrence Livermore National Lab., Livermore, CA (United States)
2005-07-01
We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses piecewise linear weight and basis functions in the finite element approximation, and it can be applied on arbitrary polygonal (2-dimensional) or polyhedral (3-dimensional) grids. We show that this new PWL method gives solutions comparable to those from Palmer's finite-volume method. However, since the PWL method produces a symmetric positive definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids. (authors)
Energy Technology Data Exchange (ETDEWEB)
Kim, S. [Purdue Univ., West Lafayette, IN (United States)
1994-12-31
Parallel iterative procedures based on domain decomposition techniques are defined and analyzed for the numerical solution of wave propagation by finite element and finite difference methods. For finite element methods, in a Lagrangian framework, an efficient way for choosing the algorithm parameter as well as the algorithm convergence are indicated. Some heuristic arguments for finding the algorithm parameter for finite difference schemes are addressed. Numerical results are presented to indicate the effectiveness of the methods.
Zohdi, T. I.
2016-03-01
In industry, particle-laden fluids, such as particle-functionalized inks, are constructed by adding fine-scale particles to a liquid solution, in order to achieve desired overall properties in both liquid and (cured) solid states. However, oftentimes undesirable particulate agglomerations arise due to some form of mutual-attraction stemming from near-field forces, stray electrostatic charges, process ionization and mechanical adhesion. For proper operation of industrial processes involving particle-laden fluids, it is important to carefully breakup and disperse these agglomerations. One approach is to target high-frequency acoustical pressure-pulses to breakup such agglomerations. The objective of this paper is to develop a computational model and corresponding solution algorithm to enable rapid simulation of the effect of acoustical pulses on an agglomeration composed of a collection of discrete particles. Because of the complex agglomeration microstructure, containing gaps and interfaces, this type of system is extremely difficult to mesh and simulate using continuum-based methods, such as the finite difference time domain or the finite element method. Accordingly, a computationally-amenable discrete element/discrete ray model is developed which captures the primary physical events in this process, such as the reflection and absorption of acoustical energy, and the induced forces on the particulate microstructure. The approach utilizes a staggered, iterative solution scheme to calculate the power transfer from the acoustical pulse to the particles and the subsequent changes (breakup) of the pulse due to the particles. Three-dimensional examples are provided to illustrate the approach.
Novel Discrete Element Method for 3D non-spherical granular particles.
Seelen, Luuk; Padding, Johan; Kuipers, Hans
2015-11-01
Granular materials are common in many industries and nature. The different properties from solid behavior to fluid like behavior are well known but less well understood. The main aim of our work is to develop a discrete element method (DEM) to simulate non-spherical granular particles. The non-spherical shape of particles is important, as it controls the behavior of the granular materials in many situations, such as static systems of packed particles. In such systems the packing fraction is determined by the particle shape. We developed a novel 3D discrete element method that simulates the particle-particle interactions for a wide variety of shapes. The model can simulate quadratic shapes such as spheres, ellipsoids, cylinders. More importantly, any convex polyhedron can be used as a granular particle shape. These polyhedrons are very well suited to represent non-rounded sand particles. The main difficulty of any non-spherical DEM is the determination of particle-particle overlap. Our model uses two iterative geometric algorithms to determine the overlap. The algorithms are robust and can also determine multiple contact points which can occur for these shapes. With this method we are able to study different applications such as the discharging of a hopper or silo. Another application the creation of a random close packing, to determine the solid volume fraction as a function of the particle shape.
Blocking Mechanism Study of Self-Compacting Concrete Based on Discrete Element Method
Zhang, Xuan; Li, Zhida; Zhang, Zhihua
2017-11-01
In order to study the influence factors of blocking mechanism of Self-Compaction Concrete (SCC), Roussel’s granular blocking model was verified and extended by establishing the discrete element model of SCC. The influence of different parameters on the filling capacity and blocking mechanism of SCC were also investigated. The results showed that: it was feasible to simulate the blocking mechanism of SCC by using Discrete Element Method (DEM). The passing ability of pebble aggregate was superior to the gravel aggregate and the passing ability of hexahedron particles was bigger than tetrahedron particles, while the tetrahedron particle simulation results were closer to the actual situation. The flow of SCC as another significant factor affected the passing ability that with the flow increased, the passing ability increased. The correction coefficient λ of the steel arrangement (channel section shape) and flow rate γ in the block model were introduced that the value of λ was 0.90-0.95 and the maximum casting rate was 7.8 L/min.
Analysis of a discrete element method and coupling with a compressible fluid flow method
International Nuclear Information System (INIS)
Monasse, L.
2011-01-01
This work aims at the numerical simulation of compressible fluid/deformable structure interactions. In particular, we have developed a partitioned coupling algorithm between a Finite Volume method for the compressible fluid and a Discrete Element method capable of taking into account fractures in the solid. A survey of existing fictitious domain methods and partitioned algorithms has led to choose an Embedded Boundary method and an explicit coupling scheme. We first showed that the Discrete Element method used for the solid yielded the correct macroscopic behaviour and that the symplectic time-integration scheme ensured the preservation of energy. We then developed an explicit coupling algorithm between a compressible inviscid fluid and an un-deformable solid. Mass, momentum and energy conservation and consistency properties were proved for the coupling scheme. The algorithm was then extended to the coupling with a deformable solid, in the form of a semi implicit scheme. Finally, we applied this method to unsteady inviscid flows around moving structures: comparisons with existing numerical and experimental results demonstrate the excellent accuracy of our method. (author) [fr
International Nuclear Information System (INIS)
Senapati, Rajeev; Zhang Jianmei
2010-01-01
Advanced ceramic materials have been extensively applied in aerospace, automobile and other industries. However, the reliability of the advanced ceramics is a major concern because of the brittle nature of the materials. In this paper, combination of nondestructive testing and numerical modeling Discrete Element Method is proposed to identify the fracture origin in ceramics. The nondestructive testing--laser scattering technology is first performed on the ceramic components to reveal the machining-induced damage such as cracks and the material-inherent flaws such as voids, then followed by the four point bending test. Discrete Element software package PFC 2D is used to simulate the four point bending test and try to identify where the fractures start. The numerical representation of the ceramic materials is done by generating a densely packed particle system using the specimen genesis procedure and then applying the suitable microparameters to the particle system. Simulation of four point bending test is performed on materials having no defects, materials having manufacturing-induced defects like cracks, and materials having material-inherent flaws like voids. The initiation and propagation of defects is modeled and the mean contact force on the loading ball is also plotted. The simulation prediction results are well in accordance with the nondestructive testing results.
Directory of Open Access Journals (Sweden)
Klejment Piotr
2018-01-01
Full Text Available Numerical analysis of cracking processes require an appropriate numerical technique. Classical engineering approach to the problem has its roots in the continuum mechanics and is based mainly on the Finite Element Method. This technique allows simulations of both elastic and large deformation processes, so it is very popular in the engineering applications. However, a final effect of cracking - fragmentation of an object at hand can hardly be described by this approach in a numerically efficient way since it requires a solution of a problem of nontrivial evolving in time boundary conditions. We focused our attention on the Discrete Element Method (DEM, which by definition implies “molecular” construction of the matter. The basic idea behind DEM is to represent an investigated body as an assemblage of discrete particles interacting with each other. Breaking interaction bonds between particles induced by external forces imeditelly implies creation/evolution of boundary conditions. In this study we used the DEM approach to simulate cracking process in the three dimensional solid material under external tension. The used numerical model, although higly simplified, can be used to describe behaviour of such materials like thin films, biological tissues, metal coatings, to name a few.
Discrete element method study of fuel relocation and dispersal during loss-of-coolant accidents
International Nuclear Information System (INIS)
Govers, K.; Verwerft, M.
2016-01-01
The fuel fragmentation, relocation and dispersal (FFRD) during LOCA transients today retain the attention of the nuclear safety community. The fine fragmentation observed at high burnup may, indeed, affect the Emergency Core Cooling System performance: accumulation of fuel debris in the cladding ballooned zone leads to a redistribution of the temperature profile, while dispersal of debris might lead to coolant blockage or to debris circulation through the primary circuit. This work presents a contribution, by discrete element method, towards a mechanistic description of the various stages of FFRD. The fuel fragments are described as a set of interacting particles, behaving as a granular medium. The model shows qualitative and quantitative agreement with experimental observations, such as the packing efficiency in the balloon, which is shown to stabilize at about 55%. The model is then applied to study fuel dispersal, for which experimental parametric studies are both difficult and expensive. - Highlights: • We performed Discrete Element Methods simulation for fuel relocation and dispersal during LOCA transients. • The approach provides a mechanistic description of these phenomena. • The approach shows the ability of the technique to reproduce experimental observations. • The packing fraction in the balloon is shown to stabilize at 50–60%.
Longoni, Gianluca
In the nuclear science and engineering field, radiation transport calculations play a key-role in the design and optimization of nuclear devices. The linear Boltzmann equation describes the angular, energy and spatial variations of the particle or radiation distribution. The discrete ordinates method (S N) is the most widely used technique for solving the linear Boltzmann equation. However, for realistic problems, the memory and computing time require the use of supercomputers. This research is devoted to the development of new formulations for the SN method, especially for highly angular dependent problems, in parallel environments. The present research work addresses two main issues affecting the accuracy and performance of SN transport theory methods: quadrature sets and acceleration techniques. New advanced quadrature techniques which allow for large numbers of angles with a capability for local angular refinement have been developed. These techniques have been integrated into the 3-D SN PENTRAN (Parallel Environment Neutral-particle TRANsport) code and applied to highly angular dependent problems, such as CT-Scan devices, that are widely used to obtain detailed 3-D images for industrial/medical applications. In addition, the accurate simulation of core physics and shielding problems with strong heterogeneities and transport effects requires the numerical solution of the transport equation. In general, the convergence rate of the solution methods for the transport equation is reduced for large problems with optically thick regions and scattering ratios approaching unity. To remedy this situation, new acceleration algorithms based on the Even-Parity Simplified SN (EP-SSN) method have been developed. A new stand-alone code system, PENSSn (Parallel Environment Neutral-particle Simplified SN), has been developed based on the EP-SSN method. The code is designed for parallel computing environments with spatial, angular and hybrid (spatial/angular) domain
Application of parallel connected power-MOSFET elements to high current d.c. power supply
International Nuclear Information System (INIS)
Matsukawa, Tatsuya; Shioyama, Masanori; Shimada, Katsuhiro; Takaku, Taku; Neumeyer, Charles; Tsuji-Iio, Shunji; Shimada, Ryuichi
2001-01-01
The low aspect ratio spherical torus (ST), which has single turn toroidal field coil, requires the extremely high d.c. current like as 20 MA to energize the coil. Considering the ratings of such extremely high current and low voltage, power-MOSFET element is employed as the switching device for the a.c./d.c. converter of power supply. One of the advantages of power-MOSFET element is low on-state resistance, which is to meet the high current and low voltage operation. Recently, the capacity of power-MOSFET element has been increased and its on-state resistance has been decreased, so that the possibility of construction of high current and low voltage a.c./d.c. converter with parallel connected power-MOSFET elements has been growing. With the aim of developing the high current d.c. power supply using power-MOSFET, the basic characteristics of parallel operation with power-MOSFET elements are experimentally investigated. And, the synchronous rectifier type and the bi-directional self commutated type a.c./d.c. converters using parallel connected power-MOSFET elements are proposed
Eigensolution of finite element problems in a completely connected parallel architecture
Akl, Fred A.; Morel, Michael R.
1989-01-01
A parallel algorithm for the solution of the generalized eigenproblem in linear elastic finite element analysis, (K)(phi)=(M)(phi)(omega), where (K) and (M) are of order N, and (omega) is of order q is presented. The parallel algorithm is based on a completely connected parallel architecture in which each processor is allowed to communicate with all other processors. The algorithm has been successfully implemented on a tightly coupled multiple-instruction-multiple-data (MIMD) parallel processing computer, Cray X-MP. A finite element model is divided into m domains each of which is assumed to process n elements. Each domain is then assigned to a processor, or to a logical processor (task) if the number of domains exceeds the number of physical processors. The macro-tasking library routines are used in mapping each domain to a user task. Computational speed-up and efficiency are used to determine the effectiveness of the algorithm. The effect of the number of domains, the number of degrees-of-freedom located along the global fronts and the dimension of the subspace on the performance of the algorithm are investigated. For a 64-element rectangular plate, speed-ups of 1.86, 3.13, 3.18 and 3.61 are achieved on two, four, six and eight processors, respectively.
International Nuclear Information System (INIS)
Tsuji, Masashi; Chiba, Gou
2000-01-01
A hierarchical domain decomposition boundary element method (HDD-BEM) for solving the multiregion neutron diffusion equation (NDE) has been fully parallelized, both for numerical computations and for data communications, to accomplish a high parallel efficiency on distributed memory message passing parallel computers. Data exchanges between node processors that are repeated during iteration processes of HDD-BEM are implemented, without any intervention of the host processor that was used to supervise parallel processing in the conventional parallelized HDD-BEM (P-HDD-BEM). Thus, the parallel processing can be executed with only cooperative operations of node processors. The communication overhead was even the dominant time consuming part in the conventional P-HDD-BEM, and the parallelization efficiency decreased steeply with the increase of the number of processors. With the parallel data communication, the efficiency is affected only by the number of boundary elements assigned to decomposed subregions, and the communication overhead can be drastically reduced. This feature can be particularly advantageous in the analysis of three-dimensional problems where a large number of processors are required. The proposed P-HDD-BEM offers a promising solution to the deterioration problem of parallel efficiency and opens a new path to parallel computations of NDEs on distributed memory message passing parallel computers. (author)
Discrete Element Modeling Results of Proppant Rearrangement in the Cooke Conductivity Cell
Energy Technology Data Exchange (ETDEWEB)
Earl Mattson; Hai Huang; Michael Conway; Lisa O' Connell
2014-02-01
The study of propped fracture conductivity began in earnest with the development of the Cooke cell which later became part of the initial API standard. Subsequent developments included a patented multicell design to conduct 4 tests in a press at the same time. Other modifications have been used by various investigators. Recent studies by the Stim-Lab proppant consortium have indicated that the flow field across a Cooke proppant conductivity testing cell may not be uniform as initially believed which resulted is significantly different conductivity results. Post test analysis of low temperature metal alloy injections at the termination of proppant testing prior to the release of the applied stress suggest that higher flow is to be expected along the sides and top of the proppant pack than compared to the middle of the pack. To evaluate these experimental findings, a physics-based two-dimensional (2-D) discrete element model (DEM) was developed and applied to simulate proppant rearrangement during stress loading in the Cooke conductivity cell and the resulting porosity field. Analysis of these simulations are critical to understanding the impact of modification to the testing cell as well as understanding key proppant conductivity issues such as how these effects are manifested in proppant concentration testing results. The 2-D DEM model was constructed to represent a realistic cross section of the Cooke cell with a distribution of four material properties, three that represented the Cooke cell (steel, sandstone,square rings), and one representing the proppant. In principle, Cooke cell materials can be approximated as assemblies of independent discrete elements (particles) of various sizes and material properties that interact via cohesive interactions, repulsive forces, and frictional forces. The macroscopic behavior can then be modeled as the collective behavior of many interacting discrete elements. This DEM model is particularly suitable for modeling proppant
Energy Technology Data Exchange (ETDEWEB)
Alleon, G. [EADS-CCR, 31 - Blagnac (France); Carpentieri, B.; Du, I.S.; Giraud, L.; Langou, J.; Martin, E. [Cerfacs, 31 - Toulouse (France)
2003-07-01
The boundary element method has become a popular tool for the solution of Maxwell's equations in electromagnetism. It discretizes only the surface of the radiating object and gives rise to linear systems that are smaller in size compared to those arising from finite element or finite difference discretizations. However, these systems are prohibitively demanding in terms of memory for direct methods and challenging to solve by iterative methods. In this paper we address the iterative solution via preconditioned Krylov methods of electromagnetic scattering problems expressed in an integral formulation, with main focus on the design of the pre-conditioner. We consider an approximate inverse method based on the Frobenius-norm minimization with a pattern prescribed in advance. The pre-conditioner is constructed from a sparse approximation of the dense coefficient matrix, and the patterns both for the pre-conditioner and for the coefficient matrix are computed a priori using geometric information from the mesh. We describe the implementation of the approximate inverse in an out-of-core parallel code that uses multipole techniques for the matrix-vector products, and show results on the numerical scalability of our method on systems of size up to one million unknowns. We propose an embedded iterative scheme based on the GMRES method and combined with multipole techniques, aimed at improving the robustness of the approximate inverse for large problems. We prove by numerical experiments that the proposed scheme enables the solution of very large and difficult problems efficiently at reduced computational and memory cost. Finally we perform a preliminary study on a spectral two-level pre-conditioner to enhance the robustness of our method. This numerical technique exploits spectral information of the preconditioned systems to build a low rank-update of the pre-conditioner. (authors)
International Nuclear Information System (INIS)
Alleon, G.; Carpentieri, B.; Du, I.S.; Giraud, L.; Langou, J.; Martin, E.
2003-01-01
The boundary element method has become a popular tool for the solution of Maxwell's equations in electromagnetism. It discretizes only the surface of the radiating object and gives rise to linear systems that are smaller in size compared to those arising from finite element or finite difference discretizations. However, these systems are prohibitively demanding in terms of memory for direct methods and challenging to solve by iterative methods. In this paper we address the iterative solution via preconditioned Krylov methods of electromagnetic scattering problems expressed in an integral formulation, with main focus on the design of the pre-conditioner. We consider an approximate inverse method based on the Frobenius-norm minimization with a pattern prescribed in advance. The pre-conditioner is constructed from a sparse approximation of the dense coefficient matrix, and the patterns both for the pre-conditioner and for the coefficient matrix are computed a priori using geometric information from the mesh. We describe the implementation of the approximate inverse in an out-of-core parallel code that uses multipole techniques for the matrix-vector products, and show results on the numerical scalability of our method on systems of size up to one million unknowns. We propose an embedded iterative scheme based on the GMRES method and combined with multipole techniques, aimed at improving the robustness of the approximate inverse for large problems. We prove by numerical experiments that the proposed scheme enables the solution of very large and difficult problems efficiently at reduced computational and memory cost. Finally we perform a preliminary study on a spectral two-level pre-conditioner to enhance the robustness of our method. This numerical technique exploits spectral information of the preconditioned systems to build a low rank-update of the pre-conditioner. (authors)
Large-Scale Parallel Finite Element Analysis of the Stress Singular Problems
International Nuclear Information System (INIS)
Noriyuki Kushida; Hiroshi Okuda; Genki Yagawa
2002-01-01
In this paper, the convergence behavior of large-scale parallel finite element method for the stress singular problems was investigated. The convergence behavior of iterative solvers depends on the efficiency of the pre-conditioners. However, efficiency of pre-conditioners may be influenced by the domain decomposition that is necessary for parallel FEM. In this study the following results were obtained: Conjugate gradient method without preconditioning and the diagonal scaling preconditioned conjugate gradient method were not influenced by the domain decomposition as expected. symmetric successive over relaxation method preconditioned conjugate gradient method converged 6% faster as maximum if the stress singular area was contained in one sub-domain. (authors)
Parallel Object-Oriented Computation Applied to a Finite Element Problem
Directory of Open Access Journals (Sweden)
Jon B. Weissman
1993-01-01
Full Text Available The conventional wisdom in the scientific computing community is that the best way to solve large-scale numerically intensive scientific problems on today's parallel MIMD computers is to use Fortran or C programmed in a data-parallel style using low-level message-passing primitives. This approach inevitably leads to nonportable codes and extensive development time, and restricts parallel programming to the domain of the expert programmer. We believe that these problems are not inherent to parallel computing but are the result of the programming tools used. We will show that comparable performance can be achieved with little effort if better tools that present higher level abstractions are used. The vehicle for our demonstration is a 2D electromagnetic finite element scattering code we have implemented in Mentat, an object-oriented parallel processing system. We briefly describe the application. Mentat, the implementation, and present performance results for both a Mentat and a hand-coded parallel Fortran version.
Morfa, Carlos Recarey; Cortés, Lucía Argüelles; Farias, Márcio Muniz de; Morales, Irvin Pablo Pérez; Valera, Roberto Roselló; Oñate, Eugenio
2018-07-01
A methodology that comprises several characterization properties for particle packings is proposed in this paper. The methodology takes into account factors such as dimension and shape of particles, space occupation, homogeneity, connectivity and isotropy, among others. This classification and integration of several properties allows to carry out a characterization process to systemically evaluate the particle packings in order to guarantee the quality of the initial meshes in discrete element simulations, in both the micro- and the macroscales. Several new properties were created, and improvements in existing ones are presented. Properties from other disciplines were adapted to be used in the evaluation of particle systems. The methodology allows to easily characterize media at the level of the microscale (continuous geometries—steels, rocks microstructures, etc., and discrete geometries) and the macroscale. A global, systemic and integral system for characterizing and evaluating particle sets, based on fuzzy logic, is presented. Such system allows researchers to have a unique evaluation criterion based on the aim of their research. Examples of applications are shown.
Cyclic loading tests on ceramic breeder pebble bed by discrete element modeling
Energy Technology Data Exchange (ETDEWEB)
Zhang, Hao [School of Nuclear Science and Technology, University of Science and Technology of China, Hefei 230027 (China); Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics, Mianyang 621900 (China); Guo, Haibing; Shi, Tao [Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics, Mianyang 621900 (China); Ye, Minyou [School of Nuclear Science and Technology, University of Science and Technology of China, Hefei 230027 (China); Huang, Hongwen, E-mail: hhw@caep.cn [Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics, Mianyang 621900 (China); Li, Zhenghong, E-mail: inpcnyb@sina.com [Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics, Mianyang 621900 (China); University of Science and Technology of China, Hefei 230027 (China)
2017-05-15
Highlights: • Methods of cyclic loading tests on the pebble beds were developed in DEM. • Size distribution and sphericity of the pebbles were considered for the specimen. • Mechanical responses of the pebble beds under cyclic loading tests were assessed. - Abstract: Complex mechanics and packing instability can be induced by loading operation on ceramic breeder pebble bed for its discrete nature. A numerical approach using discrete element method (DEM) is applied to study the mechanical performance of the ceramic breeder pebble bed under quasi-static and cyclic loads. A preloaded specimen can be made with servo-control mechanism, the quasi-static and dynamic stress-strain performances are studied during the tests. It is found that the normalized normal contact forces under quasi-static loads have the similar distributions, and increase with increasing loads. Furthermore, the relatively low volumetric strain can be absorbed by pebble bed after several loading and unloading cycles, but the peak normal contact force can be extremely high during the first cycle. Cyclic loading with target pressure is recommended for densely packing, irreversible volume reduction gradually increase with cycles, and the normal contact forces decrease with cycles.
Morfa, Carlos Recarey; Cortés, Lucía Argüelles; Farias, Márcio Muniz de; Morales, Irvin Pablo Pérez; Valera, Roberto Roselló; Oñate, Eugenio
2017-10-01
A methodology that comprises several characterization properties for particle packings is proposed in this paper. The methodology takes into account factors such as dimension and shape of particles, space occupation, homogeneity, connectivity and isotropy, among others. This classification and integration of several properties allows to carry out a characterization process to systemically evaluate the particle packings in order to guarantee the quality of the initial meshes in discrete element simulations, in both the micro- and the macroscales. Several new properties were created, and improvements in existing ones are presented. Properties from other disciplines were adapted to be used in the evaluation of particle systems. The methodology allows to easily characterize media at the level of the microscale (continuous geometries—steels, rocks microstructures, etc., and discrete geometries) and the macroscale. A global, systemic and integral system for characterizing and evaluating particle sets, based on fuzzy logic, is presented. Such system allows researchers to have a unique evaluation criterion based on the aim of their research. Examples of applications are shown.
Cyclic loading tests on ceramic breeder pebble bed by discrete element modeling
International Nuclear Information System (INIS)
Zhang, Hao; Guo, Haibing; Shi, Tao; Ye, Minyou; Huang, Hongwen; Li, Zhenghong
2017-01-01
Highlights: • Methods of cyclic loading tests on the pebble beds were developed in DEM. • Size distribution and sphericity of the pebbles were considered for the specimen. • Mechanical responses of the pebble beds under cyclic loading tests were assessed. - Abstract: Complex mechanics and packing instability can be induced by loading operation on ceramic breeder pebble bed for its discrete nature. A numerical approach using discrete element method (DEM) is applied to study the mechanical performance of the ceramic breeder pebble bed under quasi-static and cyclic loads. A preloaded specimen can be made with servo-control mechanism, the quasi-static and dynamic stress-strain performances are studied during the tests. It is found that the normalized normal contact forces under quasi-static loads have the similar distributions, and increase with increasing loads. Furthermore, the relatively low volumetric strain can be absorbed by pebble bed after several loading and unloading cycles, but the peak normal contact force can be extremely high during the first cycle. Cyclic loading with target pressure is recommended for densely packing, irreversible volume reduction gradually increase with cycles, and the normal contact forces decrease with cycles.
Papagiannis, P.; Azariadis, P.; Papanikos, P.
2017-10-01
Footwear is subject to bending and torsion deformations that affect comfort perception. Following review of Finite Element Analysis studies of sole rigidity and comfort, a three-dimensional, linear multi-material finite element sole model for quasi-static bending and torsion simulation, overcoming boundary and optimisation limitations, is described. Common footwear materials properties and boundary conditions from gait biomechanics are used. The use of normalised strain energy for product benchmarking is demonstrated along with comfort level determination through strain energy density stratification. Sensitivity of strain energy against material thickness is greater for bending than for torsion, with results of both deformations showing positive correlation. Optimization for a targeted performance level and given layer thickness is demonstrated with bending simulations sufficing for overall comfort assessment. An algorithm for comfort optimization w.r.t. bending is presented, based on a discrete approach with thickness values set in line with practical manufacturing accuracy. This work illustrates the potential of the developed finite element analysis applications to offer viable and proven aids to modern footwear sole design assessment and optimization.
Energy Technology Data Exchange (ETDEWEB)
Spellings, Matthew [Chemical Engineering, University of Michigan, 2800 Plymouth Rd., Ann Arbor, MI 48109 (United States); Biointerfaces Institute, University of Michigan, 2800 Plymouth Rd., Ann Arbor, MI 48109 (United States); Marson, Ryan L. [Materials Science & Engineering, University of Michigan, 2300 Hayward St., Ann Arbor, MI 48109 (United States); Biointerfaces Institute, University of Michigan, 2800 Plymouth Rd., Ann Arbor, MI 48109 (United States); Anderson, Joshua A. [Chemical Engineering, University of Michigan, 2800 Plymouth Rd., Ann Arbor, MI 48109 (United States); Biointerfaces Institute, University of Michigan, 2800 Plymouth Rd., Ann Arbor, MI 48109 (United States); Glotzer, Sharon C., E-mail: sglotzer@umich.edu [Chemical Engineering, University of Michigan, 2800 Plymouth Rd., Ann Arbor, MI 48109 (United States); Materials Science & Engineering, University of Michigan, 2300 Hayward St., Ann Arbor, MI 48109 (United States); Biointerfaces Institute, University of Michigan, 2800 Plymouth Rd., Ann Arbor, MI 48109 (United States)
2017-04-01
Faceted shapes, such as polyhedra, are commonly found in systems of nanoscale, colloidal, and granular particles. Many interesting physical phenomena, like crystal nucleation and growth, vacancy motion, and glassy dynamics are challenging to model in these systems because they require detailed dynamical information at the individual particle level. Within the granular materials community the Discrete Element Method has been used extensively to model systems of anisotropic particles under gravity, with friction. We provide an implementation of this method intended for simulation of hard, faceted nanoparticles, with a conservative Weeks–Chandler–Andersen (WCA) interparticle potential, coupled to a thermodynamic ensemble. This method is a natural extension of classical molecular dynamics and enables rigorous thermodynamic calculations for faceted particles.
Discrete Element Method for Modeling the Mechanical Behavior of Unsaturated Granular Material
Directory of Open Access Journals (Sweden)
K. Tourani
2016-09-01
Full Text Available Although a significant portion of conditions encountered in geotechnical engineering, for investigating engineering behavior of soil, involves unsaturated soils; the traditional analysis and design approach has been to assume the limiting conditions of soils being either completely dry or completely saturated. In unsaturated soils the capillary force produce attractive forces between particles. Discrete Element Method (DEM is an appropriate tool to consider the capillary effects. The calculations performed in DEM is based on iterative application of Newton’s second law to the particles and force-displacement law at the contacts. In the present study, the behavior of unsaturated soils in pendular regime is simulated utilizing DEM. Triaxial compression tests were modeled as two-dimensional, considering capillary force effects. Finally, capillary effects on Macro parameters of a simulated granular soil (stress, axial strain, volumetric strain and void ratio and Mohr Coulomb failure criteria parameters were studied.
Discrete Element Simulation of Elastoplastic Shock Wave Propagation in Spherical Particles
Directory of Open Access Journals (Sweden)
M. Shoaib
2011-01-01
Full Text Available Elastoplastic shock wave propagation in a one-dimensional assembly of spherical metal particles is presented by extending well-established quasistatic compaction models. The compaction process is modeled by a discrete element method while using elastic and plastic loading, elastic unloading, and adhesion at contacts with typical dynamic loading parameters. Of particular interest is to study the development of the elastoplastic shock wave, its propagation, and reflection during entire loading process. Simulation results yield information on contact behavior, velocity, and deformation of particles during dynamic loading. Effects of shock wave propagation on loading parameters are also discussed. The elastoplastic shock propagation in granular material has many practical applications including the high-velocity compaction of particulate material.
Application of discrete element method to study mechanical behaviors of ceramic breeder pebble beds
International Nuclear Information System (INIS)
An Zhiyong; Ying, Alice; Abdou, Mohamed
2007-01-01
In this paper, the discrete element method (DEM) approach has been applied to study mechanical behaviors of ceramic breeder pebble beds. Directly simulating the contact state of each individual particle by the physically based interaction laws, the DEM numerical program is capable of predicting the mechanical behaviors of non-standard packing structures. The program can also provide the data to trace the evolution of contact characteristics and forces as deformation proceeds, as well as the particle movement when the pebble bed is subjected to external loadings. Our numerical simulations focus on predicting the mechanical behaviors of ceramic breeder pebble beds, which include typical fusion breeder materials in solid breeder blankets. Current numerical results clearly show that the packing density and the bed geometry can have an impact on the mechanical stiffness of the pebble beds. Statistical data show that the contact forces are highly related to the contact status of the pebbles
A discrete element model for damage and fracture of geomaterials under fatigue loading
Gao, Xiaofeng; Koval, Georg; Chazallon, Cyrille
2017-06-01
Failure processes in geomaterials (concrete, asphalt concrete, masonry, etc.) under fatigue loading (repeated moving loads, cycles of temperature, etc.) are responsible for most of the dysfunctions in pavements, brick structures, etc. In the beginning of the lifetime of a structure, the material presents only inner defects (micro cracks, voids, etc.). Due to the effect of the cyclic loading, these small defects tend to grow in size and quantity which damage the material, reducing its stiffness. With a relatively high number of cycles, these growing micro cracks become large cracks, which characterizes the fracture behavior. From a theoretical point of view, both mechanisms are treated differently. Fracture is usually described locally, with the propagation of cracks defined by the energy release rate at the crack tip; damage is usually associated to non-local approaches. In the present work, damage and fracture mechanics are combined in a local discrete element approach.
Directory of Open Access Journals (Sweden)
André Damien
2017-01-01
Full Text Available At the macroscopic scale, such media as rocks or ceramics can be seen as homogeneous continuum. However, at the microscopic scale these materials involve sophisticated micro-structures that mix several phases. Generally, these micro-structures are composed by a large amount of inclusions embedded in a brittle matrix that ensures the cohesion of the structure. These materials generally exhibit complex non linear mechanical behaviors that result from the interactions between the different phases. This paper proposes to study the impact of the diffuse damages that result from the thermal expansion mismatch between the phases in presence. The Discrete Element Method (DEM that naturally take into account discontinuities is proposed to study these phenomena.
Discrete element method study of fuel relocation and dispersal during loss-of-coolant accidents
Govers, K.; Verwerft, M.
2016-09-01
The fuel fragmentation, relocation and dispersal (FFRD) during LOCA transients today retain the attention of the nuclear safety community. The fine fragmentation observed at high burnup may, indeed, affect the Emergency Core Cooling System performance: accumulation of fuel debris in the cladding ballooned zone leads to a redistribution of the temperature profile, while dispersal of debris might lead to coolant blockage or to debris circulation through the primary circuit. This work presents a contribution, by discrete element method, towards a mechanistic description of the various stages of FFRD. The fuel fragments are described as a set of interacting particles, behaving as a granular medium. The model shows qualitative and quantitative agreement with experimental observations, such as the packing efficiency in the balloon, which is shown to stabilize at about 55%. The model is then applied to study fuel dispersal, for which experimental parametric studies are both difficult and expensive.
Memon, Shahbaz; Vallot, Dorothée; Zwinger, Thomas; Neukirchen, Helmut
2017-04-01
Scientific communities generate complex simulations through orchestration of semi-structured analysis pipelines which involves execution of large workflows on multiple, distributed and heterogeneous computing and data resources. Modeling ice dynamics of glaciers requires workflows consisting of many non-trivial, computationally expensive processing tasks which are coupled to each other. From this domain, we present an e-Science use case, a workflow, which requires the execution of a continuum ice flow model and a discrete element based calving model in an iterative manner. Apart from the execution, this workflow also contains data format conversion tasks that support the execution of ice flow and calving by means of transition through sequential, nested and iterative steps. Thus, the management and monitoring of all the processing tasks including data management and transfer of the workflow model becomes more complex. From the implementation perspective, this workflow model was initially developed on a set of scripts using static data input and output references. In the course of application usage when more scripts or modifications introduced as per user requirements, the debugging and validation of results were more cumbersome to achieve. To address these problems, we identified a need to have a high-level scientific workflow tool through which all the above mentioned processes can be achieved in an efficient and usable manner. We decided to make use of the e-Science middleware UNICORE (Uniform Interface to Computing Resources) that allows seamless and automated access to different heterogenous and distributed resources which is supported by a scientific workflow engine. Based on this, we developed a high-level scientific workflow model for coupling of massively parallel High-Performance Computing (HPC) jobs: a continuum ice sheet model (Elmer/Ice) and a discrete element calving and crevassing model (HiDEM). In our talk we present how the use of a high
International Nuclear Information System (INIS)
Coulomb, F.
1989-06-01
The aim of this work is to study methods for solving the diffusion equation, based on a primal or mixed-dual finite elements discretization and well suited for use on multiprocessors computers; domain decomposition methods are the subject of the main part of this study, the linear systems being solved by the block-Jacobi method. The origin of the diffusion equation is explained in short, and various variational formulations are reminded. A survey of iterative methods is given. The elemination of the flux or current is treated in the case of a mixed method. Numerical tests are performed on two examples of reactors, in order to compare mixed elements and Lagrange elements. A theoretical study of domain decomposition is led in the case of Lagrange finite elements, and convergence conditions for the block-Jacobi method are derived; the dissection decomposition is previously the purpose of a particular numerical analysis. In the case of mixed-dual finite elements, a study is led on examples and is confirmed by numerical tests performed for the dissection decomposition; furthermore, after being justified, decompositions along axes of symmetry are numerically tested. In the case of a decomposition into two subdomains, the dissection decomposition and the decomposition with an integrated interface are compared. Alternative directions methods are defined; the convergence of those relative to Lagrange elements is shown; in the case of mixed elements, convergence conditions are found [fr
Directory of Open Access Journals (Sweden)
Z. M. Jaini
Full Text Available Abstract Numerical modeling of fracture failure is challenging due to various issues in the constitutive law and the transition of continuum to discrete bodies. Therefore, this study presents the application of the combined finite-discrete element method to investigate the fracture failure of reinforced concrete slabs subjected to blast loading. In numerical modeling, the interaction of non-uniform blast loading on the concrete slab was modeled using the incorporation of the finite element method with a crack rotating approach and the discrete element method to model crack, fracture onset and its post-failures. A time varying pressure-time history based on the mapping method was adopted to define blast loading. The Mohr-Coulomb with Rankine cut-off and von-Mises criteria were applied for concrete and steel reinforcement respectively. The results of scabbing, spalling and fracture show a reliable prediction of damage and fracture.
Computational Performance of a Parallelized Three-Dimensional High-Order Spectral Element Toolbox
Bosshard, Christoph; Bouffanais, Roland; Clémençon, Christian; Deville, Michel O.; Fiétier, Nicolas; Gruber, Ralf; Kehtari, Sohrab; Keller, Vincent; Latt, Jonas
In this paper, a comprehensive performance review of an MPI-based high-order three-dimensional spectral element method C++ toolbox is presented. The focus is put on the performance evaluation of several aspects with a particular emphasis on the parallel efficiency. The performance evaluation is analyzed with help of a time prediction model based on a parameterization of the application and the hardware resources. A tailor-made CFD computation benchmark case is introduced and used to carry out this review, stressing the particular interest for clusters with up to 8192 cores. Some problems in the parallel implementation have been detected and corrected. The theoretical complexities with respect to the number of elements, to the polynomial degree, and to communication needs are correctly reproduced. It is concluded that this type of code has a nearly perfect speed up on machines with thousands of cores, and is ready to make the step to next-generation petaflop machines.
International Nuclear Information System (INIS)
Calio, I.; Cannizzaro, F.; Marletta, M.; Panto, B.; D'Amore, E.
2008-01-01
In the present study a new discrete-element approach for the evaluation of the seismic resistance of composite reinforced concrete-masonry structures is presented. In the proposed model, unreinforced masonry panels are modelled by means of two-dimensional discrete-elements, conceived by the authors for modelling masonry structures, whereas the reinforced concrete elements are modelled by lumped plasticity elements interacting with the masonry panels through nonlinear interface elements. The proposed procedure was adopted for the assessment of the seismic response of a case study confined-masonry building which was conceived to be a typical representative of a wide class of residential buildings designed to the requirements of the 1909 issue of the Italian seismic code and widely adopted in the aftermath of the 1908 earthquake for the reconstruction of the cities of Messina and Reggio Calabria
3D Discrete element approach to the problem on abutment pressure in a gently dipping coal seam
Klishin, S. V.; Revuzhenko, A. F.
2017-09-01
Using the discrete element method, the authors have carried out 3D implementation of the problem on strength loss in surrounding rock mass in the vicinity of a production heading and on abutment pressure in a gently dripping coal seam. The calculation of forces at the contacts between particles accounts for friction, rolling resistance and viscosity. Between discrete particles modeling coal seam, surrounding rock mass and broken rocks, an elastic connecting element is introduced to allow simulating coherent materials. The paper presents the kinematic patterns of rock mass deformation, stresses in particles and the graph of the abutment pressure behavior in the coal seam.
Parallel and pipelined front-end for multi-element silicon detectors in scanning electron microscopy
International Nuclear Information System (INIS)
Boulin, C.; Epstein, A.
1992-01-01
This paper discusses a silicon quadrant detector (128 elements) implemented as an electron detector in a Scanning Transmission Electron Microscope. As the electron beam scans over the sample, electrons are counted during each pixel. The authors developed an ASIC for the multichannel counting system. The digital front-end carries out the readout of all elements, in four groups, and uses these data to compute linear combinations to generate up to eight simultaneous images. For the preprocessing the authors implemented a parallel and pipelined system. Dedicated software tools were developed to generate the programs for all the processors. These tools are transparently accessed by the user via a user friendly interface
A parallel finite element method for the analysis of crystalline solids
DEFF Research Database (Denmark)
Sørensen, N.J.; Andersen, B.S.
1996-01-01
A parallel finite element method suitable for the analysis of 3D quasi-static crystal plasticity problems has been developed. The method is based on substructuring of the original mesh into a number of substructures which are treated as isolated finite element models related via the interface...... conditions. The resulting interface equations are solved using a direct solution method. The method shows a good speedup when increasing the number of processors from 1 to 8 and the effective solution of 3D crystal plasticity problems whose size is much too large for a single work station becomes possible....
Simulation of incompressible flows with heat and mass transfer using parallel finite element method
Directory of Open Access Journals (Sweden)
Jalal Abedi
2003-02-01
Full Text Available The stabilized finite element formulations based on the SUPG (Stream-line-Upwind/Petrov-Galerkin and PSPG (Pressure-Stabilization/Petrov-Galerkin methods are developed and applied to solve buoyancy-driven incompressible flows with heat and mass transfer. The SUPG stabilization term allows us to solve flow problems at high speeds (advection dominant flows and the PSPG term eliminates instabilities associated with the use of equal order interpolation functions for both pressure and velocity. The finite element formulations are implemented in parallel using MPI. In parallel computations, the finite element mesh is partitioned into contiguous subdomains using METIS, which are then assigned to individual processors. To ensure a balanced load, the number of elements assigned to each processor is approximately equal. To solve nonlinear systems in large-scale applications, we developed a matrix-free GMRES iterative solver. Here we totally eliminate a need to form any matrices, even at the element levels. To measure the accuracy of the method, we solve 2D and 3D example of natural convection flows at moderate to high Rayleigh numbers.
DEFF Research Database (Denmark)
Cai, Hongzhu; Čuma, Martin; Zhdanov, Michael
2015-01-01
This paper presents a parallelized version of the edge-based finite element method with a novel post-processing approach for numerical modeling of an electromagnetic field in complex media. The method uses an unstructured tetrahedral mesh which can reduce the number of degrees of freedom signific......This paper presents a parallelized version of the edge-based finite element method with a novel post-processing approach for numerical modeling of an electromagnetic field in complex media. The method uses an unstructured tetrahedral mesh which can reduce the number of degrees of freedom...... significantly. The linear system of finite element equations is solved using parallel direct solvers which are robust for ill-conditioned systems and efficient for multiple source electromagnetic (EM) modeling. We also introduce a novel approach to compute the scalar components of the electric field from...... the tangential components along each edge based on field redatuming. The method can produce a more accurate result as compared to conventional approach. We have applied the developed algorithm to compute the EM response for a typical 3D anisotropic geoelectrical model of the off-shore HC reservoir with complex...
Finite-element discretization of 3D energy-transport equations for semiconductors
Energy Technology Data Exchange (ETDEWEB)
Gadau, Stephan
2007-07-01
In this thesis a mathematical model was derived that describes the charge and energy transport in semiconductor devices like transistors. Moreover, numerical simulations of these physical processes are performed. In order to accomplish this, methods of theoretical physics, functional analysis, numerical mathematics and computer programming are applied. After an introduction to the status quo of semiconductor device simulation methods and a brief review of historical facts up to now, the attention is shifted to the construction of a model, which serves as the basis of the subsequent derivations in the thesis. Thereby the starting point is an important equation of the theory of dilute gases. From this equation the model equations are derived and specified by means of a series expansion method. This is done in a multi-stage derivation process, which is mainly taken from a scientific paper and which does not constitute the focus of this thesis. In the following phase we specify the mathematical setting and make precise the model assumptions. Thereby we make use of methods of functional analysis. Since the equations we deal with are coupled, we are concerned with a nonstandard problem. In contrary, the theory of scalar elliptic equations is established meanwhile. Subsequently, we are preoccupied with the numerical discretization of the equations. A special finite-element method is used for the discretization. This special approach has to be done in order to make the numerical results appropriate for practical application. By a series of transformations from the discrete model we derive a system of algebraic equations that are eligible for numerical evaluation. Using self-made computer programs we solve the equations to get approximate solutions. These programs are based on new and specialized iteration procedures that are developed and thoroughly tested within the frame of this research work. Due to their importance and their novel status, they are explained and
Simulation of granular and gas-solid flows using discrete element method
Boyalakuntla, Dhanunjay S.
2003-10-01
In recent years there has been increased research activity in the experimental and numerical study of gas-solid flows. Flows of this type have numerous applications in the energy, pharmaceuticals, and chemicals process industries. Typical applications include pulverized coal combustion, flow and heat transfer in bubbling and circulating fluidized beds, hopper and chute flows, pneumatic transport of pharmaceutical powders and pellets, and many more. The present work addresses the study of gas-solid flows using computational fluid dynamics (CFD) techniques and discrete element simulation methods (DES) combined. Many previous studies of coupled gas-solid flows have been performed assuming the solid phase as a continuum with averaged properties and treating the gas-solid flow as constituting of interpenetrating continua. Instead, in the present work, the gas phase flow is simulated using continuum theory and the solid phase flow is simulated using DES. DES treats each solid particle individually, thus accounting for its dynamics due to particle-particle interactions, particle-wall interactions as well as fluid drag and buoyancy. The present work involves developing efficient DES methods for dense granular flow and coupling this simulation to continuum simulations of the gas phase flow. Simulations have been performed to observe pure granular behavior in vibrating beds. Benchmark cases have been simulated and the results obtained match the published literature. The dimensionless acceleration amplitude and the bed height are the parameters governing bed behavior. Various interesting behaviors such as heaping, round and cusp surface standing waves, as well as kinks, have been observed for different values of the acceleration amplitude for a given bed height. Furthermore, binary granular mixtures (granular mixtures with two particle sizes) in a vibrated bed have also been studied. Gas-solid flow simulations have been performed to study fluidized beds. Benchmark 2D
Nuclear reactor fuel element with a cluster of parallel fuel pins
International Nuclear Information System (INIS)
Macfall, D.; Butterfield, C.E.; Butterfield, R.S.
1977-01-01
An improvement of the design of nuclear reactor fuel elements is described and illustrated by the example of a gas-cooled, graphite-moderated nuclear reactor. The fuel element has a cluster of parallel fuel pins with an outer can of structure material and an inner sleeve, as well as tie bars and spacing devices for all of these parts. The fuel element designed according to the invention allows lasy assembling and disassembling before and after use. During use, no relative axial motions are possible; nevertheless, the graphite sleeve is at no time subject to tensile stress: the individual parts are held in position from below by a single holding device. (UWI) [de
DEFF Research Database (Denmark)
Feng, Huan; Pettinari, Matteo; Stang, Henrik
2015-01-01
In this paper, the viscoelastic behavior of asphalt mixture was studied by using discrete element method. The dynamic properties of asphalt mixture were captured by implementing Burger’s contact model. Different ways of taking into account of the normal and shear material properties of asphalt mi...
Rahmouni, Lyes; Adrian, Simon B.; Cools, Kristof; Andriulli, Francesco P.
2018-01-01
In this paper, we present a new discretization strategy for the boundary element formulation of the Electroencephalography (EEG) forward problem. Boundary integral formulations, classically solved with the Boundary Element Method (BEM), are widely used in high resolution EEG imaging because of their recognized advantages, in several real case scenarios, in terms of numerical stability and effectiveness when compared with other differential equation based techniques. Unfortunately, however, it is widely reported in literature that the accuracy of standard BEM schemes for the forward EEG problem is often limited, especially when the current source density is dipolar and its location approaches one of the brain boundary surfaces. This is a particularly limiting problem given that during an high-resolution EEG imaging procedure, several EEG forward problem solutions are required, for which the source currents are near or on top of a boundary surface. This work will first present an analysis of standardly and classically discretized EEG forward problem operators, reporting on a theoretical issue of some of the formulations that have been used so far in the community. We report on the fact that several standardly used discretizations of these formulations are consistent only with an L2-framework, requiring the expansion term to be a square integrable function (i.e., in a Petrov-Galerkin scheme with expansion and testing functions). Instead, those techniques are not consistent when a more appropriate mapping in terms of fractional-order Sobolev spaces is considered. Such a mapping allows the expansion function term to be a less regular function, thus sensibly reducing the need for mesh refinements and low-precisions handling strategies that are currently required. These more favorable mappings, however, require a different and conforming discretization, which must be suitably adapted to them. In order to appropriately fulfill this requirement, we adopt a mixed
PARALLEL ALGORITHM FOR THREE-DIMENSIONAL STOKES FLOW SIMULATION USING BOUNDARY ELEMENT METHOD
Directory of Open Access Journals (Sweden)
D. G. Pribytok
2016-01-01
Full Text Available Parallel computing technique for modeling three-dimensional viscous flow (Stokes flow using direct boundary element method is presented. The problem is solved in three phases: sampling and construction of system of linear algebraic equations (SLAE, its decision and finding the velocity of liquid at predetermined points. For construction of the system and finding the velocity, the parallel algorithms using graphics CUDA cards programming technology have been developed and implemented. To solve the system of linear algebraic equations the implemented software libraries are used. A comparison of time consumption for three main algorithms on the example of calculation of viscous fluid motion in three-dimensional cavity is performed.
Directory of Open Access Journals (Sweden)
Maitraye Sen
2017-04-01
Full Text Available A discrete element model (DEM has been developed for an industrial batch bin blender in which three different types of materials are mixed. The mixing dynamics have been evaluated from a model-based study with respect to the blend critical quality attributes (CQAs which are relative standard deviation (RSD and segregation intensity. In the actual industrial setup, a sensor mounted on the blender lid is used to determine the blend composition in this region. A model-based analysis has been used to understand the mixing efficiency in the other zones inside the blender and to determine if the data obtained near the blender-lid region are able to provide a good representation of the overall blend quality. Sub-optimal mixing zones have been identified and other potential sampling locations have been investigated in order to obtain a good approximation of the blend variability. The model has been used to study how the mixing efficiency can be improved by varying the key processing parameters, i.e., blender RPM/speed, fill level/volume and loading order. Both segregation intensity and RSD reduce at a lower fill level and higher blender RPM and are a function of the mixing time. This work demonstrates the use of a model-based approach to improve process knowledge regarding a pharmaceutical mixing process. The model can be used to acquire qualitative information about the influence of different critical process parameters and equipment geometry on the mixing dynamics.
Hancock, Bruno C; Ketterhagen, William R
2011-10-14
Discrete element model (DEM) simulations of the discharge of powders from hoppers under gravity were analyzed to provide estimates of dosage form content uniformity during the manufacture of solid dosage forms (tablets and capsules). For a system that exhibits moderate segregation the effects of sample size, number, and location within the batch were determined. The various sampling approaches were compared to current best-practices for sampling described in the Product Quality Research Institute (PQRI) Blend Uniformity Working Group (BUWG) guidelines. Sampling uniformly across the discharge process gave the most accurate results with respect to identifying segregation trends. Sigmoidal sampling (as recommended in the PQRI BUWG guidelines) tended to overestimate potential segregation issues, whereas truncated sampling (common in industrial practice) tended to underestimate them. The size of the sample had a major effect on the absolute potency RSD. The number of sampling locations (10 vs. 20) had very little effect on the trends in the data, and the number of samples analyzed at each location (1 vs. 3 vs. 7) had only a small effect for the sampling conditions examined. The results of this work provide greater understanding of the effect of different sampling approaches on the measured content uniformity of real dosage forms, and can help to guide the choice of appropriate sampling protocols. Copyright © 2011 Elsevier B.V. All rights reserved.
Discrete Element Method Modeling of the Rheological Properties of Coke/Pitch Mixtures
Directory of Open Access Journals (Sweden)
Behzad Majidi
2016-05-01
Full Text Available Rheological properties of pitch and pitch/coke mixtures at temperatures around 150 °C are of great interest for the carbon anode manufacturing process in the aluminum industry. In the present work, a cohesive viscoelastic contact model based on Burger’s model is developed using the discrete element method (DEM on the YADE, the open-source DEM software. A dynamic shear rheometer (DSR is used to measure the viscoelastic properties of pitch at 150 °C. The experimental data obtained is then used to estimate the Burger’s model parameters and calibrate the DEM model. The DSR tests were then simulated by a three-dimensional model. Very good agreement was observed between the experimental data and simulation results. Coke aggregates were modeled by overlapping spheres in the DEM model. Coke/pitch mixtures were numerically created by adding 5, 10, 20, and 30 percent of coke aggregates of the size range of 0.297–0.595 mm (−30 + 50 mesh to pitch. Adding up to 30% of coke aggregates to pitch can increase its complex shear modulus at 60 Hz from 273 Pa to 1557 Pa. Results also showed that adding coke particles increases both storage and loss moduli, while it does not have a meaningful effect on the phase angle of pitch.
Discrete Element Method Modeling of the Rheological Properties of Coke/Pitch Mixtures.
Majidi, Behzad; Taghavi, Seyed Mohammad; Fafard, Mario; Ziegler, Donald P; Alamdari, Houshang
2016-05-04
Rheological properties of pitch and pitch/coke mixtures at temperatures around 150 °C are of great interest for the carbon anode manufacturing process in the aluminum industry. In the present work, a cohesive viscoelastic contact model based on Burger's model is developed using the discrete element method (DEM) on the YADE, the open-source DEM software. A dynamic shear rheometer (DSR) is used to measure the viscoelastic properties of pitch at 150 °C. The experimental data obtained is then used to estimate the Burger's model parameters and calibrate the DEM model. The DSR tests were then simulated by a three-dimensional model. Very good agreement was observed between the experimental data and simulation results. Coke aggregates were modeled by overlapping spheres in the DEM model. Coke/pitch mixtures were numerically created by adding 5, 10, 20, and 30 percent of coke aggregates of the size range of 0.297-0.595 mm (-30 + 50 mesh) to pitch. Adding up to 30% of coke aggregates to pitch can increase its complex shear modulus at 60 Hz from 273 Pa to 1557 Pa. Results also showed that adding coke particles increases both storage and loss moduli, while it does not have a meaningful effect on the phase angle of pitch.
Lemrich, Laure; Carmeliet, Jan; Johnson, Paul A.; Guyer, Robert; Jia, Xiaoping
2017-12-01
A granular system composed of frictional glass beads is simulated using the discrete element method. The intergrain forces are based on the Hertz contact law in the normal direction with frictional tangential force. The damping due to collision is also accounted for. Systems are loaded at various stresses and their quasistatic elastic moduli are characterized. Each system is subjected to an extensive dynamic testing protocol by measuring the resonant response to a broad range of ac drive amplitudes and frequencies via a set of diagnostic strains. The system, linear at small ac drive amplitudes, has resonance frequencies that shift downward (i.e., modulus softening) with increased ac drive amplitude. Detailed testing shows that the slipping contact ratio does not contribute significantly to this dynamic modulus softening, but the coordination number is strongly correlated to this reduction. This suggests that the softening arises from the extended structural change via break and remake of contacts during the rearrangement of bead positions driven by the ac amplitude.
Flow Dynamics of green sand in the DISAMATIC moulding process using Discrete element method (DEM)
International Nuclear Information System (INIS)
Hovad, E; Walther, J H; Thorborg, J; Hattel, J H; Larsen, P
2015-01-01
The DISAMATIC casting process production of sand moulds is simulated with DEM (discrete element method). The main purpose is to simulate the dynamics of the flow of green sand, during the production of the sand mould with DEM. The sand shot is simulated, which is the first stage of the DISAMATIC casting process. Depending on the actual casting geometry the mould can be geometrically quite complex involving e.g. shadowing effects and this is directly reflected in the sand flow during the moulding process. In the present work a mould chamber with “ribs” at the walls is chosen as a baseline geometry to emulate some of these important conditions found in the real moulding process. The sand flow is simulated with the DEM and compared with corresponding video footages from the interior of the chamber during the moulding process. The effect of the rolling resistance and the static friction coefficient is analysed and discussed in relation to the experimental findings. (paper)
Directory of Open Access Journals (Sweden)
Arthur Coré
2017-01-01
Full Text Available This paper deals with the characterization and the numerical modelling of the collapse of composite hollow spherical structures developed to absorb energy during high velocity impacts. The structure is composed of hollow spheres (ϕ=2–30 mm made of epoxy resin and mineral powder. First of all, quasi-static and dynamic (v=5 mm·min−1 to v=2 m·s−1 compression tests are conducted at room temperature on a single sphere to study energy dissipation mechanisms. Fracture of the material appears to be predominant. A numerical model based on the discrete element method is investigated to simulate the single sphere crushing. The stress-strain-time relationship of the material based on the Ree-Eyring law is numerically implemented. The DEM modelling takes naturally into account the dynamic fracture and the crack path computed is close to the one observed experimentally in uniaxial compression. Eventually, high velocity impacts (v>100 m·s−1 of a hollow sphere on a rigid surface are conducted with an air cannon. The numerical results are in good agreement with the experimental data and demonstrate the ability of the present model to correctly describe the mechanical behavior of brittle materials at high strain rate.
Blank, D. G.; Morgan, J.
2017-12-01
Large earthquakes that occur on convergent plate margin interfaces have the potential to cause widespread damage and loss of life. Recent observations reveal that a wide range of different slip behaviors take place along these megathrust faults, which demonstrate both their complexity, and our limited understanding of fault processes and their controls. Numerical modeling provides us with a useful tool that we can use to simulate earthquakes and related slip events, and to make direct observations and correlations among properties and parameters that might control them. Further analysis of these phenomena can lead to a more complete understanding of the underlying mechanisms that accompany the nucleation of large earthquakes, and what might trigger them. In this study, we use the discrete element method (DEM) to create numerical analogs to subduction megathrusts with heterogeneous fault friction. Displacement boundary conditions are applied in order to simulate tectonic loading, which in turn, induces slip along the fault. A wide range of slip behaviors are observed, ranging from creep to stick slip. We are able to characterize slip events by duration, stress drop, rupture area, and slip magnitude, and to correlate the relationships among these quantities. These characterizations allow us to develop a catalog of rupture events both spatially and temporally, for comparison with slip processes on natural faults.
Vora, H.; Morgan, J.
2017-12-01
Brittle failure in rock under confined biaxial conditions is accompanied by release of seismic energy, known as acoustic emissions (AE). The objective our study is to understand the influence of elastic properties of rock and its stress state on deformation patterns, and associated seismicity in granular rocks. Discrete Element Modeling is used to simulate biaxial tests on granular rocks of defined grain size distribution. Acoustic Energy and seismic moments are calculated from microfracture events as rock is taken to conditions of failure under different confining pressure states. Dimensionless parameters such as seismic b-value and fractal parameter for deformation, D-value, are used to quantify seismic character and distribution of damage in rock. Initial results suggest that confining pressure has the largest control on distribution of induced microfracturing, while fracture energy and seismic magnitudes are highly sensitive to elastic properties of rock. At low confining pressures, localized deformation (low D-values) and high seismic b-values are observed. Deformation at high confining pressures is distributed in nature (high D-values) and exhibit low seismic b-values as shearing becomes the dominant mode of microfracturing. Seismic b-values and fractal D-values obtained from microfracturing exhibit a linear inverse relationship, similar to trends observed in earthquakes. Mode of microfracturing in our simulations of biaxial compression tests show mechanistic similarities to propagation of fractures and faults in nature.
Model of the saltation transport by Discrete Element Method coupled with wind interaction
Directory of Open Access Journals (Sweden)
Oger Luc
2017-01-01
Full Text Available We study the Aeolian saltation transport problem by analysing the collision of incident energetic beads with granular packing. We investigate the collision process for the case where the incident bead and those from the packing have identical mechanical properties. We analyse the features of the consecutive collision process. We used a molecular dynamics method known as DEM (soft Discrete Element Method with 20000 particles (2D. The grains were displayed randomly in a box (250X60. A few incident disks are launched with a constant velocity and angle with high random position to initiate the flow. A wind velocity profile is applied on the flowing zone of the saltation. The velocity profile is obtained by the calculi of the counter-flow due to the local packing fraction induced by the granular flow. We analyse the evolution of the upper surface of the disk packing. In the beginning, the saltation process can be seen as the classical “splash function” in which one bead hits a fully static dense packing. Then, the quasi-fluidized upper layer of the packing creates a completely different behaviour of the “animated splash function”. The dilation of the upper surface due to the previous collisions is responsible for a need of less input energy for launching new ejected disks. This phenomenon permits to maintain a constant granular flow with a “small” wind velocity on the surface of the disk bed.
A Review of Discrete Element Method (DEM) Particle Shapes and Size Distributions for Lunar Soil
Lane, John E.; Metzger, Philip T.; Wilkinson, R. Allen
2010-01-01
As part of ongoing efforts to develop models of lunar soil mechanics, this report reviews two topics that are important to discrete element method (DEM) modeling the behavior of soils (such as lunar soils): (1) methods of modeling particle shapes and (2) analytical representations of particle size distribution. The choice of particle shape complexity is driven primarily by opposing tradeoffs with total number of particles, computer memory, and total simulation computer processing time. The choice is also dependent on available DEM software capabilities. For example, PFC2D/PFC3D and EDEM support clustering of spheres; MIMES incorporates superquadric particle shapes; and BLOKS3D provides polyhedra shapes. Most commercial and custom DEM software supports some type of complex particle shape beyond the standard sphere. Convex polyhedra, clusters of spheres and single parametric particle shapes such as the ellipsoid, polyellipsoid, and superquadric, are all motivated by the desire to introduce asymmetry into the particle shape, as well as edges and corners, in order to better simulate actual granular particle shapes and behavior. An empirical particle size distribution (PSD) formula is shown to fit desert sand data from Bagnold. Particle size data of JSC-1a obtained from a fine particle analyzer at the NASA Kennedy Space Center is also fitted to a similar empirical PSD function.
Discrete element simulation of charging and mixed layer formation in the ironmaking blast furnace
Mitra, Tamoghna; Saxén, Henrik
2016-11-01
The burden distribution in the ironmaking blast furnace plays an important role for the operation as it affects the gas flow distribution, heat and mass transfer, and chemical reactions in the shaft. This work studies certain aspects of burden distribution by small-scale experiments and numerical simulation by the discrete element method (DEM). Particular attention is focused on the complex layer-formation process and the problems associated with estimating the burden layer distribution by burden profile measurements. The formation of mixed layers is studied, and a computational method for estimating the extent of the mixed layer, as well as its voidage, is proposed and applied on the results of the DEM simulations. In studying a charging program and its resulting burden distribution, the mixed layers of coke and pellets were found to show lower voidage than the individual burden layers. The dynamic evolution of the mixed layer during the charging process is also analyzed. The results of the study can be used to gain deeper insight into the complex charging process of the blast furnace, which is useful in the design of new charging programs and for mathematical models that do not consider the full behavior of the particles in the burden layers.
Features and validation of discrete element method for simulating pebble flow in reactor core
International Nuclear Information System (INIS)
Xu Yong; Li Yanjie
2005-01-01
The core of a High-Temperature Gas-cooled Reactor (HTGR) is composed of big number of fuel pebbles, their kinetic behaviors are of great importance in estimating the path and residence time of individual pebble, the evolution of the mixing zone for the assessment of the efficiency of a reactor. Numerical method is highlighted in modern reactor design. In view of granular flow, the Discrete Element Model based on contact mechanics of spheres was briefly described. Two typical examples were presented to show the capability of the DEM method. The former is piling with glass/steel spheres, which provides validated evidences that the simulated angles of repose are in good coincidence with the experimental results. The later is particle discharge in a flat- bottomed silo, which shows the effects of material modulus and demonstrates several features. The two examples show the DEM method enables to predict the behaviors, such as the evolution of pebble profiles, streamlines etc., and provides sufficient information for pebble flow analysis and core design. In order to predict the cyclic pebble flow in a HTGR core precisely and efficiently, both model and code improvement are needed, together with rational specification of physical properties with proper measuring techniques. Strategic and methodological considerations were also discussed. (authors)
Study on small-strain behaviours of methane hydrate sandy sediments using discrete element method
Energy Technology Data Exchange (ETDEWEB)
Yu Yanxin; Cheng Yipik [Department of Civil, Environmental and Geomatic Engineering, University College London (UCL), Gower Street, London, WC1E 6BT (United Kingdom); Xu Xiaomin; Soga, Kenichi [Geotechnical and Environmental Research Group, Department of Engineering, University of Cambridge, Trumpington Street, Cambridge, CB2 1PZ (United Kingdom)
2013-06-18
Methane hydrate bearing soil has attracted increasing interest as a potential energy resource where methane gas can be extracted from dissociating hydrate-bearing sediments. Seismic testing techniques have been applied extensively and in various ways, to detect the presence of hydrates, due to the fact that hydrates increase the stiffness of hydrate-bearing sediments. With the recognition of the limitations of laboratory and field tests, wave propagation modelling using Discrete Element Method (DEM) was conducted in this study in order to provide some particle-scale insights on the hydrate-bearing sandy sediment models with pore-filling and cementation hydrate distributions. The relationship between shear wave velocity and hydrate saturation was established by both DEM simulations and analytical solutions. Obvious differences were observed in the dependence of wave velocity on hydrate saturation for these two cases. From the shear wave velocity measurement and particle-scale analysis, it was found that the small-strain mechanical properties of hydrate-bearing sandy sediments are governed by both the hydrate distribution patterns and hydrate saturation.
Shale Fracture Analysis using the Combined Finite-Discrete Element Method
Carey, J. W.; Lei, Z.; Rougier, E.; Knight, E. E.; Viswanathan, H.
2014-12-01
Hydraulic fracturing (hydrofrac) is a successful method used to extract oil and gas from highly carbonate rocks like shale. However, challenges exist for industry experts estimate that for a single $10 million dollar lateral wellbore fracking operation, only 10% of the hydrocarbons contained in the rock are extracted. To better understand how to improve hydrofrac recovery efficiencies and to lower its costs, LANL recently funded the Laboratory Directed Research and Development (LDRD) project: "Discovery Science of Hydraulic Fracturing: Innovative Working Fluids and Their Interactions with Rocks, Fractures, and Hydrocarbons". Under the support of this project, the LDRD modeling team is working with the experimental team to understand fracture initiation and propagation in shale rocks. LANL's hybrid hydro-mechanical (HM) tool, the Hybrid Optimization Software Suite (HOSS), is being used to simulate the complex fracture and fragment processes under a variety of different boundary conditions. HOSS is based on the combined finite-discrete element method (FDEM) and has been proven to be a superior computational tool for multi-fracturing problems. In this work, the comparison of HOSS simulation results to triaxial core flooding experiments will be presented.
Simpson, R. N.; Liu, Z.; Vázquez, R.; Evans, J. A.
2018-06-01
We outline the construction of compatible B-splines on 3D surfaces that satisfy the continuity requirements for electromagnetic scattering analysis with the boundary element method (method of moments). Our approach makes use of Non-Uniform Rational B-splines to represent model geometry and compatible B-splines to approximate the surface current, and adopts the isogeometric concept in which the basis for analysis is taken directly from CAD (geometry) data. The approach allows for high-order approximations and crucially provides a direct link with CAD data structures that allows for efficient design workflows. After outlining the construction of div- and curl-conforming B-splines defined over 3D surfaces we describe their use with the electric and magnetic field integral equations using a Galerkin formulation. We use Bézier extraction to accelerate the computation of NURBS and B-spline terms and employ H-matrices to provide accelerated computations and memory reduction for the dense matrices that result from the boundary integral discretization. The method is verified using the well known Mie scattering problem posed over a perfectly electrically conducting sphere and the classic NASA almond problem. Finally, we demonstrate the ability of the approach to handle models with complex geometry directly from CAD without mesh generation.
Estimations of impact strength on reinforced concrete structures by the discrete element method
International Nuclear Information System (INIS)
Morikawa, H.; Kusano, N.; Koshika, N.; Aoyagi, T.; Hagiwara, Y.; Sawamoto, Y.
1993-01-01
There has been a rising interest in the response of reinforced concrete structures to impact loading, from the point of view in particular of disaster prevention at nuclear power facilities, and there is an urgent requirement for establishment of design methods against such type of loads. Structural damage on reinforced concrete structures under impact load includes local damage and global damage. The behavior of local damage, such as penetration into the structures, rear face scabbing, perforation, or spalling, has been difficult to estimate by numerical analysis, but over recent years research has advantaged and various analytical methods have been tried. The authors proposed a new approach for assessing local damage characteristics by applying the discrete element method (DEM), and verified that the behavior of a concrete slab suffering local damage may be qualitatively expressed. This was followed by the discussion of the quantitative evaluation of various constants used in the DEM analysis in reference. The authors apply the DEM to the simulation analysis of impact tests on reinforced concrete panels and analytical investigations are made on the local damage characteristics and response values that are difficult to assess through tests, in an attempt to evaluate the mechanism of local damage according to the hardness of the missiles
Numerical sedimentation particle-size analysis using the Discrete Element Method
Bravo, R.; Pérez-Aparicio, J. L.; Gómez-Hernández, J. J.
2015-12-01
Sedimentation tests are widely used to determine the particle size distribution of a granular sample. In this work, the Discrete Element Method interacts with the simulation of flow using the well known one-way-coupling method, a computationally affordable approach for the time-consuming numerical simulation of the hydrometer, buoyancy and pipette sedimentation tests. These tests are used in the laboratory to determine the particle-size distribution of fine-grained aggregates. Five samples with different particle-size distributions are modeled by about six million rigid spheres projected on two-dimensions, with diameters ranging from 2.5 ×10-6 m to 70 ×10-6 m, forming a water suspension in a sedimentation cylinder. DEM simulates the particle's movement considering laminar flow interactions of buoyant, drag and lubrication forces. The simulation provides the temporal/spatial distributions of densities and concentrations of the suspension. The numerical simulations cannot replace the laboratory tests since they need the final granulometry as initial data, but, as the results show, these simulations can identify the strong and weak points of each method and eventually recommend useful variations and draw conclusions on their validity, aspects very difficult to achieve in the laboratory.
A discrete element based simulation framework to investigate particulate spray deposition processes
Mukherjee, Debanjan
2015-06-01
© 2015 Elsevier Inc. This work presents a computer simulation framework based on discrete element method to analyze manufacturing processes that comprise a loosely flowing stream of particles in a carrier fluid being deposited on a target surface. The individual particulate dynamics under the combined action of particle collisions, fluid-particle interactions, particle-surface contact and adhesive interactions is simulated, and aggregated to obtain global system behavior. A model for deposition which incorporates the effect of surface energy, impact velocity and particle size, is developed. The fluid-particle interaction is modeled using appropriate spray nozzle gas velocity distributions and a one-way coupling between the phases. It is found that the particle response times and the release velocity distribution of particles have a combined effect on inter-particle collisions during the flow along the spray. It is also found that resolution of the particulate collisions close to the target surface plays an important role in characterizing the trends in the deposit pattern. Analysis of the deposit pattern using metrics defined from the particle distribution on the target surface is provided to characterize the deposition efficiency, deposit size, and scatter due to collisions.
Yushi, Zou; Xinfang, Ma; Tong, Zhou; Ning, Li; Ming, Chen; Sihai, Li; Yinuo, Zhang; Han, Li
2017-09-01
Hydraulic fracture (HF) height containment tends to occur in layered formations, and it significantly influences the entire HF geometry or the stimulated reservoir volume. This study aims to explore the influence of preexisting bedding planes (BPs) on the HF height growth in layered formations. Laboratory fracturing experiments were performed to confirm the occurrence of HF height containment in natural shale that contains multiple weak and high-permeability BPs under triaxial stresses. Numerical simulations were then conducted to further illustrate the manner in which vertical stress, BP permeability, BP density(or spacing), pump rate, and fluid viscosity control HF height growth using a 3D discrete element method-based fracturing model. In this model, the rock matrix was considered transversely isotropic and multiple BPs can be explicitly represented. Experimental and numerical results show that the vertically growing HF tends to be limited by multi-high-permeability BPs, even under higher vertical stress. When the vertically growing HF intersects with the multi-high-permeability BPs, the injection pressure will be sharply reduced. If a low pumping rate or a low-viscosity fluid is used, the excess fracturing fluid leak-off into the BPs obviously decreases the rate of pressure build up, which will then limit the growth of HF. Otherwise, a higher pumping rate and/or a higher viscosity will reduce the leak-off time and fluid volume, but increase the injection pressure to drive the HF to grow and to penetrate through the BPs.
Directory of Open Access Journals (Sweden)
Neng Wan
2014-01-01
Full Text Available In terms of the poor geometric adaptability of spline element method, a geometric precision spline method, which uses the rational Bezier patches to indicate the solution domain, is proposed for two-dimensional viscous uncompressed Navier-Stokes equation. Besides fewer pending unknowns, higher accuracy, and computation efficiency, it possesses such advantages as accurate representation of isogeometric analysis for object boundary and the unity of geometry and analysis modeling. Meanwhile, the selection of B-spline basis functions and the grid definition is studied and a stable discretization format satisfying inf-sup conditions is proposed. The degree of spline functions approaching the velocity field is one order higher than that approaching pressure field, and these functions are defined on one-time refined grid. The Dirichlet boundary conditions are imposed through the Nitsche variational principle in weak form due to the lack of interpolation properties of the B-splines functions. Finally, the validity of the proposed method is verified with some examples.
Son, Kwon Joong
2018-02-01
Hindering particle agglomeration and re-dispersion processes, gravitational sedimentation of suspended particles in magnetorheological (MR) fluids causes inferior performance and controllability of MR fluids in response to a user-specified magnetic field. Thus, suspension stability is one of the principal factors to be considered in synthesizing MR fluids. However, only a few computational studies have been reported so far on the sedimentation characteristics of suspended particles under gravity. In this paper, the settling dynamics of paramagnetic particles suspended in MR fluids was investigated via discrete element method (DEM) simulations. This work focuses particularly on developing accurate fluid-particle and particle-particle interaction models which can account for the influence of stabilizing surfactants on the MR fluid sedimentation. Effect of the stabilizing surfactants on interparticle interactions was incorporated into the derivation of a reliable contact-impact model for DEM computation. Also, the influence of the stabilizing additives on fluid-particle interactions was considered by incorporating Stokes drag with shape and wall correction factors into DEM formulation. The results of simulations performed for model validation purposes showed a good agreement with the published sedimentation measurement data in terms of an initial sedimentation velocity and a final sedimentation ratio.
Rigid missiles impact on reinforced concrete structures: analysis by discrete element method
International Nuclear Information System (INIS)
Shiu, W.J.
2008-10-01
The constructions likely to be subjected to some extreme loadings like reactor containment buildings have to be dimensioned accordingly. As a part of study of concrete structures, this thesis focuses on numerical modelling of rigid missile impacts against a rigid reinforced concrete slab. Based on some experiment tests data, an elasto-plastic-damaged constitutive law has been implanted into a discrete element numerical code. To calibrate certain parameters of the numerical model, some quasi static tests have been first simulated. Once the model calibration was done, some missile impact simulation tests have then been carried out. The numerical results are well agree with these provided by French Atomic Energy Agency (Cea) and the French Electrical power Company (EDF) in terms of the trajectory of the missile. We were able to show the need of a constitutive law taking into account the compaction behaviour of the concrete when the predictions of penetration and perforation of a thick slab was demanded. Finally, a parametric study confirmed that the numerical model can be used the way predictive as well as the empirical prediction law, while the first can provide additional significant mechanical description. (author)
Experimental Behavior Evaluation of Series and Parallel Connected Constant Phase Elements
Tsirimokou, Georgia
2017-01-28
Fractional-order capacitors are the core building blocks for implementing fractional-order circuits. Due to the absence of their commercial availability, they can be approximated through appropriately configured passive or active integer-order element topologies. Such a topology, constructed using Operational Transconductance Amplifiers (OTAs) and capacitors has been implemented in monolithic form through the AMS 0.35μm CMOS process, and the fabricated chips are employed here for the experimental evaluation of the behavior of networks constructed from fractional-order capacitors connected in series or in parallel.
Modeling reservoir geomechanics using discrete element method : Application to reservoir monitoring
Energy Technology Data Exchange (ETDEWEB)
Alassi, Haitham Tayseer
2008-09-15
Understanding reservoir geomechanical behavior is becoming more and more important for the petroleum industry. Reservoir compaction, which may result in surface subsidence and fault reactivation, occurs during reservoir depletion. Stress changes and possible fracture development inside and outside a depleting reservoir can be monitored using time-lapse (so-called '4D') seismic and/or passive seismic, and this can give valuable information about the conditions of a given reservoir during production. In this study we will focus on using the (particle-based) Discrete Element Method (DEM) to model reservoir geomechanical behavior during depletion and fluid injection. We show in this study that DEM can be used in modeling reservoir geomechanical behavior by comparing results obtained from DEM to those obtained from analytical solutions. The match of the displacement field between DEM and the analytical solution is good, however there is mismatch of the stress field which is related to the way stress is measured in DEM. A good match is however obtained by measuring the stress field carefully. We also use DEM to model reservoir geomechanical behavior beyond the elasticity limit where fractures can develop and faults can reactivate. A general technique has been developed to relate DEM parameters to rock properties. This is necessary in order to use correct reservoir geomechanical properties during modeling. For any type of particle packing there is a limitation that the maximum ratio between P- and S-wave velocity Vp/Vs that can be modeled is 3 . The static behavior for a loose packing is different from the dynamic behavior. Empirical relations are needed for the static behavior based on numerical test observations. The dynamic behavior for both dense and loose packing can be given by analytical relations. Cosserat continuum theory is needed to derive relations for Vp and Vs. It is shown that by constraining the particle rotation, the S-wave velocity can be
Coupled large eddy simulation and discrete element model of bedload motion
Furbish, D.; Schmeeckle, M. W.
2011-12-01
We combine a three-dimensional large eddy simulation of turbulence to a three-dimensional discrete element model of turbulence. The large eddy simulation of the turbulent fluid is extended into the bed composed of non-moving particles by adding resistance terms to the Navier-Stokes equations in accordance with the Darcy-Forchheimer law. This allows the turbulent velocity and pressure fluctuations to penetrate the bed of discrete particles, and this addition of a porous zone results in turbulence structures above the bed that are similar to previous experimental and numerical results for hydraulically-rough beds. For example, we reproduce low-speed streaks that are less coherent than those over smooth-beds due to the episodic outflow of fluid from the bed. Local resistance terms are also added to the Navier-Stokes equations to account for the drag of individual moving particles. The interaction of the spherical particles utilizes a standard DEM soft-sphere Hertz model. We use only a simple drag model to calculate the fluid forces on the particles. The model reproduces an exponential distribution of bedload particle velocities that we have found experimentally using high-speed video of a flat bed of moving sand in a recirculating water flume. The exponential distribution of velocity results from the motion of many particles that are nearly constantly in contact with other bed particles and come to rest after short distances, in combination with a relatively few particles that are entrained further above the bed and have velocities approaching that of the fluid. Entrainment and motion "hot spots" are evident that are not perfectly correlated with the local, instantaneous fluid velocity. Zones of the bed that have recently experienced motion are more susceptible to motion because of the local configuration of particle contacts. The paradigm of a characteristic saltation hop length in riverine bedload transport has infused many aspects of geomorphic thought, including
Mesh Partitioning Algorithm Based on Parallel Finite Element Analysis and Its Actualization
Directory of Open Access Journals (Sweden)
Lei Zhang
2013-01-01
Full Text Available In parallel computing based on finite element analysis, domain decomposition is a key technique for its preprocessing. Generally, a domain decomposition of a mesh can be realized through partitioning of a graph which is converted from a finite element mesh. This paper discusses the method for graph partitioning and the way to actualize mesh partitioning. Relevant softwares are introduced, and the data structure and key functions of Metis and ParMetis are introduced. The writing, compiling, and testing of the mesh partitioning interface program based on these key functions are performed. The results indicate some objective law and characteristics to guide the users who use the graph partitioning algorithm and software to write PFEM program, and ideal partitioning effects can be achieved by actualizing mesh partitioning through the program. The interface program can also be used directly by the engineering researchers as a module of the PFEM software. So that it can reduce the application of the threshold of graph partitioning algorithm, improve the calculation efficiency, and promote the application of graph theory and parallel computing.
International Nuclear Information System (INIS)
Nakamachi, Eiji
2005-01-01
A crystallographic homogenization procedure is introduced to the conventional static-explicit and dynamic-explicit finite element formulation to develop a multi scale - double scale - analysis code to predict the plastic strain induced texture evolution, yield loci and formability of sheet metal. The double-scale structure consists of a crystal aggregation - micro-structure - and a macroscopic elastic plastic continuum. At first, we measure crystal morphologies by using SEM-EBSD apparatus, and define a unit cell of micro structure, which satisfy the periodicity condition in the real scale of polycrystal. Next, this crystallographic homogenization FE code is applied to 3N pure-iron and 'Benchmark' aluminum A6022 polycrystal sheets. It reveals that the initial crystal orientation distribution - the texture - affects very much to a plastic strain induced texture and anisotropic hardening evolutions and sheet deformation. Since, the multi-scale finite element analysis requires a large computation time, a parallel computing technique by using PC cluster is developed for a quick calculation. In this parallelization scheme, a dynamic workload balancing technique is introduced for quick and efficient calculations
A study of unstable rock failures using finite difference and discrete element methods
Garvey, Ryan J.
Case histories in mining have long described pillars or faces of rock failing violently with an accompanying rapid ejection of debris and broken material into the working areas of the mine. These unstable failures have resulted in large losses of life and collapses of entire mine panels. Modern mining operations take significant steps to reduce the likelihood of unstable failure, however eliminating their occurrence is difficult in practice. Researchers over several decades have supplemented studies of unstable failures through the application of various numerical methods. The direction of the current research is to extend these methods and to develop improved numerical tools with which to study unstable failures in underground mining layouts. An extensive study is first conducted on the expression of unstable failure in discrete element and finite difference methods. Simulated uniaxial compressive strength tests are run on brittle rock specimens. Stable or unstable loading conditions are applied onto the brittle specimens by a pair of elastic platens with ranging stiffnesses. Determinations of instability are established through stress and strain histories taken for the specimen and the system. Additional numerical tools are then developed for the finite difference method to analyze unstable failure in larger mine models. Instability identifiers are established for assessing the locations and relative magnitudes of unstable failure through measures of rapid dynamic motion. An energy balance is developed which calculates the excess energy released as a result of unstable equilibria in rock systems. These tools are validated through uniaxial and triaxial compressive strength tests and are extended to models of coal pillars and a simplified mining layout. The results of the finite difference simulations reveal that the instability identifiers and excess energy calculations provide a generalized methodology for assessing unstable failures within potentially complex
Farrell, L. L.; McGovern, P. J.; Morgan, J. K.
2008-12-01
We have carried out 2-D numerical simulations using the discrete element method (DEM) to investigate density-driven deformation in volcanic edifices on Earth (e.g., Hawaii) and Mars (e.g., Olympus Mons and Arsia Mons). Located within volcanoes are series of magma chambers, reservoirs, and conduits where magma travels and collects. As magma differentiates, dense minerals settle out, building thick accumulations referred to as cumulates that can flow ductilely due to stresses imparted by gravity. To simulate this process, we construct granular piles subject to Coulomb frictional rheology, incrementally capture internal rectangular regions to which higher densities and lower interparticle friction values are assigned (analogs for denser, weaker cumulates), and then bond the granular edifice. Thus, following each growth increment, the edifice is allowed to relax gravitationally with a reconfigured weak cumulate core. The presence and outward spreading of the cumulate causes the development of distinctive structural and stratigraphic patterns. We obtained a range of volcanic shapes that vary from broad, shallowly dipping flanks reminiscent of those of Olympus Mons, to short, steep surface slopes more similar to Arsia Mons. Edifices lacking internal cumulate exhibit relatively horizontal strata compared to the high-angle, inward dipping strata that develops within the cumulate-bearing edifices. Our simulated volcanoes also illustrate a variety of gravity driven deformation features, including regions of thrust faulting within the flanks and large-scale flank collapses, as observed in Hawaii and inferred on Olympus Mons. We also see significant summit subsidence, and of particular interest, distinct summit calderas. The broad, flat caldera and convex upward profile of Arsia Mons appears to be well-simulated by cumulate-driven volcanic spreading. In contrast, the concave upward slopes of Olympus Mons are more challenging to reproduce, and instead are attributed to volcanic
Discrete element simulation studies of angles of repose and shear flow of wet, flexible fibers.
Guo, Y; Wassgren, C; Ketterhagen, W; Hancock, B; Curtis, J
2018-04-18
A discrete element method (DEM) model is developed to simulate the dynamics of wet, flexible fibers. The angles of repose of dry and wet fibers are simulated, and the simulation results are in good agreement with experimental results, validating the wet, flexible fiber model. To study wet fiber flow behavior, the model is used to simulate shear flows of wet fibers in a periodic domain under Lees-Edwards boundary conditions. Significant agglomeration is observed in dilute shear flows of wet fibers. The size of the largest agglomerate in the flow is found to depend on a Bond number, which is proportional to liquid surface tension and inversely proportional to the square of the shear strain rate. This Bond number reflects the relative importance of the liquid-bridge force to the particle's inertial force, with a larger Bond number leading to a larger agglomerate. As the fiber aspect ratio (AR) increases, the size of the largest agglomerate increases, while the coordination number in the largest agglomerate initially decreases and then increases when the AR is greater than four. A larger agglomerate with a larger coordination number is more likely to form for more flexible fibers with a smaller bond elastic modulus due to better connectivity between the more flexible fibers. Liquid viscous force resists pulling of liquid bridges and separation of contacting fibers, and therefore it facilitates larger agglomerate formation. The effect of liquid viscous force is more significant at larger shear strain rates. The solid-phase shear stress is increased due to the presence of liquid bridges in moderately dense flows. As the solid volume fraction increases, the effect of fiber-fiber friction coefficient increases sharply. When the solid volume fraction approaches the maximum packing density, the fiber-fiber friction coefficient can be a more dominant factor than the liquid bridge force in determining the solid-phase shear stress.
Discrete Element Modeling of the Mobilization of Coarse Gravel Beds by Finer Gravel Particles
Hill, K. M.; Tan, D.
2012-12-01
Recent research has shown that the addition of fine gravel particles to a coarse bed will mobilize the coarser bed, and that the effect is sufficiently strong that a pulse of fine gravel particles can mobilize an impacted coarser bed. Recent flume experiments have demonstrated that the degree of bed mobilization by finer particles is primarily dependent on the particle size ratio of the coarse and fine particles, rather than absolute size of either particle, provided both particles are sufficiently large. However, the mechanism behind the mobilization is not understood. It has previously been proposed that the mechanism is driven by a combination of geometric effects and hydraulic effects. For example, it has been argued that smaller particles fill in gaps along the bed, resulting in a smoother bed over which the larger particles are less likely to be disentrained and a reduced near-bed flow velocity and subsequent increased drag on protruding particles. Altered near-bed turbulence has also been cited as playing an important role. We perform simulations using the discrete element method with one-way fluid-solid coupling to conduct simulations of mobilization of a gravel bed by fine gravel particles. By independently and artificially controlling average and fluctuating velocity profiles, we systematically investigate the relative role that may be played by particle-particle interactions, average near-bed velocity profiles, and near-bed turbulence statistics. The simulations indicate that the relative importance of these mechanisms changes with the degree of mobilization of the bed. For higher bed mobility similar to bed sheets, particle-particle interactions, plays a significant role in an apparent rheology in the bed sheets, not unlike that observed in a dense granular flow of particles of different sizes. For conditions closer to a critical shear stress for bedload transport, the near-bed velocity profiles and turbulence statistics become increasingly important.
Efficiency determination of an electrostatic lunar dust collector by discrete element method
Afshar-Mohajer, Nima; Wu, Chang-Yu; Sorloaica-Hickman, Nicoleta
2012-07-01
Lunar grains become charged by the sun's radiation in the tenuous atmosphere of the moon. This leads to lunar dust levitation and particle deposition which often create serious problems in the costly system deployed in lunar exploration. In this study, an electrostatic lunar dust collector (ELDC) is proposed to address the issue and the discrete element method (DEM) is used to investigate the effects of electrical particle-particle interactions, non-uniformity of the electrostatic field, and characteristics of the ELDC. The simulations on 20-μm-sized lunar particles reveal the electrical particle-particle interactions of the dust particles within the ELDC plates require 29% higher electrostatic field strength than that without the interactions for 100% collection efficiency. For the given ELDC geometry, consideration of non-uniformity of the electrostatic field along with electrical interactions between particles on the same ELDC geometry leads to a higher requirement of ˜3.5 kV/m to ensure 100% particle collection. Notably, such an electrostatic field is about 103 times less than required for electrodynamic self-cleaning methods. Finally, it is shown for a "half-size" system that the DEM model predicts greater collection efficiency than the Eulerian-based model at all voltages less than required for 100% efficiency. Halving the ELDC dimensions boosts the particle concentration inside the ELDC, as well as the resulting field strength for a given voltage. Though a lunar photovoltaic system was the subject, the results of this study are useful for evaluation of any system for collecting charged particles in other high vacuum environment using an electrostatic field.
Koester, Martin; García, R Edwin; Thommes, Markus
2014-12-30
Spheronization is an important pharmaceutical manufacturing technique to produce spherical agglomerates of 0.5-2mm diameter. These pellets have a narrow size distribution and a spherical shape. During the spheronization process, the extruded cylindrical strands break in short cylinders and evolve from a cylindrical to a spherical state by deformation and attrition/agglomeration mechanisms. Using the discrete element method, an integrated modeling-experimental framework is presented, that captures the particle motion during the spheronization process. Simulations were directly compared and validated against particle image velocimetry (PIV) experiments with monodisperse spherical and dry γ-Al2O3 particles. demonstrate a characteristic torus like flow pattern, with particle velocities about three times slower than the rotation speed of the friction plate. Five characteristic zones controlling the spheronization process are identified: Zone I, where particles undergo shear forces that favors attrition and contributes material to the agglomeration process; Zone II, where the static wall contributes to the mass exchange between particles; Zone III, where gravitational forces combined with particle motion induce particles to collide with the moving plate and re-enter Zone I; Zone IV, where a subpopulation of particles are ejected into the air when in contact with the friction plate structure; and Zone V where the low poloidal velocity favors a stagnant particle population and is entirely controlled by the batch size. These new insights in to the particle motion are leading to deeper process understanding, e.g., the effect of load and rotation speed to the pellet formation kinetics. This could be beneficial for the optimization of a manufacturing process as well as for the development of new formulations. Copyright © 2014 Elsevier B.V. All rights reserved.
International Nuclear Information System (INIS)
Andre, Damien; Iordanoff, Ivan; Charles, Jean-luc; Jebahi, Mohamed; Neauport, Jerome
2013-01-01
The mechanical behavior of materials is usually simulated by a continuous mechanics approach. However, non-continuous phenomena such as multi-fracturing cannot be accurately simulated using a continuous description. The discrete element method (DEM) naturally accounts for discontinuities and is therefore a good alternative to the continuum approach. This work uses a discrete element model based on interaction given by 3D beam model. This model has proved to correctly simulate the elastic properties at the macroscopic scale. The simulation of brittle cracks is now tackled. This goal is attained by computing a failure criterion based on an equivalent hydrostatic stress. This microscopic criterion is then calibrated to fit experimental values of the macroscopic failure stress. Then, the simulation results are compared to experimental results of indentation tests in which a spherical indenter is used to load a silica glass, which is considered to be a perfectly brittle elastic material. (authors)
Bosch, Jessica; Stoll, Martin; Benner, Peter
2014-01-01
We consider the efficient solution of the Cahn-Hilliard variational inequality using an implicit time discretization, which is formulated as an optimal control problem with pointwise constraints on the control. By applying a semi-smooth Newton
Jan Nečas; Jakub Hlosta; David Žurovec; Martin Žídek; Jiří Rozbroj; Jiří Zegzulka
2017-01-01
This paper describes optimisation of a conveyor from an underground hopper intended for a coal transfer station. The original solution was designed with a chain conveyor encountered operational problems that have limited its continuous operation. The Discrete Element Modeling (DEM) was chosen to optimise the transport. DEM simulations allow device design modifications directly in the 3D CAD model, and then the simulation makes it possible to evaluate whether the adjustment was successful. By...
International Nuclear Information System (INIS)
Lorence, L.J. Jr.; Martin, W.R.; Luskin, M.
1985-01-01
We prove the convergence of a finite element discretization of the neutron transport equation. The iterative solution of the resulting linear system by a block Gauss-Seidel method is also analyzed. This procedure is shown to require less storage than the direct solution by Gaussian elimination, and an estimate for the rate of convergence is used to show that fewer arithmetic operations are required
International Nuclear Information System (INIS)
Liu Wenyan; Tang, Z.P.; Liu Yunxin
2000-01-01
In recent years, more attention has been paid to a better understanding of the failure behavior and mechanism of heterogeneous materials at the meso-scale level. In this paper, the crack initiation and development in epoxy composites reinforced with short steel fibers under dynamic loading were simulated and analyzed with the 2D Discrete Meso-Element Dynamic Method. Results show that the damage process depends greatly on the binding property between matrix and fibers
Makedonska, N.; Sparks, D. W.; Aharonov, E.
2012-12-01
Pressure solution (also termed chemical compaction) is considered the most important ductile deformation mechanism operating in the Earth's upper crust. This mechanism is a major player in a variety of geological processes, including evolution of sedimentary basins, hydrocarbon reservoirs, aquifers, earthquake recurrence cycles, and fault healing. Pressure solution in massive rocks often localizes into solution seams or stylolites. Field observations of stylolites often show elastic/brittle interactions in regions between pressure solution features, including and shear fractures, veins and pull-apart features. To understand these interactions, we use a grain-scale model based on the Discrete Element Method that allows granular dissolution at stressed contacts between grains. The new model captures both the slow chemical compaction process and the more abrupt brittle fracturing and sliding between grains. We simulate a sample of rock as a collection of particles, each representing either a grain or a unit of rock, bonded to each other with breakable cement. We apply external stresses to this sample, and calculate elastic and frictional interactions between the grains. Dissolution is modeled by an irreversible penetration of contacting grains into each other at a rate that depends on the contact stress and an adjustable rate constant. Experiments have shown that dissolution rates at grain contacts are greatly enhanced when there is a mineralogical contrast. Therefore, we dissolution rate constant can be increased to account for an amount of impurities (e.g. clay in a quartz or calcite sandstone) that can accumulate on dissolving contacts. This approach allows large compaction and shear strains within the rock, while allowing examination of local grain-scale heterogeneity. For example, we will describe the effect of pressure solution on the distribution of contact forces magnitudes and orientations. Contact forces in elastic granular packings are inherently
Fish passage through hydropower turbines: Simulating blade strike using the discrete element method
International Nuclear Information System (INIS)
Richmond, M C; Romero-Gomez, P
2014-01-01
Among the hazardous hydraulic conditions affecting anadromous and resident fish during their passage though hydro-turbines two common physical processes can lead to injury and mortality: collisions/blade-strike and rapid decompression. Several methods are currently available to evaluate these stressors in installed turbines, e.g. using live fish or autonomous sensor devices, and in reduced-scale physical models, e.g. registering collisions from plastic beads. However, a priori estimates with computational modeling approaches applied early in the process of turbine design can facilitate the development of fish-friendly turbines. In the present study, we evaluated the frequency of blade strike and rapid pressure change by modeling potential fish trajectories with the Discrete Element Method (DEM) applied to fish-like composite particles. In the DEM approach, particles are subjected to realistic hydraulic conditions simulated with computational fluid dynamics (CFD), and particle-structure interactions-representing fish collisions with turbine components such as blades-are explicitly recorded and accounted for in the calculation of particle trajectories. We conducted transient CFD simulations by setting the runner in motion and allowing for unsteady turbulence using detached eddy simulation (DES), as compared to the conventional practice of simulating the system in steady state (which was also done here for comparison). While both schemes yielded comparable bulk hydraulic performance values, transient conditions exhibited an improvement in describing flow temporal and spatial variability. We released streamtraces (in the steady flow solution) and DEM particles (transient solution) at the same locations where sensor fish (SF) were released in previous field studies of the advanced turbine unit. The streamtrace- based results showed a better agreement with SF data than the DEM-based nadir pressures did because the former accounted for the turbulent dispersion at the
International Nuclear Information System (INIS)
Ferdowsi, B.
2014-01-01
Recent seismological observations based on new, more sensitive instrumentation show that seismic waves radiated from large earthquakes can trigger other earthquakes globally. This phenomenon is called dynamic earthquake triggering and is well-documented for over 30 of the largest earthquakes worldwide. Granular materials are at the core of mature earthquake faults and play a key role in fault triggering by exhibiting a rich nonlinear response to external perturbations. The stick-slip dynamics in sheared granular layers is analogous to the seismic cycle for earthquake fault systems. In this research effort, we characterize the macroscopic scale statistics and the grain-scale mechanisms of triggered slip in sheared granular layers. We model the granular fault gouge using three dimensional discrete element method simulations. The modeled granular system is put into stick-slip dynamics by applying a conning pressure and a shear load. The dynamic triggering is simulated by perturbing the spontaneous stick-slip dynamics using an external vibration applied to the boundary of the layer. The influences of the triggering consist in a frictional weakening during the vibration interval, a clock advance of the next expected large slip event and long term effects in the form of suppression and recovery of the energy released from the granular layer. Our study suggests that above a critical amplitude, vibration causes a significant clock advance of large slip events. We link this clock advance to a major decline in the slipping contact ratio as well as a decrease in shear modulus and weakening of the granular gouge layer. We also observe that shear vibration is less effective in perturbing the stick-slip dynamics of the granular layer. Our study suggests that in order to have an effective triggering, the input vibration must also explore the granular layer at length scales about or less than the average grain size. The energy suppression and the subsequent recovery and increased
Tsamados, Michel; Heorton, Harry; Feltham, Daniel; Muir, Alan; Baker, Steven
2016-04-01
The new elastic-plastic anisotropic (EAP) rheology that explicitly accounts for the sub-continuum anisotropy of the sea ice cover has been implemented into the latest version of the Los Alamos sea ice model CICE. The EAP rheology is widely used in the climate modeling scientific community (i.e. CPOM stand alone, RASM high resolution regional ice-ocean model, MetOffice fully coupled model). Early results from sensitivity studies (Tsamados et al, 2013) have shown the potential for an improved representation of the observed main sea ice characteristics with a substantial change of the spatial distribution of ice thickness and ice drift relative to model runs with the reference visco-plastic (VP) rheology. The model contains one new prognostic variable, the local structure tensor, which quantifies the degree of anisotropy of the sea ice, and two parameters that set the time scale of the evolution of this tensor. Observations from high resolution satellite SAR imagery as well as numerical simulation results from a discrete element model (DEM, see Wilchinsky, 2010) have shown that these individual floes can organize under external wind and thermal forcing to form an emergent isotropic sea ice state (via thermodynamic healing, thermal cracking) or an anisotropic sea ice state (via Coulombic failure lines due to shear rupture). In this work we use for the first time in the context of sea ice research a mathematical metric, the Tensorial Minkowski functionals (Schroeder-Turk, 2010), to measure quantitatively the degree of anisotropy and alignment of the sea ice at different scales. We apply the methodology on the GlobICE Envisat satellite deformation product (www.globice.info), on a prototype modified version of GlobICE applied on Sentinel-1 Synthetic Aperture Radar (SAR) imagery and on the DEM ice floe aggregates. By comparing these independent measurements of the sea ice anisotropy as well as its temporal evolution against the EAP model we are able to constrain the
Byun, Chansup; Guruswamy, Guru P.; Kutler, Paul (Technical Monitor)
1994-01-01
In recent years significant advances have been made for parallel computers in both hardware and software. Now parallel computers have become viable tools in computational mechanics. Many application codes developed on conventional computers have been modified to benefit from parallel computers. Significant speedups in some areas have been achieved by parallel computations. For single-discipline use of both fluid dynamics and structural dynamics, computations have been made on wing-body configurations using parallel computers. However, only a limited amount of work has been completed in combining these two disciplines for multidisciplinary applications. The prime reason is the increased level of complication associated with a multidisciplinary approach. In this work, procedures to compute aeroelasticity on parallel computers using direct coupling of fluid and structural equations will be investigated for wing-body configurations. The parallel computer selected for computations is an Intel iPSC/860 computer which is a distributed-memory, multiple-instruction, multiple data (MIMD) computer with 128 processors. In this study, the computational efficiency issues of parallel integration of both fluid and structural equations will be investigated in detail. The fluid and structural domains will be modeled using finite-difference and finite-element approaches, respectively. Results from the parallel computer will be compared with those from the conventional computers using a single processor. This study will provide an efficient computational tool for the aeroelastic analysis of wing-body structures on MIMD type parallel computers.
International Nuclear Information System (INIS)
Lu Yujie; Zhu Banghe; Rasmussen, John C; Sevick-Muraca, Eva M; Shen Haiou; Wang Ge
2010-01-01
Fluorescence molecular imaging/tomography may play an important future role in preclinical research and clinical diagnostics. Time- and frequency-domain fluorescence imaging can acquire more measurement information than the continuous wave (CW) counterpart, improving the image quality of fluorescence molecular tomography. Although diffusion approximation (DA) theory has been extensively applied in optical molecular imaging, high-order photon migration models need to be further investigated to match quantitation provided by nuclear imaging. In this paper, a frequency-domain parallel adaptive finite element solver is developed with simplified spherical harmonics (SP N ) approximations. To fully evaluate the performance of the SP N approximations, a fast time-resolved tetrahedron-based Monte Carlo fluorescence simulator suitable for complex heterogeneous geometries is developed using a convolution strategy to realize the simulation of the fluorescence excitation and emission. The validation results show that high-order SP N can effectively correct the modeling errors of the diffusion equation, especially when the tissues have high absorption characteristics or when high modulation frequency measurements are used. Furthermore, the parallel adaptive mesh evolution strategy improves the modeling precision and the simulation speed significantly on a realistic digital mouse phantom. This solver is a promising platform for fluorescence molecular tomography using high-order approximations to the radiative transfer equation.
A parallel direct solver for the self-adaptive hp Finite Element Method
Paszyński, Maciej R.
2010-03-01
In this paper we present a new parallel multi-frontal direct solver, dedicated for the hp Finite Element Method (hp-FEM). The self-adaptive hp-FEM generates in a fully automatic mode, a sequence of hp-meshes delivering exponential convergence of the error with respect to the number of degrees of freedom (d.o.f.) as well as the CPU time, by performing a sequence of hp refinements starting from an arbitrary initial mesh. The solver constructs an initial elimination tree for an arbitrary initial mesh, and expands the elimination tree each time the mesh is refined. This allows us to keep track of the order of elimination for the solver. The solver also minimizes the memory usage, by de-allocating partial LU factorizations computed during the elimination stage of the solver, and recomputes them for the backward substitution stage, by utilizing only about 10% of the computational time necessary for the original computations. The solver has been tested on 3D Direct Current (DC) borehole resistivity measurement simulations problems. We measure the execution time and memory usage of the solver over a large regular mesh with 1.5 million degrees of freedom as well as on the highly non-regular mesh, generated by the self-adaptive h p-FEM, with finite elements of various sizes and polynomial orders of approximation varying from p = 1 to p = 9. From the presented experiments it follows that the parallel solver scales well up to the maximum number of utilized processors. The limit for the solver scalability is the maximum sequential part of the algorithm: the computations of the partial LU factorizations over the longest path, coming from the root of the elimination tree down to the deepest leaf. © 2009 Elsevier Inc. All rights reserved.
A fractional model with parallel fractional Maxwell elements for amorphous thermoplastics
Lei, Dong; Liang, Yingjie; Xiao, Rui
2018-01-01
We develop a fractional model to describe the thermomechanical behavior of amorphous thermoplastics. The fractional model is composed of two parallel fractional Maxwell elements. The first fractional Maxwell model is used to describe the glass transition, while the second component is aimed at describing the viscous flow. We further derive the analytical solutions for the stress relaxation modulus and complex modulus through Laplace transform. We then demonstrate the model is able to describe the master curves of the stress relaxation modulus, storage modulus and loss modulus, which all show two distinct transition regions. The obtained parameters show that the modulus of the two fractional Maxwell elements differs in 2-3 orders of magnitude, while the relaxation time differs in 7-9 orders of magnitude. Finally, we apply the model to describe the stress response of constant strain rate tests. The model, together with the parameters obtained from fitting the master curve of stress relaxation modulus, can accurately predict the temperature and strain rate dependent stress response.
Fourier two-level analysis for discontinuous Galerkin discretization with linear elements
P.W. Hemker (Piet); W. Hoffmann; M.H. van Raalte (Marc)
2002-01-01
textabstractIn this paper we study the convergence of a multigrid method for the solution of a linear second order elliptic equation, discretized by discontinuous Galerkin (DG) methods, and we give a detailed analysis of the convergence fordifferent block-relaxation strategies. In addition to an
Discrete element modeling approach to porosimetry for durability risk estimation of concrete
Stroeven, P.; Le, N.L.B.; Stroeven, M.; Sluys, L.J.
2011-01-01
The paper introduces a novel approach to porosimetry in virtual concrete, denoted as random node structuring (RNS). The fresh state of this particulate material is produced by the DEM system HADES. Hydration simulation is a hybrid approach making use of wellknown discretization and vector methods.
CSIR Research Space (South Africa)
Govender, Nicolin
2015-09-01
Full Text Available consideration due to the architectural differences between CPU and GPU platforms. This paper describes the DEM algorithms and heuristics that are optimized for the parallel NVIDIA Kepler GPU architecture in detail. This includes a GPU optimized collision...
Discrete element method based scale-up model for material synthesis using ball milling
Santhanam, Priya Radhi
Mechanical milling is a widely used technique for powder processing in various areas. In this work, a scale-up model for describing this ball milling process is developed. The thesis is a combination of experimental and modeling efforts. Initially, Discrete Element Model (DEM) is used to describe energy transfer from milling tools to the milled powder for shaker, planetary, and attritor mills. The rolling and static friction coefficients are determined experimentally. Computations predict a quasisteady rate of energy dissipation, E d, for each experimental configuration. It is proposed that the milling dose defined as a product of Ed and milling time, t, divided by the mass of milled powder, mp characterizes the milling progress independently of the milling device or milling conditions used. Once the milling dose is determined for one experimental configuration, it can be used to predict the milling time required to prepare the same material in any milling configuration, for which Ed is calculated. The concept is validated experimentally for DEM describing planetary and shaker mills. For attritor, the predicted Ed includes substantial contribution from milling tool interaction events with abnormally high forces (>103 N). The energy in such events is likely dissipated to heat or plastically deform milling tools rather than refine material. Indeed, DEM predictions for the attritor correlate with experiments when such events are ignored in the analysis. With an objective of obtaining real-time indicators of milling progress, power, torque, and rotation speed of the impeller of an attritor mill are measured during preparation of metal matrix composite powders in the subsequent portion of this thesis. Two material systems are selected and comparisons made between in-situ parameters and experimental milling progress indicators. It is established that real-time measurements can certainly be used to describe milling progress. However, they need to be interpreted carefully
Hancock, W.; Weatherley, D.; Wruck, B.; Chitombo, G. P.
2012-04-01
The flow dynamics of granular materials is of broad interest in both the geosciences (e.g. landslides, fault zone evolution, and brecchia pipe formation) and many engineering disciplines (e.g chemical engineering, food sciences, pharmaceuticals and materials science). At the interface between natural and human-induced granular media flow, current underground mass-mining methods are trending towards the induced failure and subsequent gravitational flow of large volumes of broken rock, a method known as cave mining. Cave mining relies upon the undercutting of a large ore body, inducement of fragmentation of the rock and subsequent extraction of ore from below, via hopper-like outlets. Design of such mines currently relies upon a simplified kinematic theory of granular flow in hoppers, known as the ellipsoid theory of mass movement. This theory assumes that the zone of moving material grows as an ellipsoid above the outlet of the silo. The boundary of the movement zone is a shear band and internal to the movement zone, the granular material is assumed to have a uniformly high bulk porosity compared with surrounding stagnant regions. There is however, increasing anecdotal evidence and field measurements suggesting this theory fails to capture the full complexity of granular material flow within cave mines. Given the practical challenges obstructing direct measurement of movement both in laboratory experiments and in-situ, the Discrete Element Method (DEM [1]) is a popular alternative to investigate granular media flow. Small-scale DEM studies (c.f. [3] and references therein) have confirmed that movement within DEM silo flow models matches that predicted by ellipsoid theory, at least for mono-disperse granular material freely outflowing at a constant rate. A major draw-back of these small-scale DEM studies is that the initial bulk porosity of the simulated granular material is significantly higher than that of broken, prismatic rock. In this investigation, more
Zampini, Stefano; Keyes, David E.
2016-01-01
Balancing Domain Decomposition by Constraints (BDDC) methods have proven to be powerful preconditioners for large and sparse linear systems arising from the finite element discretization of elliptic PDEs. Condition number bounds can be theoretically
Directory of Open Access Journals (Sweden)
J. Ochoa-Avendaño
2017-01-01
Full Text Available This paper presents the formulation, implementation, and validation of a simplified qualitative model to determine the crack path of solids considering static loads, infinitesimal strain, and plane stress condition. This model is based on finite element method with a special meshing technique, where nonlinear link elements are included between the faces of the linear triangular elements. The stiffness loss of some link elements represents the crack opening. Three experimental tests of bending beams are simulated, where the cracking pattern calculated with the proposed numerical model is similar to experimental result. The advantages of the proposed model compared to discrete crack approaches with interface elements can be the implementation simplicity, the numerical stability, and the very low computational cost. The simulation with greater values of the initial stiffness of the link elements does not affect the discontinuity path and the stability of the numerical solution. The exploded mesh procedure presented in this model avoids a complex nonlinear analysis and regenerative or adaptive meshes.
DEFF Research Database (Denmark)
Feng, Huan; Pettinari, Matteo; Stang, Henrik
2016-01-01
modulus. Three different approaches have been used and compared for calibrating the Burger's contact model. Values of the dynamic modulus and phase angle of asphalt mixtures were predicted by conducting DE simulation under dynamic strain control loading. The excellent agreement between the predicted......In this paper the viscoelastic behavior of asphalt mixture was investigated by employing a three-dimensional discrete element method. Combined with Burger's model, three contact models were used for the construction of constitutive asphalt mixture model with viscoelastic properties...
Monteiro, André O.; Da Costa, Pedro M. F. J.; Cachim, Paulo Barreto
2013-01-01
The mechanical response to a uniaxial compressive force of a single carbon nanotube (CNT) filled (or partially-filled) with ZnS has been modelled. A semi-empirical approach based on the finite element method was used whereby modelling outcomes were closely matched to experimental observations. This is the first example of the use of the continuum approach to model the mechanical behaviour of discrete filled CNTs. In contrast to more computationally demanding methods such as density functional theory or molecular dynamics, our approach provides a viable and expedite alternative to model the mechanics of filled multi-walled CNTs. © 2013 Springer Science+Business Media New York.
Monteiro, André O.
2013-09-25
The mechanical response to a uniaxial compressive force of a single carbon nanotube (CNT) filled (or partially-filled) with ZnS has been modelled. A semi-empirical approach based on the finite element method was used whereby modelling outcomes were closely matched to experimental observations. This is the first example of the use of the continuum approach to model the mechanical behaviour of discrete filled CNTs. In contrast to more computationally demanding methods such as density functional theory or molecular dynamics, our approach provides a viable and expedite alternative to model the mechanics of filled multi-walled CNTs. © 2013 Springer Science+Business Media New York.
Matuttis, Hans-Georg
2014-01-01
Gives readers a more thorough understanding of DEM and equips researchers for independent work and an ability to judge methods related to simulation of polygonal particles Introduces DEM from the fundamental concepts (theoretical mechanics and solidstate physics), with 2D and 3D simulation methods for polygonal particlesProvides the fundamentals of coding discrete element method (DEM) requiring little advance knowledge of granular matter or numerical simulationHighlights the numerical tricks and pitfalls that are usually only realized after years of experience, with relevant simple experiment
Feasibility Study of Parallel Finite Element Analysis on Cluster-of-Clusters
Muraoka, Masae; Okuda, Hiroshi
With the rapid growth of WAN infrastructure and development of Grid middleware, it's become a realistic and attractive methodology to connect cluster machines on wide-area network for the execution of computation-demanding applications. Many existing parallel finite element (FE) applications have been, however, designed and developed with a single computing resource in mind, since such applications require frequent synchronization and communication among processes. There have been few FE applications that can exploit the distributed environment so far. In this study, we explore the feasibility of FE applications on the cluster-of-clusters. First, we classify FE applications into two types, tightly coupled applications (TCA) and loosely coupled applications (LCA) based on their communication pattern. A prototype of each application is implemented on the cluster-of-clusters. We perform numerical experiments executing TCA and LCA on both the cluster-of-clusters and a single cluster. Thorough these experiments, by comparing the performances and communication cost in each case, we evaluate the feasibility of FEA on the cluster-of-clusters.
Directory of Open Access Journals (Sweden)
Pavel A. Akimov
2017-12-01
Full Text Available As is well known, the formulation of a multipoint boundary problem involves three main components: a description of the domain occupied by the structure and the corresponding subdomains; description of the conditions inside the domain and inside the corresponding subdomains, the description of the conditions on the boundary of the domain, conditions on the boundaries between subdomains. This paper is a continuation of another work published earlier, in which the formulation and general principles of the approximation of the multipoint boundary problem of a static analysis of deep beam on the basis of the joint application of the finite element method and the discrete-continual finite element method were considered. It should be noted that the approximation within the fragments of a domain that have regular physical-geometric parameters along one of the directions is expedient to be carried out on the basis of the discrete-continual finite element method (DCFEM, and for the approximation of all other fragments it is necessary to use the standard finite element method (FEM. In the present publication, the formulas for the computing of displacements partial derivatives of displacements, strains and stresses within the finite element model (both within the finite element and the corresponding nodal values (with the use of averaging are presented. Boundary conditions between subdomains (respectively, discrete models and discrete-continual models and typical conditions such as “hinged support”, “free edge”, “perfect contact” (twelve basic (basic variants are available are under consideration as well. Governing formulas for computing of elements of the corresponding matrices of coefficients and vectors of the right-hand sides are given for each variant. All formulas are fully adapted for algorithmic implementation.
Discrete conservation properties for shallow water flows using mixed mimetic spectral elements
Lee, D.; Palha, A.; Gerritsma, M.
2018-01-01
A mixed mimetic spectral element method is applied to solve the rotating shallow water equations. The mixed method uses the recently developed spectral element histopolation functions, which exactly satisfy the fundamental theorem of calculus with respect to the standard Lagrange basis functions in
Bosch, Jessica
2014-04-01
We consider the efficient solution of the Cahn-Hilliard variational inequality using an implicit time discretization, which is formulated as an optimal control problem with pointwise constraints on the control. By applying a semi-smooth Newton method combined with a Moreau-Yosida regularization technique for handling the control constraints we show superlinear convergence in function space. At the heart of this method lies the solution of large and sparse linear systems for which we propose the use of preconditioned Krylov subspace solvers using an effective Schur complement approximation. Numerical results illustrate the competitiveness of this approach. © 2014 Elsevier Inc.
Directory of Open Access Journals (Sweden)
Akimov Pavel
2016-01-01
Full Text Available The distinctive paper is devoted to the two-dimensional semi-analytical solution of boundary problems of analysis of shear walls with the use of discrete-continual finite element method (DCFEM. This approach allows obtaining the exact analytical solution in one direction (so-called “basic” direction, also decrease the size of the problem to one-dimensional common finite element analysis. The resulting multipoint boundary problem for the first-order system of ordinary differential equations with piecewise constant coefficients is solved analytically. The proposed method is rather efficient for evaluation of the boundary effect (such as the stress field near the concentrated force. DCFEM also has a completely computer-oriented algorithm, computational stability, optimal conditionality of resultant system and it is applicable for the various loads at an arbitrary point or a region of the wall.
Vescovi, D.; Berzi, D.; Richard, P.; Brodu, N.
2014-05-01
We use existing 3D Discrete Element simulations of simple shear flows of spheres to evaluate the radial distribution function at contact that enables kinetic theory to correctly predict the pressure and the shear stress, for different values of the collisional coefficient of restitution. Then, we perform 3D Discrete Element simulations of plane flows of frictionless, inelastic spheres, sheared between walls made bumpy by gluing particles in a regular array, at fixed average volume fraction and distance between the walls. The results of the numerical simulations are used to derive boundary conditions appropriated in the cases of large and small bumpiness. Those boundary conditions are, then, employed to numerically integrate the differential equations of Extended Kinetic Theory, where the breaking of the molecular chaos assumption at volume fraction larger than 0.49 is taken into account in the expression of the dissipation rate. We show that the Extended Kinetic Theory is in very good agreement with the numerical simulations, even for coefficients of restitution as low as 0.50. When the bumpiness is increased, we observe that some of the flowing particles are stuck in the gaps between the wall spheres. As a consequence, the walls are more dissipative than expected, and the flows resemble simple shear flows, i.e., flows of rather constant volume fraction and granular temperature.
International Nuclear Information System (INIS)
Vescovi, D.; Berzi, D.; Richard, P.; Brodu, N.
2014-01-01
We use existing 3D Discrete Element simulations of simple shear flows of spheres to evaluate the radial distribution function at contact that enables kinetic theory to correctly predict the pressure and the shear stress, for different values of the collisional coefficient of restitution. Then, we perform 3D Discrete Element simulations of plane flows of frictionless, inelastic spheres, sheared between walls made bumpy by gluing particles in a regular array, at fixed average volume fraction and distance between the walls. The results of the numerical simulations are used to derive boundary conditions appropriated in the cases of large and small bumpiness. Those boundary conditions are, then, employed to numerically integrate the differential equations of Extended Kinetic Theory, where the breaking of the molecular chaos assumption at volume fraction larger than 0.49 is taken into account in the expression of the dissipation rate. We show that the Extended Kinetic Theory is in very good agreement with the numerical simulations, even for coefficients of restitution as low as 0.50. When the bumpiness is increased, we observe that some of the flowing particles are stuck in the gaps between the wall spheres. As a consequence, the walls are more dissipative than expected, and the flows resemble simple shear flows, i.e., flows of rather constant volume fraction and granular temperature
Discrete element method applied to the vibration process of coke particles
Majidi, Behzad
2012-01-01
Les propriétés physiques, mécaniques et chimiques des matières premières ont un effet majeur sur la qualité des anodes en carbone pour le procédé de production d’aluminium. Ce travail tente d’étudier la faisabilité de l’application de simulation de la Méthode des Élément Discrets (DEM) à la technologie de production d’anodes. L’effet de la forme des particules et de la distribution de leurs tailles sur la densité apparente vibrée (VBD) d’échantillons de coke sec est étudié. Les particules de ...
Wielandt method applied to the diffusion equations discretized by finite element nodal methods
International Nuclear Information System (INIS)
Mugica R, A.; Valle G, E. del
2003-01-01
Nowadays the numerical methods of solution to the diffusion equation by means of algorithms and computer programs result so extensive due to the great number of routines and calculations that should carry out, this rebounds directly in the execution times of this programs, being obtained results in relatively long times. This work shows the application of an acceleration method of the convergence of the classic method of those powers that it reduces notably the number of necessary iterations for to obtain reliable results, what means that the compute times they see reduced in great measure. This method is known in the literature like Wielandt method and it has incorporated to a computer program that is based on the discretization of the neutron diffusion equations in plate geometry and stationary state by polynomial nodal methods. In this work the neutron diffusion equations are described for several energy groups and their discretization by means of those called physical nodal methods, being illustrated in particular the quadratic case. It is described a model problem widely described in the literature which is solved for the physical nodal grade schemes 1, 2, 3 and 4 in three different ways: to) with the classic method of the powers, b) method of the powers with the Wielandt acceleration and c) method of the powers with the Wielandt modified acceleration. The results for the model problem as well as for two additional problems known as benchmark problems are reported. Such acceleration method can also be implemented to problems of different geometry to the proposal in this work, besides being possible to extend their application to problems in 2 or 3 dimensions. (Author)
Iterative algorithms for large sparse linear systems on parallel computers
Adams, L. M.
1982-01-01
Algorithms for assembling in parallel the sparse system of linear equations that result from finite difference or finite element discretizations of elliptic partial differential equations, such as those that arise in structural engineering are developed. Parallel linear stationary iterative algorithms and parallel preconditioned conjugate gradient algorithms are developed for solving these systems. In addition, a model for comparing parallel algorithms on array architectures is developed and results of this model for the algorithms are given.
Wake Instabilities Behind Discrete Roughness Elements in High Speed Boundary Layers
Choudhari, Meelan; Li, Fei; Chang, Chau-Lyan; Norris, Andrew; Edwards, Jack
2013-01-01
Computations are performed to study the flow past an isolated, spanwise symmetric roughness element in zero pressure gradient boundary layers at Mach 3.5 and 5.9, with an emphasis on roughness heights of less than 55 percent of the local boundary layer thickness. The Mach 5.9 cases include flow conditions that are relevant to both ground facility experiments and high altitude flight ("cold wall" case). Regardless of the Mach number, the mean flow distortion due to the roughness element is characterized by long-lived streamwise streaks in the roughness wake, which can support instability modes that did not exist in the absence of the roughness element. The higher Mach number cases reveal a variety of instability mode shapes with velocity fluctuations concentrated in different localized regions of high base flow shear. The high shear regions vary from the top of a mushroom shaped structure characterizing the centerline streak to regions that are concentrated on the sides of the mushroom. Unlike the Mach 3.5 case with nearly same values of scaled roughness height k/delta and roughness height Reynolds number Re(sub kk), the odd wake modes in both Mach 5.9 cases are significantly more unstable than the even modes of instability. Additional computations for a Mach 3.5 boundary layer indicate that the presence of a roughness element can also enhance the amplification of first mode instabilities incident from upstream. Interactions between multiple roughness elements aligned along the flow direction are also explored.
Directory of Open Access Journals (Sweden)
E. Larour
2016-11-01
Full Text Available Within the framework of sea-level rise projections, there is a strong need for hindcast validation of the evolution of polar ice sheets in a way that tightly matches observational records (from radar, gravity, and altimetry observations mainly. However, the computational requirements for making hindcast reconstructions possible are severe and rely mainly on the evaluation of the adjoint state of transient ice-flow models. Here, we look at the computation of adjoints in the context of the NASA/JPL/UCI Ice Sheet System Model (ISSM, written in C++ and designed for parallel execution with MPI. We present the adaptations required in the way the software is designed and written, but also generic adaptations in the tools facilitating the adjoint computations. We concentrate on the use of operator overloading coupled with the AdjoinableMPI library to achieve the adjoint computation of the ISSM. We present a comprehensive approach to (1 carry out type changing through the ISSM, hence facilitating operator overloading, (2 bind to external solvers such as MUMPS and GSL-LU, and (3 handle MPI-based parallelism to scale the capability. We demonstrate the success of the approach by computing sensitivities of hindcast metrics such as the misfit to observed records of surface altimetry on the northeastern Greenland Ice Stream, or the misfit to observed records of surface velocities on Upernavik Glacier, central West Greenland. We also provide metrics for the scalability of the approach, and the expected performance. This approach has the potential to enable a new generation of hindcast-validated projections that make full use of the wealth of datasets currently being collected, or already collected, in Greenland and Antarctica.
Morita, Yukinori; Mori, Takahiro; Migita, Shinji; Mizubayashi, Wataru; Tanabe, Akihito; Fukuda, Koichi; Matsukawa, Takashi; Endo, Kazuhiko; O'uchi, Shin-ichi; Liu, Yongxun; Masahara, Meishoku; Ota, Hiroyuki
2014-12-01
The performance of parallel electric field tunnel field-effect transistors (TFETs), in which band-to-band tunneling (BTBT) was initiated in-line to the gate electric field was evaluated. The TFET was fabricated by inserting an epitaxially-grown parallel-plate tunnel capacitor between heavily doped source wells and gate insulators. Analysis using a distributed-element circuit model indicated there should be a limit of the drain current caused by the self-voltage-drop effect in the ultrathin channel layer.
Studies of multiperiodic structures by means of circuits with discrete elements
International Nuclear Information System (INIS)
Tran, D.T.
In modern linear accelerators, magnetrons, and travelling wave tubes, to reduce the beam loading effect and to reconcile the structure efficiency and its sensitiveness to mechanical errors, sophisticated structures are often designed by associating several elementary circuits. Because several pass-bands can interfere, the dispersion properties of such multiband structures were studied. Using matrix calculus and applying the positive real properties of impedance, the behavior of series-coupled and parallel-coupled structures is derived. Forms of dispersion curves of biperiodic, triperiodic structure, deflecting structure, interdigital structure, and others are discussed. Experimental work is presented on a few modern structures to illustrate the theoretical work. A new structure, derived from the organ pipe structure and proposed recently as a variable energy accelerating structure, is discussed, and interdigital structures are considered
Prinz, Jan-Hendrik; Chodera, John D; Pande, Vijay S; Swope, William C; Smith, Jeremy C; Noé, Frank
2011-06-28
Parallel tempering (PT) molecular dynamics simulations have been extensively investigated as a means of efficient sampling of the configurations of biomolecular systems. Recent work has demonstrated how the short physical trajectories generated in PT simulations of biomolecules can be used to construct the Markov models describing biomolecular dynamics at each simulated temperature. While this approach describes the temperature-dependent kinetics, it does not make optimal use of all available PT data, instead estimating the rates at a given temperature using only data from that temperature. This can be problematic, as some relevant transitions or states may not be sufficiently sampled at the temperature of interest, but might be readily sampled at nearby temperatures. Further, the comparison of temperature-dependent properties can suffer from the false assumption that data collected from different temperatures are uncorrelated. We propose here a strategy in which, by a simple modification of the PT protocol, the harvested trajectories can be reweighted, permitting data from all temperatures to contribute to the estimated kinetic model. The method reduces the statistical uncertainty in the kinetic model relative to the single temperature approach and provides estimates of transition probabilities even for transitions not observed at the temperature of interest. Further, the method allows the kinetics to be estimated at temperatures other than those at which simulations were run. We illustrate this method by applying it to the generation of a Markov model of the conformational dynamics of the solvated terminally blocked alanine peptide.
Least-squares finite element discretizations of neutron transport equations in 3 dimensions
Energy Technology Data Exchange (ETDEWEB)
Manteuffel, T.A [Univ. of Colorado, Boulder, CO (United States); Ressel, K.J. [Interdisciplinary Project Center for Supercomputing, Zurich (Switzerland); Starkes, G. [Universtaet Karlsruhe (Germany)
1996-12-31
The least-squares finite element framework to the neutron transport equation introduced in is based on the minimization of a least-squares functional applied to the properly scaled neutron transport equation. Here we report on some practical aspects of this approach for neutron transport calculations in three space dimensions. The systems of partial differential equations resulting from a P{sub 1} and P{sub 2} approximation of the angular dependence are derived. In the diffusive limit, the system is essentially a Poisson equation for zeroth moment and has a divergence structure for the set of moments of order 1. One of the key features of the least-squares approach is that it produces a posteriori error bounds. We report on the numerical results obtained for the minimum of the least-squares functional augmented by an additional boundary term using trilinear finite elements on a uniform tesselation into cubes.
Than, Vinh-Du; Tang, Anh-Minh; Roux, Jean-Noël; Pereira, Jean-Michel; Aimedieu, Patrick; Bornert, Michel
2017-06-01
We present an investigation into macroscopic and microscopic behaviors of wet granular soils using the discrete element method (DEM) and the X-ray Computed Tomography (XRCT) observations. The specimens are first prepared in very loose states, with frictional spherical grains in the presence of a small amount of an interstitial liquid. Experimental oedometric tests are carried out with small glass beads, while DEM simulations implement a model of spherical grains joined by menisci. Both in experiments and in simulations, loose configurations with solid fraction as low as 0.30 are prepared under low stress, and undergo a gradual collapse in compression, until the solid fraction of cohesionless bead packs (0.58 to 0.6) is obtained. In the XRCT tests, four 3D tomography images corresponding to different typical stages of the compression curve are used to characterize the microstructure.
Virgo, Simon; Ankit, Kumar; Nestler, Britta; Urai, Janos L.
2016-04-01
Crack-seal veins form in a complex interplay of coupled thermal, hydraulic, mechanical and chemical processes. Their formation and cyclic growth involves brittle fracturing and dilatancy, phases of increased fluid flow and the growth of crystals that fill the voids and reestablish the mechanical strength. Existing numerical models of vein formation focus on selected aspects of the coupled process. Until today, no model exists that is able to use a realistic representation of the fracturing AND sealing processes, simultaneously. To address this challenge, we propose the bidirectional coupling of two numerical methods that have proven themselves as very powerful to model the fundamental processes acting in crack-seal systems: Phase-field and the Discrete Element Method (DEM). The phase-field Method was recently successfully extended to model the precipitation of quartz crystals from an aqueous solution and applied to model the sealing of a vein over multiple opening events (Ankit et al., 2013; Ankit et al., 2015a; Ankit et al., 2015b). The advantage over former, purely kinematic approaches is that in phase-field, the crystal growth is modeled based on thermodynamic and kinetic principles. Different driving forces for microstructure evolution, such as chemical bulk free energy, interfacial energy, elastic strain energy and different transport processes, such as mass diffusion and advection, can be coupled and the effect on the evolution process can be studied in 3D. The Discrete Element Method was already used in several studies to model the fracturing of rocks and the incremental growth of veins by repeated fracturing (Virgo et al., 2013; Virgo et al., 2014). Materials in DEM are represented by volumes of packed spherical particles and the response to the material to stress is modeled by interaction of the particles with their nearest neighbours. For rocks, in 3D, the method provides a realistic brittle failure behaviour. Exchange Routines are being developed that
Czech Academy of Sciences Publication Activity Database
Marcinkowski, L.; Rahman, T.; Loneland, A.; Valdman, Jan
2016-01-01
Roč. 56, č. 3 (2016), s. 967-993 ISSN 0006-3835 R&D Projects: GA ČR GA13-18652S Institutional support: RVO:67985556 Keywords : Domain decomposition * Additive Schwarz method * Finite volume element * GMRES Subject RIV: BA - General Mathematics Impact factor: 1.670, year: 2016 http://library.utia.cas.cz/separaty/2015/MTR/valdman-0447835.pdf
Ji, S.; Hanes, D.M.; Shen, H.H.
2009-01-01
In this study, we report a direct comparison between a physical test and a computer simulation of rapidly sheared granular materials. An annular shear cell experiment was conducted. All parameters were kept the same between the physical and the computational systems to the extent possible. Artificially softened particles were used in the simulation to reduce the computational time to a manageable level. Sensitivity study on the particle stiffness ensured such artificial modification was acceptable. In the experiment, a range of normal stress was applied to a given amount of particles sheared in an annular trough with a range of controlled shear speed. Two types of particles, glass and Delrin, were used in the experiment. Qualitatively, the required torque to shear the materials under different rotational speed compared well with those in the physical experiments for both the glass and the Delrin particles. However, the quantitative discrepancies between the measured and simulated shear stresses were nearly a factor of two. Boundary conditions, particle size distribution, particle damping and friction, including a sliding and rolling, contact force model, were examined to determine their effects on the computational results. It was found that of the above, the rolling friction between particles had the most significant effect on the macro stress level. This study shows that discrete element simulation is a viable method for engineering design for granular material systems. Particle level information is needed to properly conduct these simulations. However, not all particle level information is equally important in the study regime. Rolling friction, which is not commonly considered in many discrete element models, appears to play an important role. ?? 2009 Elsevier Ltd.
Discrete conservation properties for shallow water flows using mixed mimetic spectral elements
Lee, D.; Palha, A.; Gerritsma, M.
2018-03-01
A mixed mimetic spectral element method is applied to solve the rotating shallow water equations. The mixed method uses the recently developed spectral element histopolation functions, which exactly satisfy the fundamental theorem of calculus with respect to the standard Lagrange basis functions in one dimension. These are used to construct tensor product solution spaces which satisfy the generalized Stokes theorem, as well as the annihilation of the gradient operator by the curl and the curl by the divergence. This allows for the exact conservation of first order moments (mass, vorticity), as well as higher moments (energy, potential enstrophy), subject to the truncation error of the time stepping scheme. The continuity equation is solved in the strong form, such that mass conservation holds point wise, while the momentum equation is solved in the weak form such that vorticity is globally conserved. While mass, vorticity and energy conservation hold for any quadrature rule, potential enstrophy conservation is dependent on exact spatial integration. The method possesses a weak form statement of geostrophic balance due to the compatible nature of the solution spaces and arbitrarily high order spatial error convergence.
International Nuclear Information System (INIS)
Guan, P B; Tingatinga, E A; Longalong, R E; Saguid, J
2016-01-01
During the past decades, the complexity of conventional methods to perform seismic performance assessment of buildings led to the development of more effective approaches. The rigid body spring-discrete element method (RBS-DEM) is one of these approaches and has recently been applied to the study of the behavior of reinforced concrete (RC) buildings subjected to strong earthquakes. In this paper, the governing equations of RBS-DEM planar elements subjected to lateral loads and horizontal ground motion are presented and used to replicate the hysteretic behavior of experimental RC columns. The RBS-DEM models of columns are made up of rigid components connected by systems of springs that simulate axial, shear, and bending behavior of an RC section. The parameters of springs were obtained using Response-2000 software and the hysteretic response of the models of select columns from the Pacific Earthquake Engineering Research (PEER) Structural Performance Database were computed numerically. Numerical examples show that one-component models were able to simulate the initial stiffness reasonably, while the displacement capacity of actual columns undergoing large displacements were underestimated. (paper)
Directory of Open Access Journals (Sweden)
Jan Nečas
2017-09-01
Full Text Available This paper describes optimisation of a conveyor from an underground hopper intended for a coal transfer station. The original solution was designed with a chain conveyor encountered operational problems that have limited its continuous operation. The Discrete Element Modeling (DEM was chosen to optimise the transport. DEM simulations allow device design modifications directly in the 3D CAD model, and then the simulation makes it possible to evaluate whether the adjustment was successful. By simulating the initial state of coal extraction using a chain conveyor, trouble spots were identified that caused operational failures. The main problem has been the increased resistance during removal of material from the underground hopper. Revealed resistances against material movement were not considered in the original design at all. In the next step, structural modifications of problematic nodes were made. For example, the following changes have been made: reduction of storage space or installation of passive elements into the interior of the underground hopper. These modifications made were not effective enough, so the type of the conveyor was changed from a drag chain conveyor to a belt conveyor. The simulation of the material extraction using a belt conveyor showed a significant reduction in resistance parameters while maintaining the required transport performance.
Xu, Jason; Guttorp, Peter; Kato-Maeda, Midori; Minin, Vladimir N
2015-12-01
Continuous-time birth-death-shift (BDS) processes are frequently used in stochastic modeling, with many applications in ecology and epidemiology. In particular, such processes can model evolutionary dynamics of transposable elements-important genetic markers in molecular epidemiology. Estimation of the effects of individual covariates on the birth, death, and shift rates of the process can be accomplished by analyzing patient data, but inferring these rates in a discretely and unevenly observed setting presents computational challenges. We propose a multi-type branching process approximation to BDS processes and develop a corresponding expectation maximization algorithm, where we use spectral techniques to reduce calculation of expected sufficient statistics to low-dimensional integration. These techniques yield an efficient and robust optimization routine for inferring the rates of the BDS process, and apply broadly to multi-type branching processes whose rates can depend on many covariates. After rigorously testing our methodology in simulation studies, we apply our method to study intrapatient time evolution of IS6110 transposable element, a genetic marker frequently used during estimation of epidemiological clusters of Mycobacterium tuberculosis infections. © 2015, The International Biometric Society.
Directory of Open Access Journals (Sweden)
Yongliang Wang
2018-01-01
Full Text Available Hydrofracturing technology of perforated horizontal well has been widely used to stimulate the tight hydrocarbon reservoirs for gas production. To predict the hydraulic fracture propagation, the microseismicity can be used to infer hydraulic fractures state; by the effective numerical methods, microseismic events can be addressed from changes of the computed stresses. In numerical models, due to the challenges in accurately representing the complex structure of naturally fractured reservoir, the interaction between hydraulic and pre-existing fractures has not yet been considered and handled satisfactorily. To overcome these challenges, the adaptive finite element-discrete element method is used to refine mesh, effectively identify the fractures propagation, and investigate microseismic modelling. Numerical models are composed of hydraulic fractures, pre-existing fractures, and microscale pores, and the seepage analysis based on the Darcy’s law is used to determine fluid flow; then moment tensors in microseismicity are computed based on the computed stresses. Unfractured and naturally fractured models are compared to assess the influences of pre-existing fractures on hydrofracturing. The damaged and contact slip events were detected by the magnitudes, B-values, Hudson source type plots, and focal spheres.
Energy Technology Data Exchange (ETDEWEB)
Milind Deo; Chung-Kan Huang; Huabing Wang
2008-08-31
Black-oil, compositional and thermal simulators have been developed to address different physical processes in reservoir simulation. A number of different types of discretization methods have also been proposed to address issues related to representing the complex reservoir geometry. These methods are more significant for fractured reservoirs where the geometry can be particularly challenging. In this project, a general modular framework for reservoir simulation was developed, wherein the physical models were efficiently decoupled from the discretization methods. This made it possible to couple any discretization method with different physical models. Oil characterization methods are becoming increasingly sophisticated, and it is possible to construct geologically constrained models of faulted/fractured reservoirs. Discrete Fracture Network (DFN) simulation provides the option of performing multiphase calculations on spatially explicit, geologically feasible fracture sets. Multiphase DFN simulations of and sensitivity studies on a wide variety of fracture networks created using fracture creation/simulation programs was undertaken in the first part of this project. This involved creating interfaces to seamlessly convert the fracture characterization information into simulator input, grid the complex geometry, perform the simulations, and analyze and visualize results. Benchmarking and comparison with conventional simulators was also a component of this work. After demonstration of the fact that multiphase simulations can be carried out on complex fracture networks, quantitative effects of the heterogeneity of fracture properties were evaluated. Reservoirs are populated with fractures of several different scales and properties. A multiscale fracture modeling study was undertaken and the effects of heterogeneity and storage on water displacement dynamics in fractured basements were investigated. In gravity-dominated systems, more oil could be recovered at a given pore
Directory of Open Access Journals (Sweden)
Mustafa Ucgul
2015-09-01
Full Text Available The energy required for tillage processes accounts for a significant proportion of total energy used in crop production. In many tillage processes decreasing the draft and upward vertical forces is often desired for reduced fuel use and improved penetration, respectively. Recent studies have proved that the discrete element modelling (DEM can effectively be used to model the soil–tool interaction. In his study, Fielke (1994 [1] examined the effect of the various tool cutting edge geometries, namely; cutting edge height, length of underside rub, angle of underside clearance, on draft and vertical forces. In this paper the experimental parameters of Fielke (1994 [1] were simulated using 3D discrete element modelling techniques. In the simulations a hysteretic spring contact model integrated with a linear cohesion model that considers the plastic deformation behaviour of the soil hence provides better vertical force prediction was employed. DEM parameters were determined by comparing the experimental and simulation results of angle of repose and penetration tests. The results of the study showed that the simulation results of the soil-various tool cutting edge geometries agreed well with the experimental results of Fielke (1994 [1]. The modelling was then used to simulate a further range of cutting edge geometries to better define the effect of sweep tool cutting edge geometry parameters on tillage forces. The extra simulations were able to show that by using a sharper cutting edge with zero vertical cutting edge height the draft and upward vertical force were further reduced indicating there is benefit from having a really sharp cutting edge. The extra simulations also confirmed that the interpolated trends for angle of underside clearance as suggested by Fielke (1994 [1] where correct with a linear reduction in draft and upward vertical force for angle of underside clearance between the ranges of −25 and −5°, and between −5 and 0°. The
International Nuclear Information System (INIS)
Candel, A.; Kabel, A.; Ko, K.; Lee, L.; Li, Z.; Limborg, C.; Ng, C.; Prudencio, E.; Schussman, G.; Uplenchwar, R.
2007-01-01
Over the past years, SLAC's Advanced Computations Department (ACD) has developed the parallel finite element (FE) particle-in-cell code Pic3P (Pic2P) for simulations of beam-cavity interactions dominated by space-charge effects. As opposed to standard space-charge dominated beam transport codes, which are based on the electrostatic approximation, Pic3P (Pic2P) includes space-charge, retardation and boundary effects as it self-consistently solves the complete set of Maxwell-Lorentz equations using higher-order FE methods on conformal meshes. Use of efficient, large-scale parallel processing allows for the modeling of photoinjectors with unprecedented accuracy, aiding the design and operation of the next-generation of accelerator facilities. Applications to the Linac Coherent Light Source (LCLS) RF gun are presented
Tomar, S.K.
2002-01-01
It is well known that elliptic problems when posed on non-smooth domains, develop singularities. We examine such problems within the framework of spectral element methods and resolve the singularities with exponential accuracy.
Gutmann, R. J.; Borrego, J. M.
1978-01-01
Rectenna conversion efficiencies (RF to dc) approximating 85 percent were demonstrated on a small scale, clearly indicating the feasibility and potential of efficiency of microwave power to dc. The overall cost estimates of the solar power satellite indicate that the baseline rectenna subsystem will be between 25 to 40 percent of the system cost. The directional receiving elements and element extensions were studied, along with power combining evaluation and evaluation extensions.
Townsend, Kevin C; Thomas-Aitken, Holly D; Rudert, M James; Kern, Andrew M; Willey, Michael C; Anderson, Donald D; Goetz, Jessica E
2018-01-23
Evaluation of abnormalities in joint contact stress that develop after inaccurate reduction of an acetabular fracture may provide a potential means for predicting the risk of developing post-traumatic osteoarthritis. Discrete element analysis (DEA) is a computational technique for calculating intra-articular contact stress distributions in a fraction of the time required to obtain the same information using the more commonly employed finite element analysis technique. The goal of this work was to validate the accuracy of DEA-computed contact stress against physical measurements of contact stress made in cadaveric hips using Tekscan sensors. Four static loading tests in a variety of poses from heel-strike to toe-off were performed in two different cadaveric hip specimens with the acetabulum intact and again with an intentionally malreduced posterior wall acetabular fracture. DEA-computed contact stress was compared on a point-by-point basis to stress measured from the physical experiments. There was good agreement between computed and measured contact stress over the entire contact area (correlation coefficients ranged from 0.88 to 0.99). DEA-computed peak contact stress was within an average of 0.5 MPa (range 0.2-0.8 MPa) of the Tekscan peak stress for intact hips, and within an average of 0.6 MPa (range 0-1.6 MPa) for fractured cases. DEA-computed contact areas were within an average of 33% of the Tekscan-measured areas (range: 1.4-60%). These results indicate that the DEA methodology is a valid method for accurately estimating contact stress in both intact and fractured hips. Copyright © 2017 Elsevier Ltd. All rights reserved.
Tran, Quoc Anh; Chevalier, Bastien; Benz, Miguel; Breul, Pierre; Gourvès, Roland
2017-06-01
The recent technological developments made on the light dynamic penetration test Panda 3 ® provide a dynamic load-penetration curve σp - sp for each impact. This curve is influenced by the mechanical and physical properties of the investigated granular media. In order to analyze and exploit the load-penetration curve, a numerical model of penetration test using 3D Discrete Element Method is proposed for reproducing tests in dynamic conditions in granular media. All parameters of impact used in this model have at first been calibrated by respecting mechanical and geometrical properties of the hammer and the rod. There is a good agreement between experimental results and the ones obtained from simulations in 2D or 3D. After creating a sample, we will simulate the Panda 3 ®. It is possible to measure directly the dynamic load-penetration curve occurring at the tip for each impact. Using the force and acceleration measured in the top part of the rod, it is possible to separate the incident and reflected waves and then calculate the tip's load-penetration curve. The load-penetration curve obtained is qualitatively similar with that obtained by experimental tests. In addition, the frequency analysis of the measured signals present also a good compliance with that measured in reality when the tip resistance is qualitatively similar.
Energy Technology Data Exchange (ETDEWEB)
Van Lew, Jon T., E-mail: jtvanlew@fusion.ucla.edu; Ying, Alice; Abdou, Mohamed
2014-10-15
The discrete element method (DEM) is used to study the thermal effects of pebble failure in an ensemble of lithium ceramic spheres. Some pebbles crushing in a large system is unavoidable and this study provides correlations between the extent of pebble failure and the reduction in effective thermal conductivity of the bed. In the model, we homogeneously induced failure and applied nuclear heating until dynamic and thermal steady-state. Conduction between pebbles and from pebbles to the boundary is the only mode of heat transfer presently modeled. The effective thermal conductivity was found to decrease rapidly as a function of the percent of failed pebbles in the bed. It was found that the dominant contributor to the reduction was the drop in inter-particle forces as pebbles fail; implying the extent of failure induced may not occur in real pebble beds. The results are meant to assist designers in the fusion energy community who are planning to use packed beds of ceramic pebbles. The evolution away from experimentally measured thermomechanical properties as pebbles fail is necessary for proper operation of fusion reactors.
Energy Technology Data Exchange (ETDEWEB)
Huang, Hai; Plummer, Mitchell; Podgorney, Robert
2013-02-01
Advancement of EGS requires improved prediction of fracture development and growth during reservoir stimulation and long-term operation. This, in turn, requires better understanding of the dynamics of the strongly coupled thermo-hydro-mechanical (THM) processes within fractured rocks. We have developed a physically based rock deformation and fracture propagation simulator by using a quasi-static discrete element model (DEM) to model mechanical rock deformation and fracture propagation induced by thermal stress and fluid pressure changes. We also developed a network model to simulate fluid flow and heat transport in both fractures and porous rock. In this paper, we describe results of simulations in which the DEM model and network flow & heat transport model are coupled together to provide realistic simulation of the changes of apertures and permeability of fractures and fracture networks induced by thermal cooling and fluid pressure changes within fractures. Various processes, such as Stokes flow in low velocity pores, convection-dominated heat transport in fractures, heat exchange between fluid-filled fractures and solid rock, heat conduction through low-permeability matrices and associated mechanical deformations are all incorporated into the coupled model. The effects of confining stresses, developing thermal stress and injection pressure on the permeability evolution of fracture and fracture networks are systematically investigated. Results are summarized in terms of implications for the development and evolution of fracture distribution during hydrofracturing and thermal stimulation for EGS.
Carlos Varas, Álvaro E; Peters, E A J F; Kuipers, J A M
2017-05-17
We report a computational fluid dynamics-discrete element method (CFD-DEM) simulation study on the interplay between mass transfer and a heterogeneous catalyzed chemical reaction in cocurrent gas-particle flows as encountered in risers. Slip velocity, axial gas dispersion, gas bypassing, and particle mixing phenomena have been evaluated under riser flow conditions to study the complex system behavior in detail. The most important factors are found to be directly related to particle cluster formation. Low air-to-solids flux ratios lead to more heterogeneous systems, where the cluster formation is more pronounced and mass transfer more influenced. Falling clusters can be partially circumvented by the gas phase, which therefore does not fully interact with the cluster particles, leading to poor gas-solid contact efficiencies. Cluster gas-solid contact efficiencies are quantified at several gas superficial velocities, reaction rates, and dilution factors in order to gain more insight regarding the influence of clustering phenomena on the performance of riser reactors.
Herman, Agnieszka
2017-11-01
In this paper, a coupled sea ice-wave model is developed and used to analyze wave-induced stress and breaking in sea ice for a range of wave and ice conditions. The sea ice module is a discrete-element bonded-particle model, in which ice is represented as cuboid grains floating on the water surface that can be connected to their neighbors by elastic joints. The joints may break if instantaneous stresses acting on them exceed their strength. The wave module is based on an open-source version of the Non-Hydrostatic WAVE model (NHWAVE). The two modules are coupled with proper boundary conditions for pressure and velocity, exchanged at every wave model time step. In the present version, the model operates in two dimensions (one vertical and one horizontal) and is suitable for simulating compact ice in which heave and pitch motion dominates over surge. In a series of simulations with varying sea ice properties and incoming wavelength it is shown that wave-induced stress reaches maximum values at a certain distance from the ice edge. The value of maximum stress depends on both ice properties and characteristics of incoming waves, but, crucially for ice breaking, the location at which the maximum occurs does not change with the incoming wavelength. Consequently, both regular and random (Jonswap spectrum) waves break the ice into floes with almost identical sizes. The width of the zone of broken ice depends on ice strength and wave attenuation rates in the ice.
Directory of Open Access Journals (Sweden)
Guodong Liu
2013-01-01
Full Text Available Modular pebble-bed nuclear reactor (MPBNR technology is promising due to its attractive features such as high fuel performance and inherent safety. Particle motion of fuel and graphite pebbles is highly associated with the performance of pebbled-bed modular nuclear reactor. To understand the mechanism of pebble’s motion in the reactor, we numerically studied the influence of number ratio of fuel and graphite pebbles, funnel angle of the reactor, height of guide ring on the distribution of pebble position, and velocity by means of discrete element method (DEM in a two-dimensional MPBNR. Velocity distributions at different areas of the reactor as well as mixing characteristics of fuel and graphite pebbles were investigated. Both fuel and graphite pebbles moved downward, and a uniform motion was formed in the column zone, while pebbles motion in the cone zone was accelerated due to the decrease of the cross sectional flow area. The number ratio of fuel and graphite pebbles and the height of guide ring had a minor influence on the velocity distribution of pebbles, while the variation of funnel angle had an obvious impact on the velocity distribution. Simulated results agreed well with the work in the literature.
Discrete Curvatures and Discrete Minimal Surfaces
Sun, Xiang
2012-06-01
This thesis presents an overview of some approaches to compute Gaussian and mean curvature on discrete surfaces and discusses discrete minimal surfaces. The variety of applications of differential geometry in visualization and shape design leads to great interest in studying discrete surfaces. With the rich smooth surface theory in hand, one would hope that this elegant theory can still be applied to the discrete counter part. Such a generalization, however, is not always successful. While discrete surfaces have the advantage of being finite dimensional, thus easier to treat, their geometric properties such as curvatures are not well defined in the classical sense. Furthermore, the powerful calculus tool can hardly be applied. The methods in this thesis, including angular defect formula, cotangent formula, parallel meshes, relative geometry etc. are approaches based on offset meshes or generalized offset meshes. As an important application, we discuss discrete minimal surfaces and discrete Koenigs meshes.
Energy Technology Data Exchange (ETDEWEB)
Fischer, P.F. [Brown Univ., Providence, RI (United States)
1996-12-31
Efficient solution of the Navier-Stokes equations in complex domains is dependent upon the availability of fast solvers for sparse linear systems. For unsteady incompressible flows, the pressure operator is the leading contributor to stiffness, as the characteristic propagation speed is infinite. In the context of operator splitting formulations, it is the pressure solve which is the most computationally challenging, despite its elliptic origins. We seek to improve existing spectral element iterative methods for the pressure solve in order to overcome the slow convergence frequently observed in the presence of highly refined grids or high-aspect ratio elements.
A parallel direct solver for the self-adaptive hp Finite Element Method
Paszyński, Maciej R.; Pardo, David; Torres-Verdí n, Carlos; Demkowicz, Leszek F.; Calo, Victor M.
2010-01-01
measurement simulations problems. We measure the execution time and memory usage of the solver over a large regular mesh with 1.5 million degrees of freedom as well as on the highly non-regular mesh, generated by the self-adaptive h p-FEM, with finite elements
Fraser, Graham M.; Goldman, Daniel; Ellis, Christopher G.
2013-01-01
Objective We compare Reconstructed Microvascular Networks (RMN) to Parallel Capillary Arrays (PCA) under several simulated physiological conditions to determine how the use of different vascular geometry affects oxygen transport solutions. Methods Three discrete networks were reconstructed from intravital video microscopy of rat skeletal muscle (84×168×342 μm, 70×157×268 μm and 65×240×571 μm) and hemodynamic measurements were made in individual capillaries. PCAs were created based on statistical measurements from RMNs. Blood flow and O2 transport models were applied and the resulting solutions for RMN and PCA models were compared under 4 conditions (rest, exercise, ischemia and hypoxia). Results Predicted tissue PO2 was consistently lower in all RMN simulations compared to the paired PCA. PO2 for 3D reconstructions at rest were 28.2±4.8, 28.1±3.5, and 33.0±4.5 mmHg for networks I, II, and III compared to the PCA mean values of 31.2±4.5, 30.6±3.4, and 33.8±4.6 mmHg. Simulated exercise yielded mean tissue PO2 in the RMN of 10.1±5.4, 12.6±5.7, and 19.7±5.7 mmHg compared to 15.3±7.3, 18.8±5.3, and 21.7±6.0 in PCA. Conclusions These findings suggest that volume matched PCA yield different results compared to reconstructed microvascular geometries when applied to O2 transport modeling; the predominant characteristic of this difference being an over estimate of mean tissue PO2. Despite this limitation, PCA models remain important for theoretical studies as they produce PO2 distributions with similar shape and parameter dependence as RMN. PMID:23841679
Koldan, Jelena; Puzyrev, Vladimir; de la Puente, Josep; Houzeaux, Guillaume; Cela, José María
2014-06-01
We present an elaborate preconditioning scheme for Krylov subspace methods which has been developed to improve the performance and reduce the execution time of parallel node-based finite-element (FE) solvers for 3-D electromagnetic (EM) numerical modelling in exploration geophysics. This new preconditioner is based on algebraic multigrid (AMG) that uses different basic relaxation methods, such as Jacobi, symmetric successive over-relaxation (SSOR) and Gauss-Seidel, as smoothers and the wave front algorithm to create groups, which are used for a coarse-level generation. We have implemented and tested this new preconditioner within our parallel nodal FE solver for 3-D forward problems in EM induction geophysics. We have performed series of experiments for several models with different conductivity structures and characteristics to test the performance of our AMG preconditioning technique when combined with biconjugate gradient stabilized method. The results have shown that, the more challenging the problem is in terms of conductivity contrasts, ratio between the sizes of grid elements and/or frequency, the more benefit is obtained by using this preconditioner. Compared to other preconditioning schemes, such as diagonal, SSOR and truncated approximate inverse, the AMG preconditioner greatly improves the convergence of the iterative solver for all tested models. Also, when it comes to cases in which other preconditioners succeed to converge to a desired precision, AMG is able to considerably reduce the total execution time of the forward-problem code-up to an order of magnitude. Furthermore, the tests have confirmed that our AMG scheme ensures grid-independent rate of convergence, as well as improvement in convergence regardless of how big local mesh refinements are. In addition, AMG is designed to be a black-box preconditioner, which makes it easy to use and combine with different iterative methods. Finally, it has proved to be very practical and efficient in the
Energy Technology Data Exchange (ETDEWEB)
Cwik, T. [California Institute of Technology, Pasadena, CA (United States); Katz, D.S. [Cray Research, El Segundo, CA (United States)
1996-12-31
Finite element modeling has proven useful for accurately simulating scattered or radiated electromagnetic fields from complex three-dimensional objects whose geometry varies on the scale of a fraction of an electrical wavelength. An unstructured finite element model of realistic objects leads to a large, sparse, system of equations that needs to be solved efficiently with regard to machine memory and execution time. Both factorization and iterative solvers can be used to produce solutions to these systems of equations. Factorization leads to high memory requirements that limit the electrical problem size of three-dimensional objects that can be modeled. An iterative solver can be used to efficiently solve the system without excessive memory use and in a minimal amount of time if the convergence rate is controlled.
Energy Technology Data Exchange (ETDEWEB)
Birkholzer, J.; Karasaki, K. [Lawrence Berkeley National Lab., CA (United States). Earth Sciences Div.
1996-07-01
Fracture network simulators have extensively been used in the past for obtaining a better understanding of flow and transport processes in fractured rock. However, most of these models do not account for fluid or solute exchange between the fractures and the porous matrix, although diffusion into the matrix pores can have a major impact on the spreading of contaminants. In the present paper a new finite element code TRIPOLY is introduced which combines a powerful fracture network simulator with an efficient method to account for the diffusive interaction between the fractures and the adjacent matrix blocks. The fracture network simulator used in TRIPOLY features a mixed Lagrangian-Eulerian solution scheme for the transport in fractures, combined with an adaptive gridding technique to account for sharp concentration fronts. The fracture-matrix interaction is calculated with an efficient method which has been successfully used in the past for dual-porosity models. Discrete fractures and matrix blocks are treated as two different systems, and the interaction is modeled by introducing sink/source terms in both systems. It is assumed that diffusive transport in the matrix can be approximated as a one-dimensional process, perpendicular to the adjacent fracture surfaces. A direct solution scheme is employed to solve the coupled fracture and matrix equations. The newly developed combination of the fracture network simulator and the fracture-matrix interaction module allows for detailed studies of spreading processes in fractured porous rock. The authors present a sample application which demonstrate the codes ability of handling large-scale fracture-matrix systems comprising individual fractures and matrix blocks of arbitrary size and shape.
Jiang, Mingjing; He, Jie; Wang, Jianfeng; Zhou, Yaping; Zhu, Fangyuan
2017-12-01
Due to increasing global energy demands, research is being conducted on the mechanical properties of methane hydrate-bearing soils (MHBSs), from which methane hydrate (MH) will be explored. This paper presents a numerical approach to study the mechanical properties of MHBSs. The relationship between the level of MH saturation and the interparticle bond thickness is first obtained by analyzing the scanning electron microscope images of MHBS samples, in which is the bridge connecting the micromechanical behavior captured by the DEM with the macroscopic properties of MHBSs. A simplified thermal-hydromechanical (THM) bond model that considers the different bond thicknesses is then proposed to describe the contact behavior between the soil particles and those incorporated into the discrete element method (DEM). Finally, a series of biaxial compression tests are carried out with different MH saturations under different effective confining pressures to analyze the mechanical properties of deep-sea MHBSs. The results of the DEM numerical simulation are also compared with the findings from triaxial compression tests. The results show that the macromechanical properties of deep-sea MHBSs can be qualitatively captured by the proposed DEM. The shear strength, cohesion, and volumetric contraction of deep-sea MHBSs increase with increasing MH saturation, although its influence on the internal friction angle is obscure. The shear strength and volumetric contraction increase with increasing effective confining pressure. The peak shear strength and the dilation of MHBSs increase as the critical bond thickness increases, while the residual deviator stress largely remains the same at a larger axial strain. With increasing the axial strain, the percentage of broken bonds increases, along with the expansion of the shear band.
International Nuclear Information System (INIS)
Konopka, Ladislav; Kosek, Juraj
2015-01-01
Polyethylene particles of various sizes are present in industrial gas-dispersion reactors and downstream processing units. The contact of the particles with a device wall as well as the mutual particle collisions cause electrons on the particle surface to redistribute in the system. The undesirable triboelectric charging results in several operational problems and safety risks in industrial systems, for example in the fluidized-bed polymerization reactor. We studied the charging of polyethylene particles caused by the particle-particle interactions in gas. Our model employs the Discrete Element Method (DEM) describing the particle dynamics and incorporates the ‘Trapped Electron Approach’ as the physical basis for the considered charging mechanism. The model predicts the particle charge distribution for systems with various particle size distributions and various level of segregation. Simulation results are in a qualitative agreement with experimental observations of similar particulate systems specifically in two aspects: 1) Big particles tend to gain positive charge and small particles the negative one. 2) The wider the particle size distribution is, the more pronounced is the charging process. Our results suggest that not only the size distribution, but also the effect of the spatial segregation of the polyethylene particles significantly influence the resulting charge distribution ‘generated’ in the system. The level of particle segregation as well as the particle size distribution of polyethylene particles can be in practice adjusted by the choice of supported catalysts, by the conditions in the fluidized-bed polymerization reactor and by the fluid dynamics. We also attempt to predict how the reactor temperature affects the triboelectric charging of particles. (paper)
Directory of Open Access Journals (Sweden)
Daniel Marcsa
2015-01-01
Full Text Available The analysis and design of electromechanical devices involve the solution of large sparse linear systems, and require therefore high performance algorithms. In this paper, the primal Domain Decomposition Method (DDM with parallel forward-backward and with parallel Preconditioned Conjugate Gradient (PCG solvers are introduced in two-dimensional parallel time-stepping finite element formulation to analyze rotating machine considering the electromagnetic field, external circuit and rotor movement. The proposed parallel direct and the iterative solver with two preconditioners are analyzed concerning its computational efficiency and number of iterations of the solver with different preconditioners. Simulation results of a rotating machine is also presented.
Katili, Irwan
1993-06-01
A new three-node nine-degree-of-freedom triangular plate bending element is proposed which is valid for the analysis of both thick and thin plates. The element, called the discrete Kirchhoff-Mindlin triangle (DKMT), has a proper rank, passes the patch test for thin and thick plates in an arbitrary mesh, and is free of shear locking. As an extension of the DKMT element, a four-node element with 3 degrees of freedom per node is developed. The element, referred to as DKMQ (discrete Kirchhoff-Mindlin quadrilateral) is found to provide good results for both thin and thick plates without any compatibility problems.
International Nuclear Information System (INIS)
Giuliani, Giovanni; Giuliani, Silvano.
1980-01-01
The FORTRAN IV subroutine SURF has been designed to help visualising the results of Finite Element computations. It drawns the axonometric projection of a surface generated in 3-dimensional space by a scalar function over a discretized plane domain. The most important characteristic of the routine is to remove the hidden lines and in this way it enables a clear vision of the details of the generated surface
Directory of Open Access Journals (Sweden)
Rek Václav
2016-11-01
Full Text Available In this paper, the form of modifications of the existing sequential code written in C or C++ programming language for the calculation of various kind of structures using the explicit form of the Finite Element Method (Dynamic Relaxation Method, Explicit Dynamics in the NEXX system is introduced. The NEXX system is the core of engineering software NEXIS, Scia Engineer, RFEM and RENEX. It has the possibilities of multithreaded running, which can now be supported at the level of native C++ programming language using standard libraries. Thanks to the high degree of abstraction that a contemporary C++ programming language provides, a respective library created in this way can be very generalized for other purposes of usage of parallelism in computational mechanics.
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Lyakhovich Leonid
2017-01-01
Full Text Available This paper is devoted to formulation and general principles of approximation of multipoint boundary problem of static analysis of deep beam with the use of combined application of finite element method (FEM discrete-continual finite element method (DCFEM. The field of application of DCFEM comprises structures with regular physical and geometrical parameters in some dimension (“basic” dimension. DCFEM presupposes finite element approximation for non-basic dimension while in the basic dimension problem remains continual. DCFEM is based on analytical solutions of resulting multipoint boundary problems for systems of ordinary differential equations with piecewise-constant coefficients.
Yoon, Jeoung Seok; Zang, Arno; Zimmermann, Günter; Stephansson, Ove
2016-04-01
, Ellsworth WL, Stump BW, Hayward C, Frohlich C, Oldham HR, Olson JE, Magnani MB, Brokaw C, Luetgert JH, 2015, Causal factors for seismicity near Azle, Texas, nature communications 6:6728, DOI: 10.1038/ncomms7728 [3] Yoon JS, Zimmermann G, Zang A, Stephansson O, 2015, Discrete element modeling of fluid injection-induced seismicity and activation of nearby fault, Can Geotech J 52: 1457-1465, DOI: 10.1139/cgj-2014-0435.
Ochoa-Avendaño, J.; Garzon-Alvarado, D. A.; Linero, Dorian L.; Cerrolaza, M.
2017-01-01
This paper presents the formulation, implementation, and validation of a simplified qualitative model to determine the crack path of solids considering static loads, infinitesimal strain, and plane stress condition. This model is based on finite element method with a special meshing technique, where nonlinear link elements are included between the faces of the linear triangular elements. The stiffness loss of some link elements represents the crack opening. Three experimental tests of bending...
International Nuclear Information System (INIS)
Masoud Ziaei-Rad
2010-01-01
In this paper, a two-dimensional numerical scheme is presented for the simulation of turbulent, viscous, transient compressible flows in the simultaneously developing hydraulic and thermal boundary layer region. The numerical procedure is a finite-volume-based finite-element method applied to unstructured grids. This combination together with a new method applied for the boundary conditions allows for accurate computation of the variables in the entrance region and for a wide range of flow fields from subsonic to transonic. The Roe-Riemann solver is used for the convective terms, whereas the standard Galerkin technique is applied for the viscous terms. A modified κ-ε model with a two-layer equation for the near-wall region combined with a compressibility correction is used to predict the turbulent viscosity. Parallel processing is also employed to divide the computational domain among the different processors to reduce the computational time. The method is applied to some test cases in order to verify the numerical accuracy. The results show significant differences between incompressible and compressible flows in the friction coefficient, Nusselt number, shear stress and the ratio of the compressible turbulent viscosity to the molecular viscosity along the developing region. A transient flow generated after an accidental rupture in a pipeline was also studied as a test case. The results show that the present numerical scheme is stable, accurate and efficient enough to solve the problem of transient wall-bounded flow.
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R. Daud
2013-06-01
Full Text Available Shielding interaction effects of two parallel edge cracks in finite thickness plates subjected to remote tension load is analyzed using a developed finite element analysis program. In the present study, the crack interaction limit is evaluated based on the fitness of service (FFS code, and focus is given to the weak crack interaction region as the crack interval exceeds the length of cracks (b > a. Crack interaction factors are evaluated based on stress intensity factors (SIFs for Mode I SIFs using a displacement extrapolation technique. Parametric studies involved a wide range of crack-to-width (0.05 ≤ a/W ≤ 0.5 and crack interval ratios (b/a > 1. For validation, crack interaction factors are compared with single edge crack SIFs as a state of zero interaction. Within the considered range of parameters, the proposed numerical evaluation used to predict the crack interaction factor reduces the error of existing analytical solution from 1.92% to 0.97% at higher a/W. In reference to FFS codes, the small discrepancy in the prediction of the crack interaction factor validates the reliability of the numerical model to predict crack interaction limits under shielding interaction effects. In conclusion, the numerical model gave a successful prediction in estimating the crack interaction limit, which can be used as a reference for the shielding orientation of other cracks.
Setsompop, Kawin; Alagappan, Vijayanand; Gagoski, Borjan; Witzel, Thomas; Polimeni, Jonathan; Potthast, Andreas; Hebrank, Franz; Fontius, Ulrich; Schmitt, Franz; Wald, Lawrence L; Adalsteinsson, Elfar
2008-12-01
Slice-selective RF waveforms that mitigate severe B1+ inhomogeneity at 7 Tesla using parallel excitation were designed and validated in a water phantom and human studies on six subjects using a 16-element degenerate stripline array coil driven with a butler matrix to utilize the eight most favorable birdcage modes. The parallel RF waveform design applied magnitude least-squares (MLS) criteria with an optimized k-space excitation trajectory to significantly improve profile uniformity compared to conventional least-squares (LS) designs. Parallel excitation RF pulses designed to excite a uniform in-plane flip angle (FA) with slice selection in the z-direction were demonstrated and compared with conventional sinc-pulse excitation and RF shimming. In all cases, the parallel RF excitation significantly mitigated the effects of inhomogeneous B1+ on the excitation FA. The optimized parallel RF pulses for human B1+ mitigation were only 67% longer than a conventional sinc-based excitation, but significantly outperformed RF shimming. For example the standard deviations (SDs) of the in-plane FA (averaged over six human studies) were 16.7% for conventional sinc excitation, 13.3% for RF shimming, and 7.6% for parallel excitation. This work demonstrates that excitations with parallel RF systems can provide slice selection with spatially uniform FAs at high field strengths with only a small pulse-duration penalty. (c) 2008 Wiley-Liss, Inc.
KIM, Jong Woon; LEE, Young-Ouk
2017-09-01
As computing power gets better and better, computer codes that use a deterministic method seem to be less useful than those using the Monte Carlo method. In addition, users do not like to think about space, angles, and energy discretization for deterministic codes. However, a deterministic method is still powerful in that we can obtain a solution of the flux throughout the problem, particularly as when particles can barely penetrate, such as in a deep penetration problem with small detection volumes. Recently, a new state-of-the-art discrete-ordinates code, ATTILA, was developed and has been widely used in several applications. ATTILA provides the capabilities to solve geometrically complex 3-D transport problems by using an unstructured tetrahedral mesh. Since 2009, we have been developing our own code by benchmarking ATTILA. AETIUS is a discrete ordinates code that uses an unstructured tetrahedral mesh such as ATTILA. For pre- and post- processing, Gmsh is used to generate an unstructured tetrahedral mesh by importing a CAD file (*.step) and visualizing the calculation results of AETIUS. Using a CAD tool, the geometry can be modeled very easily. In this paper, we describe a brief overview of AETIUS and provide numerical results from both AETIUS and a Monte Carlo code, MCNP5, in a deep penetration problem with small detection volumes. The results demonstrate the effectiveness and efficiency of AETIUS for such calculations.
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Pooya Hamdi
2015-12-01
Full Text Available Heterogeneity is an inherent component of rock and may be present in different forms including mineral heterogeneity, geometrical heterogeneity, weak grain boundaries and micro-defects. Microcracks are usually observed in crystalline rocks in two forms: natural and stress-induced; the amount of stress-induced microcracking increases with depth and in-situ stress. Laboratory results indicate that the physical properties of rocks such as strength, deformability, P-wave velocity and permeability are influenced by increase in microcrack intensity. In this study, the finite-discrete element method (FDEM is used to model microcrack heterogeneity by introducing into a model sample sets of microcracks using the proposed micro discrete fracture network (μDFN approach. The characteristics of the microcracks required to create μDFN models are obtained through image analyses of thin sections of Lac du Bonnet granite adopted from published literature. A suite of two-dimensional laboratory tests including uniaxial, triaxial compression and Brazilian tests is simulated and the results are compared with laboratory data. The FDEM-μDFN models indicate that micro-heterogeneity has a profound influence on both the mechanical behavior and resultant fracture pattern. An increase in the microcrack intensity leads to a reduction in the strength of the sample and changes the character of the rock strength envelope. Spalling and axial splitting dominate the failure mode at low confinement while shear failure is the dominant failure mode at high confinement. Numerical results from simulated compression tests show that microcracking reduces the cohesive component of strength alone, and the frictional strength component remains unaffected. Results from simulated Brazilian tests show that the tensile strength is influenced by the presence of microcracks, with a reduction in tensile strength as microcrack intensity increases. The importance of microcrack heterogeneity in
Fenchel, Michael; Nael, Kambiz; Deshpande, Vibhas S; Finn, J Paul; Kramer, Ulrich; Miller, Stephan; Ruehm, Stefan; Laub, Gerhard
2006-09-01
The aim of the present study was to assess the feasibility of renal magnetic resonance angiography at 3.0 T using a phased-array coil system with 32-coil elements. Specifically, high parallel imaging factors were used for an increased spatial resolution and anatomic coverage of the whole abdomen. Signal-to-noise values and the g-factor distribution of the 32 element coil were examined in phantom studies for the magnetic resonance angiography (MRA) sequence. Eleven volunteers (6 men, median age of 30.0 years) were examined on a 3.0-T MR scanner (Magnetom Trio, Siemens Medical Solutions, Malvern, PA) using a 32-element phased-array coil (prototype from In vivo Corp.). Contrast-enhanced 3D-MRA (TR 2.95 milliseconds, TE 1.12 milliseconds, flip angle 25-30 degrees , bandwidth 650 Hz/pixel) was acquired with integrated generalized autocalibrating partially parallel acquisition (GRAPPA), in both phase- and slice-encoding direction. Images were assessed by 2 independent observers with regard to image quality, noise and presence of artifacts. Signal-to-noise levels of 22.2 +/- 22.0 and 57.9 +/- 49.0 were measured with (GRAPPAx6) and without parallel-imaging, respectively. The mean g-factor of the 32-element coil for GRAPPA with an acceleration of 3 and 2 in the phase-encoding and slice-encoding direction, respectively, was 1.61. High image quality was found in 9 of 11 volunteers (2.6 +/- 0.8) with good overall interobserver agreement (k = 0.87). Relatively low image quality with higher noise levels were encountered in 2 volunteers. MRA at 3.0 T using a 32-element phased-array coil is feasible in healthy volunteers. High diagnostic image quality and extended anatomic coverage could be achieved with application of high parallel imaging factors.
Sarper, Bugra; Saglam, Mehmet; Aydin, Orhan; Avci, Mete
2018-04-01
In this study, natural convection in a vertical channel is studied experimentally and numerically. One of the channel walls is heated discretely by two flush-mounted heaters while the other is insulated. The effects of the clearance between the heaters on heat transfer and hot spot temperature while total length of the heaters keeps constant are investigated. Four different settlements of two discrete heaters are comparatively examined. Air is used as the working fluid. The range of the modified Grashof number covers the values between 9.6 × 105 and 1.53 × 10.7 Surface to surface radiation is taken into account. Flow visualizations and temperature measurements are performed in the experimental study. Numerical computations are performed using the commercial CFD code ANSYS FLUENT. The results are represented as the variations of surface temperature, hot spot temperature and Nusselt number with the modified Grashof number and the clearance between the heaters as well as velocity and temperature variations of the fluid.
Zampini, Stefano
2016-06-02
Balancing Domain Decomposition by Constraints (BDDC) methods have proven to be powerful preconditioners for large and sparse linear systems arising from the finite element discretization of elliptic PDEs. Condition number bounds can be theoretically established that are independent of the number of subdomains of the decomposition. The core of the methods resides in the design of a larger and partially discontinuous finite element space that allows for fast application of the preconditioner, where Cholesky factorizations of the subdomain finite element problems are additively combined with a coarse, global solver. Multilevel and highly-scalable algorithms can be obtained by replacing the coarse Cholesky solver with a coarse BDDC preconditioner. BDDC methods have the remarkable ability to control the condition number, since the coarse space of the preconditioner can be adaptively enriched at the cost of solving local eigenproblems. The proper identification of these eigenproblems extends the robustness of the methods to any heterogeneity in the distribution of the coefficients of the PDEs, not only when the coefficients jumps align with the subdomain boundaries or when the high contrast regions are confined to lie in the interior of the subdomains. The specific adaptive technique considered in this paper does not depend upon any interaction of discretization and partition; it relies purely on algebraic operations. Coarse space adaptation in BDDC methods has attractive algorithmic properties, since the technique enhances the concurrency and the arithmetic intensity of the preconditioning step of the sparse implicit solver with the aim of controlling the number of iterations of the Krylov method in a black-box fashion, thus reducing the number of global synchronization steps and matrix vector multiplications needed by the iterative solver; data movement and memory bound kernels in the solve phase can be thus limited at the expense of extra local ops during the setup of
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Xiaoqing Wang
2016-01-01
Full Text Available Parallel analyses about the dynamic responses of a large-scale water conveyance tunnel under seismic excitation are presented in this paper. A full three-dimensional numerical model considering the water-tunnel-soil coupling is established and adopted to investigate the tunnel’s dynamic responses. The movement and sloshing of the internal water are simulated using the multi-material Arbitrary Lagrangian Eulerian (ALE method. Nonlinear fluid–structure interaction (FSI between tunnel and inner water is treated by using the penalty method. Nonlinear soil-structure interaction (SSI between soil and tunnel is dealt with by using the surface to surface contact algorithm. To overcome computing power limitations and to deal with such a large-scale calculation, a parallel algorithm based on the modified recursive coordinate bisection (MRCB considering the balance of SSI and FSI loads is proposed and used. The whole simulation is accomplished on Dawning 5000 A using the proposed MRCB based parallel algorithm optimized to run on supercomputers. The simulation model and the proposed approaches are validated by comparison with the added mass method. Dynamic responses of the tunnel are analyzed and the parallelism is discussed. Besides, factors affecting the dynamic responses are investigated. Better speedup and parallel efficiency show the scalability of the parallel method and the analysis results can be used to aid in the design of water conveyance tunnels.
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Chong Shi
2017-10-01
Full Text Available Fractured seepage is an important factor affecting the interface stability of rock mass. It is closely related to fracture properties and hydraulic conditions. In this study, the law of seepage in a single fracture surface based on modified cubic law is described, and the three-dimensional discrete element method is used to simulate the dam foundation structure of the Capulin San Pablo (Costa Rica hydropower station. The effect of construction joints and developed structure on dam stability is studied, and its permeability law and sliding stability are also evaluated. It is found that the hydraulic-mechanical coupling with strength reduction method in DEM is more appropriate to use to study the seepage-related problems of fractured rock mass, which considers practical conditions, such as the roughness of and the width of fracture. The strength reduction method provides a more accurate safety factor of dam when considering the deformation coordination with bedrocks. It is an important method with which to study the stability of seepage conditions in complex structures. The discrete method also provided an effective and reasonable way of determining seepage control measures.
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Vadim N. Glinskiy
2017-05-01
Full Text Available In memory of an outstanding palaeoichthyologist Elga Mark-Kurik The range of diversity of psammosteids from the family Psammosteidae is still poorly known. Here a new species, Psammosteus ramosus sp. nov. Glinskiy, from the Amata Regional Stage of the Main Devonian Field is described. Its morphology, ornamentation, histology of exoskeletal plates, and micromeric elements are compared with those of other representatives of the family Psammosteidae. The comparison shows a close relationship of the new species with Psammosteus falcatus Obruchev, P. kiaeri Halstead Tarlo and P. pectinatus Obruchev, a group of species that is significantly different from other representatives of the genus Psammosteus and constitutes a separate evolutionary lineage. On the basis of morphological and histological features we here differentiate in the fields of tesserae of Psammosteidae the discrete micromeric elements of the ‘basic type’, known in Psammosteus bergi (Obruchev, P. levis Obruchev, P. livonicus Obruchev, P. maeandrinus Agassiz, P. megalopteryx (Trautschold, P. praecursor Obruchev and Karelosteus weberi Obruchev, and micromeric elements of the ‘progressive type’, known in Psammosteus falcatus, P. cf. kiaeri and P. ramosus sp. nov. Glinskiy.
International Nuclear Information System (INIS)
Hennart, J.P.; Valle, E. del.
1995-01-01
A generalized nodal finite element formalism is presented, which covers virtually all known finit difference approximation to the discrete ordinates equations in slab geometry. This paper (Part 1) presents the theory of the so called open-quotes continuous moment methodsclose quotes, which include such well-known methods as the open-quotes diamond differenceclose quotes and the open-quotes characteristicclose quotes schemes. In a second paper (hereafter referred to as Part II), the authors will present the theory of the open-quotes discontinuous moment methodsclose quotes, consisting in particular of the open-quotes linear discontinuousclose quotes scheme as well as of an entire new class of schemes. Corresponding numerical results are available for all these schemes and will be presented in a third paper (Part III). 12 refs
International Nuclear Information System (INIS)
Longoni, G.; Haghighat, A.; Sjoden, G.
2005-01-01
This paper discusses a new preconditioned Sn algorithm referred to as FAST (Flux Acceleration Sn Transport). This algorithm uses the PENSSn code as the pre-conditioner, and the PENTRANSSn code system as the transport solver. PENSSn is developed based on the even-parity simplified Sn formulation in a parallel environment, and PENTRAN-SSn is a version of PENTRAN that uses PENSSn as the pre-conditioner with the FAST system. The paper briefly discusses the EP-SSn formulation and important numerical features of PENSSn. The FAST algorithm is discussed and tested for the C5G7 MOX eigenvalue benchmark problem. It is demonstrated that FAST leads to significant speedups (∼7) over the standard PENTRAN code. Moreover, FAST shows closer agreement with a reference Monte Carlo simulation. (authors)
Energy Technology Data Exchange (ETDEWEB)
Jafarzadeh, Hassan; Moradinasab, Nazanin; Gerami, Ali
2017-07-01
Adjusted discrete Multi-Objective Invasive Weed Optimization (DMOIWO) algorithm, which uses fuzzy dominant approach for ordering, has been proposed to solve No-wait two-stage flexible flow shop scheduling problem. Design/methodology/approach: No-wait two-stage flexible flow shop scheduling problem by considering sequence-dependent setup times and probable rework in both stations, different ready times for all jobs and rework times for both stations as well as unrelated parallel machines with regards to the simultaneous minimization of maximum job completion time and average latency functions have been investigated in a multi-objective manner. In this study, the parameter setting has been carried out using Taguchi Method based on the quality indicator for beater performance of the algorithm. Findings: The results of this algorithm have been compared with those of conventional, multi-objective algorithms to show the better performance of the proposed algorithm. The results clearly indicated the greater performance of the proposed algorithm. Originality/value: This study provides an efficient method for solving multi objective no-wait two-stage flexible flow shop scheduling problem by considering sequence-dependent setup times, probable rework in both stations, different ready times for all jobs, rework times for both stations and unrelated parallel machines which are the real constraints.
International Nuclear Information System (INIS)
Jafarzadeh, Hassan; Moradinasab, Nazanin; Gerami, Ali
2017-01-01
Adjusted discrete Multi-Objective Invasive Weed Optimization (DMOIWO) algorithm, which uses fuzzy dominant approach for ordering, has been proposed to solve No-wait two-stage flexible flow shop scheduling problem. Design/methodology/approach: No-wait two-stage flexible flow shop scheduling problem by considering sequence-dependent setup times and probable rework in both stations, different ready times for all jobs and rework times for both stations as well as unrelated parallel machines with regards to the simultaneous minimization of maximum job completion time and average latency functions have been investigated in a multi-objective manner. In this study, the parameter setting has been carried out using Taguchi Method based on the quality indicator for beater performance of the algorithm. Findings: The results of this algorithm have been compared with those of conventional, multi-objective algorithms to show the better performance of the proposed algorithm. The results clearly indicated the greater performance of the proposed algorithm. Originality/value: This study provides an efficient method for solving multi objective no-wait two-stage flexible flow shop scheduling problem by considering sequence-dependent setup times, probable rework in both stations, different ready times for all jobs, rework times for both stations and unrelated parallel machines which are the real constraints.
Witkowska, Agnieszka; Lewandowska, Anita; Falkowska, Lucyna M
2016-03-15
Parallel studies on organic and elemental carbon in PM1 and PM2.5 aerosols and in wet deposition in various forms of its occurrence were conducted in the urbanised coastal zone of the Baltic Sea. The carbon load introduced into the sea water was mainly affected by the form of precipitation. Dry deposition load of carbon was on average a few orders of magnitude smaller than wet deposition. The suspended organic carbon was more effectively removed from the air with rain than snow, while an inverse relationship was found for elemental carbon. However the highest flux of water insoluble organic carbon was recorded in precipitation of a mixed nature. The atmospheric cleaning of highly dissolved organic carbon was observed to be the most effective on the first day of precipitation, while the hydrophobic elemental carbon was removed more efficiently when the precipitation lasted longer than a day. Copyright © 2016 Elsevier Ltd. All rights reserved.
International Nuclear Information System (INIS)
Fields, D.E.; Hetrick, D.M.
1978-12-01
A model has been developed to study the feasibility of simulating one-dimensional transport of radioisotope-tagged sediment in tidal-dominated estuaries. A preliminary one-dimensional model for simulating hydrodynamic, thermal, and dissolved radionuclide concentrations in tidal estuaries was merged with an improved version of the SEDTRN model, a multi-sediment-size class model of bedload and suspended sediment transport. The improved SEDTRN model, which employs a velocity-based rather than an energy-based sediment transport rate calculation and accounts for nonzero channel bed slope, is given credence by comparing its results in stand-alone form to those obtained using the parent model. Results of the latter model have been shown to compare favorably to field measurements. The combined preliminary model is called HOTSED. Details of model modifications, the addition of printer plot output capability, and a discussion of input and output structures are included. The HOTSED model is applied to the Hudson River under tidal-transient conditions and the transport ''tagged'' or radioisotope-bearing sediment is simulated. The code is designed specifically for applications with dominant tidal cycling. It requires, for a 76-element channel system, 270 thousand bytes of storage and, for a simulation of 25 hours, has an execution time of approximately five minutes on the IBM System 360/91 computer
Directory of Open Access Journals (Sweden)
James Wolfer
2015-02-01
Full Text Available Traditionally, topics such as parallel computing, computer graphics, and artificial intelligence have been taught as stand-alone courses in the computing curriculum. Often these are elective courses, limiting the material to the subset of students choosing to take the course. Recently there has been movement to distribute topics across the curriculum in order to ensure that all graduates have been exposed to concepts such as parallel computing. Previous work described an attempt to systematically weave a tapestry of topics into the undergraduate computing curriculum. This paper reviews that work and expands it with representative examples of assignments, demonstrations, and results as well as describing how the tools and examples deployed for these classes have a residual effect on classes such as Comptuer Literacy.
Energy Technology Data Exchange (ETDEWEB)
Zhou, Jing [Idaho National Lab. (INL), Idaho Falls, ID (United States); Huang, Hai [Idaho National Lab. (INL), Idaho Falls, ID (United States); Mattson, Earl [Idaho National Lab. (INL), Idaho Falls, ID (United States); Wang, Herb F. [Univ. of Wisconsin, Madison, WI (United States); Haimson, Bezalel C. [Univ. of Wisconsin, Madison, WI (United States); Doe, Thomas W. [Golder Associates Inc., Redmond, VA (United States); Oldenburg, Curtis M. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Dobson, Patrick F. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
2017-02-01
Aimed at supporting the design of hydraulic fracturing experiments at the kISMET site, ~1500 m below ground in a deep mine, we performed pre-experimental hydraulic fracturing simulations in order to estimate the breakdown pressure, propagation pressure, fracture geometry, and the magnitude of induced seismicity using a newly developed fully coupled three-dimensional (3D) network flow and quasi-static discrete element model (DEM). The quasi-static DEM model, which is constructed by Delaunay tessellation of the rock volume, considers rock fabric heterogeneities by using the “disordered” DEM mesh and adding random perturbations to the stiffness and tensile/shear strengths of individual DEM elements and the elastic beams between them. A conjugate 3D flow network based on the DEM lattice is constructed to calculate the fluid flow in both the fracture and porous matrix. One distinctive advantage of the model is that fracturing is naturally described by the breakage of elastic beams between DEM elements. It is also extremely convenient to introduce mechanical anisotropy into the model by simply assigning orientation-dependent tensile/shear strengths to the elastic beams. In this paper, the 3D hydraulic fracturing model was verified against the analytic solution for a penny-shaped crack model. We applied the model to simulate fracture propagation from a vertical open borehole based on initial estimates of rock mechanical properties and in-situ stress conditions. The breakdown pressure and propagation pressure are directly obtained from the simulation. In addition, the released elastic strain energies of individual fracturing events were calculated and used as a conservative estimate for the magnitudes of the potential induced seismic activities associated with fracturing. The comparisons between model predictions and experimental results are still ongoing.
Zou, Feng; Yuan, De-Yi; Gao, Chao; Liao, Ting; Chen, Wen-Tao; Han, Zhi-Qiang; Zhang, Lin
2014-04-01
In order to elucidate the nutrition of Camellia olei fera at pollination and fertilization stages, the contents of mineral elements were determined by auto discrete analyzers and atomic absorption spectrophotometer, and the change in the contents of mineral elements was studied and analysed under the condition of self- and cross-pollination. The results are showed that nine kinds of mineral elements contents were of "S" or "W" type curve changes at the pollination and fertilization stages of Camellia olei fera. N, K, Zn, Cu, Ca, Mn element content changes showed "S" curve under the self- and out-crossing, the content of N reaching the highest was 3.445 8 mg x g(-1) in self-pollination of 20 d; K content reaching the highest at the cross-pollination 20 d was 6.275 5 mg x g(-1); Zn content in self-pollination of 10 d reaching the highest was 0.070 5 mg x g(-1); Cu content in the cross-pollination of 5 d up to the highest was 0.061 0 mg x g(-1); Ca content in the cross-pollination of 15 d up to the highest was 3.714 5 mg x g(-1); the content of Mn reaching the highest in self-pollination 30 d was 2. 161 5 mg x g(-1). Fe, P, Mg element content changes was of "S" type curve in selfing and was of "W" type curve in outcrossing, Fe content in the self-pollination 10 d up to the highest was 0.453 0 mg x g(-1); P content in self-pollination of 20 d reaching the highest was 6.731 8 mg x g(-1); the content of Mg up to the highest in self-pollination 25 d was 2.724 0 mg x g(-1). The results can be used as a reference for spraying foliar fertilizer, and improving seed setting rate and yield in Camellia olei fera.
Energy Technology Data Exchange (ETDEWEB)
Lober, R.R.; Tautges, T.J.; Vaughan, C.T.
1997-03-01
Paving is an automated mesh generation algorithm which produces all-quadrilateral elements. It can additionally generate these elements in varying sizes such that the resulting mesh adapts to a function distribution, such as an error function. While powerful, conventional paving is a very serial algorithm in its operation. Parallel paving is the extension of serial paving into parallel environments to perform the same meshing functions as conventional paving only on distributed, discretized models. This extension allows large, adaptive, parallel finite element simulations to take advantage of paving`s meshing capabilities for h-remap remeshing. A significantly modified version of the CUBIT mesh generation code has been developed to host the parallel paving algorithm and demonstrate its capabilities on both two dimensional and three dimensional surface geometries and compare the resulting parallel produced meshes to conventionally paved meshes for mesh quality and algorithm performance. Sandia`s {open_quotes}tiling{close_quotes} dynamic load balancing code has also been extended to work with the paving algorithm to retain parallel efficiency as subdomains undergo iterative mesh refinement.
DEFF Research Database (Denmark)
Sørensen, John Aasted
2011-01-01
The objectives of Discrete Mathematics (IDISM2) are: The introduction of the mathematics needed for analysis, design and verification of discrete systems, including the application within programming languages for computer systems. Having passed the IDISM2 course, the student will be able...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics......; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...
Ngoma, Jeff; Philippe, Pierre; Bonelli, Stéphane; Radjaï, Farhang; Delenne, Jean-Yves
2018-05-01
We present here a numerical study dedicated to the fluidization of a submerged granular medium induced by a localized fluid injection. To this end, a two-dimensional (2D) model is used, coupling the lattice Boltzmann method (LBM) with the discrete element method (DEM) for a relevant description of fluid-grains interaction. An extensive investigation has been carried out to analyze the respective influences of the different parameters of our configuration, both geometrical (bed height, grain diameter, injection width) and physical (fluid viscosity, buoyancy). Compared to previous experimental works, the same qualitative features are recovered as regards the general phenomenology including transitory phase, stationary states, and hysteretic behavior. We also present quantitative findings about transient fluidization, for which several dimensionless quantities and scaling laws are proposed, and about the influence of the injection width, from localized to homogeneous fluidization. Finally, the impact of the present 2D geometry is discussed, by comparison to the real three-dimensional (3D) experiments, as well as the crucial role of the prevailing hydrodynamic regime within the expanding cavity, quantified through a cavity Reynolds number, that can presumably explain some substantial differences observed regarding upward expansion process of the fluidized zone when the fluid viscosity is changed.
International Nuclear Information System (INIS)
Laufer, Michael R.; Bickel, Jeffrey E.; Buster, Grant C.; Krumwiede, David L.; Peterson, Per F.
2014-01-01
This paper presents a facility description, preliminary results, and future test program of the new X-Ray Pebble Recirculation Experiment (X-PREX), which is now operational and being used to collect data on the behavior of slow dense granular flows relevant to pebble bed reactor core designs. The X-PREX facility uses digital x-ray tomography methods to track both the translational and rotational motion of spherical pebbles, which provides unique experimental results that can be used to validate discrete element method (DEM) simulations of pebble motion. The validation effort supported by the X-PREX facility provides a means to build confidence in analysis of pebble bed configuration and residence time distributions that impact the neutronics, thermal hydraulics, and safety analysis of pebble bed reactor cores. Preliminary experimental and DEM simulation results are reported for silo drainage, a classical problem in the granular flow literature, at several hopper angles. These studies include conventional converging and novel diverging geometries that provide additional flexibility in the design of pebble bed reactor cores. Excellent agreement is found between the X-PREX experimental and DEM simulation results. Finally, this paper discusses additional studies in progress relevant to the design and analysis of pebble bed reactor cores including pebble recirculation in cylindrical core geometries and evaluation of forces on shut down blades inserted directly into a packed pebble bed. (author)
Directory of Open Access Journals (Sweden)
Yan Zilin
2017-01-01
Full Text Available The behaviour of various powder systems during high temperature sintering has been investigated by coupling X-ray microtomography and discrete element method (DEM. Both methods are particularly relevant to analyse particle interactions and porosity changes occurring during sintering. Two examples are presented. The first one deals with a copper powder including artificially created pores which sintering has been observed in situ at the European synchrotron and simulated by DEM. 3D images with a resolution of 1.5 μm have been taken at various times of the sintering cycle. The comparison of the real displacement of particle centers with the displacement derived from the mean field assumption demonstrates significant particle rearrangement in some regions of the sample. Although DEM simulation showed less rearrangement, it has been able to accurately predict the densification kinetics. The second example concerns multilayer ceramic capacitors (MLCCs composed of hundreds of alternated metal electrode and ceramic dielectric layers. The observation of Ni-based MLCCs by synchrotron nanotomography at Argon National Laboratory with a spatial resolution between 10 and 50 nm allowed understanding the origin of heterogeneities formed in Ni layers during sintering. DEM simulations confirmed this analysis and provided clues for reducing these defects.
Parallel computing solution of Boltzmann neutron transport equation
International Nuclear Information System (INIS)
Ansah-Narh, T.
2010-01-01
The focus of the research was on developing parallel computing algorithm for solving Eigen-values of the Boltzmam Neutron Transport Equation (BNTE) in a slab geometry using multi-grid approach. In response to the problem of slow execution of serial computing when solving large problems, such as BNTE, the study was focused on the design of parallel computing systems which was an evolution of serial computing that used multiple processing elements simultaneously to solve complex physical and mathematical problems. Finite element method (FEM) was used for the spatial discretization scheme, while angular discretization was accomplished by expanding the angular dependence in terms of Legendre polynomials. The eigenvalues representing the multiplication factors in the BNTE were determined by the power method. MATLAB Compiler Version 4.1 (R2009a) was used to compile the MATLAB codes of BNTE. The implemented parallel algorithms were enabled with matlabpool, a Parallel Computing Toolbox function. The option UseParallel was set to 'always' and the default value of the option was 'never'. When those conditions held, the solvers computed estimated gradients in parallel. The parallel computing system was used to handle all the bottlenecks in the matrix generated from the finite element scheme and each domain of the power method generated. The parallel algorithm was implemented on a Symmetric Multi Processor (SMP) cluster machine, which had Intel 32 bit quad-core x 86 processors. Convergence rates and timings for the algorithm on the SMP cluster machine were obtained. Numerical experiments indicated the designed parallel algorithm could reach perfect speedup and had good stability and scalability. (au)
A parallel version of a multigrid algorithm for isotropic transport equations
International Nuclear Information System (INIS)
Manteuffel, T.; McCormick, S.; Yang, G.; Morel, J.; Oliveira, S.
1994-01-01
The focus of this paper is on a parallel algorithm for solving the transport equations in a slab geometry using multigrid. The spatial discretization scheme used is a finite element method called the modified linear discontinuous (MLD) scheme. The MLD scheme represents a lumped version of the standard linear discontinuous (LD) scheme. The parallel algorithm was implemented on the Connection Machine 2 (CM2). Convergence rates and timings for this algorithm on the CM2 and Cray-YMP are shown
Parallel Auxiliary Space AMG Solver for $H(div)$ Problems
Energy Technology Data Exchange (ETDEWEB)
Kolev, Tzanio V. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2012-12-18
We present a family of scalable preconditioners for matrices arising in the discretization of $H(div)$ problems using the lowest order Raviart--Thomas finite elements. Our approach belongs to the class of “auxiliary space''--based methods and requires only the finite element stiffness matrix plus some minimal additional discretization information about the topology and orientation of mesh entities. Also, we provide a detailed algebraic description of the theory, parallel implementation, and different variants of this parallel auxiliary space divergence solver (ADS) and discuss its relations to the Hiptmair--Xu (HX) auxiliary space decomposition of $H(div)$ [SIAM J. Numer. Anal., 45 (2007), pp. 2483--2509] and to the auxiliary space Maxwell solver AMS [J. Comput. Math., 27 (2009), pp. 604--623]. Finally, an extensive set of numerical experiments demonstrates the robustness and scalability of our implementation on large-scale $H(div)$ problems with large jumps in the material coefficients.
Discrete variational Hamiltonian mechanics
International Nuclear Information System (INIS)
Lall, S; West, M
2006-01-01
The main contribution of this paper is to present a canonical choice of a Hamiltonian theory corresponding to the theory of discrete Lagrangian mechanics. We make use of Lagrange duality and follow a path parallel to that used for construction of the Pontryagin principle in optimal control theory. We use duality results regarding sensitivity and separability to show the relationship between generating functions and symplectic integrators. We also discuss connections to optimal control theory and numerical algorithms
DEFF Research Database (Denmark)
Sørensen, John Aasted
2011-01-01
; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics...... to new problems. Relations and functions: Define a product set; define and apply equivalence relations; construct and apply functions. Apply these concepts to new problems. Natural numbers and induction: Define the natural numbers; apply the principle of induction to verify a selection of properties...
DEFF Research Database (Denmark)
Busch, Peter Andre; Zinner Henriksen, Helle
2018-01-01
discretion is suggested to reduce this footprint by influencing or replacing their discretionary practices using ICT. What is less researched is whether digital discretion can cause changes in public policy outcomes, and under what conditions such changes can occur. Using the concept of public service values......This study reviews 44 peer-reviewed articles on digital discretion published in the period from 1998 to January 2017. Street-level bureaucrats have traditionally had a wide ability to exercise discretion stirring debate since they can add their personal footprint on public policies. Digital......, we suggest that digital discretion can strengthen ethical and democratic values but weaken professional and relational values. Furthermore, we conclude that contextual factors such as considerations made by policy makers on the macro-level and the degree of professionalization of street...
International Nuclear Information System (INIS)
Yamada, Tomonori
2010-01-01
The safety requirement of nuclear power plant attracts much attention nowadays. With the growing computing power, numerical simulation is one of key technologies to meet this safety requirement. Center for Computational Science and e-Systems of Japan Atomic Energy Agency has been developing a finite element analysis code for assembled structure to accurately evaluate the structural integrity of nuclear power plant in its entirety under seismic events. Because nuclear power plant is very huge assembled structure with tens of millions of mechanical components, the finite element model of each component is assembled into one structure and non-conforming meshes of mechanical components are bonded together inside the code. The main technique to bond these mechanical components is triple sparse matrix multiplication with multiple point constrains and global stiffness matrix. In our code, this procedure is conducted in a component by component manner, so that the working memory size and computing time for this multiplication are available on the current computing environment. As an illustrative example, seismic simulation of a real nuclear reactor of High Temperature engineering Test Reactor, which is located at the O-arai research and development center of JAEA, with 80 major mechanical components was conducted. Consequently, our code successfully simulated detailed elasto-plastic deformation of nuclear reactor and its computational performance was investigated. (author)
Discrete differential geometry. Consistency as integrability
Bobenko, Alexander I.; Suris, Yuri B.
2005-01-01
A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete geometry studies geometric shapes with finite number of elements (such as polyhedra), the discrete differential geometry aims at the development of discrete equivalents of notions and methods of smooth surface theory. Current interest in this field derives not ...
Directory of Open Access Journals (Sweden)
Xiaolin Huang
2016-12-01
Full Text Available This paper numerically investigates the seismic response of the filled joint under high amplitude stress waves using the combined finite-discrete element method (FDEM. A thin layer of independent polygonal particles are used to simulate the joint fillings. Each particle is meshed using the Delaunay triangulation scheme and can be crushed when the load exceeds its strength. The propagation of the 1D longitude wave through a single filled joint is studied, considering the influences of the joint thickness and the characteristics of the incident wave, such as the amplitude and frequency. The results show that the filled particles under high amplitude stress waves mainly experience three deformation stages: (i initial compaction stage; (ii crushing stage; and (iii crushing and compaction stage. In the initial compaction stage and crushing and compaction stage, compaction dominates the mechanical behavior of the joint, and the particle area distribution curve varies little. In these stages, the transmission coefficient increases with the increase of the amplitude, i.e., peak particle velocity (PPV, of the incident wave. On the other hand, in the crushing stage, particle crushing plays the dominant role. The particle size distribution curve changes abruptly with the PPV due to the fragments created by the crushing process. This process consumes part of wave energy and reduces the stiffness of the filled joint. The transmission coefficient decreases with increasing PPV in this stage because of the increased amount of energy consumed by crushing. Moreover, with the increase of the frequency of the incident wave, the transmission coefficient decreases and fewer particles can be crushed. Under the same incident wave, the transmission coefficient decreases when the filled thickness increases and the filled particles become more difficult to be crushed.
Simonson, Scott; Hua, Peng; Luobin, Yan; Zhi, Chen
2016-04-01
Important to the evolution of Danxia landforms is how the rock cliffs are in large part shaped by rock collapse events, ranging from small break offs to large collapses. Quantitative research of Danxia landform evolution is still relatively young. In 2013-2014, Chinese and Slovak researchers conducted joint research to measure deformation of two large rock walls. In situ measurements of one rock wall found it to be stable, and Ps-InSAR measurements of the other were too few to be validated. Research conducted this year by Chinese researchers modeled the stress states of a stone pillar at Mt. Langshan, in Hunan Province, that toppled over in 2009. The model was able to demonstrate how stress states within the pillar changed as the soft basal layer retreated, but was not able to show the stress states at the point of complete collapse. According to field observations, the back side of the pillar fell away from the entire cliff mass before the complete collapse, and no models have been able to demonstrate the mechanisms behind this behavior. A further understanding of the mechanisms controlling rockfall events in Danxia landforms is extremely important because these stunning sceneries draw millions of tourists each year. Protecting the tourists and the infrastructure constructed to accommodate tourism is of utmost concern. This research will employ a UAV to as universally as possible photograph a stone pillar at Mt. Langshan that stands next to where the stone pillar collapsed in 2009. Using the recently developed structure-from-motion technique, a 3D model of the pillar will be constructed in order to extract geometrical data of the entire slope and its structural fabric. Also in situ measurements will be taken of the slope's toe during the field work exercises. These data are essential to constructing a realistic discrete element model using the 3DEC code and perform a kinematic analysis of the rock mass. Intact rock behavior will be based on the Mohr Coulomb
Parallel Fast Legendre Transform
Alves de Inda, M.; Bisseling, R.H.; Maslen, D.K.
1998-01-01
We discuss a parallel implementation of a fast algorithm for the discrete polynomial Legendre transform We give an introduction to the DriscollHealy algorithm using polynomial arithmetic and present experimental results on the eciency and accuracy of our implementation The algorithms were
High-Fidelity RF Gun Simulations with the Parallel 3D Finite Element Particle-In-Cell Code Pic3P
Energy Technology Data Exchange (ETDEWEB)
Candel, A; Kabel, A.; Lee, L.; Li, Z.; Limborg, C.; Ng, C.; Schussman, G.; Ko, K.; /SLAC
2009-06-19
SLAC's Advanced Computations Department (ACD) has developed the first parallel Finite Element 3D Particle-In-Cell (PIC) code, Pic3P, for simulations of RF guns and other space-charge dominated beam-cavity interactions. Pic3P solves the complete set of Maxwell-Lorentz equations and thus includes space charge, retardation and wakefield effects from first principles. Pic3P uses higher-order Finite Elementmethods on unstructured conformal meshes. A novel scheme for causal adaptive refinement and dynamic load balancing enable unprecedented simulation accuracy, aiding the design and operation of the next generation of accelerator facilities. Application to the Linac Coherent Light Source (LCLS) RF gun is presented.
DEFF Research Database (Denmark)
Sørensen, John Aasted
2010-01-01
The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Spring 2010 Ectent: 5 ects Class size: 18......The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Spring 2010 Ectent: 5 ects Class size: 18...
DEFF Research Database (Denmark)
Sørensen, John Aasted
2010-01-01
The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Autumn 2010 Ectent: 5 ects Class size: 15......The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Autumn 2010 Ectent: 5 ects Class size: 15...
Is Discrete Mathematics the New Math of the Eighties?
Hart, Eric W.
1985-01-01
Considered are what discrete mathematics includes, some parallels and differences between new math and discrete mathematics (listed in a table), and lessons to be learned. A list of references is included. (MNS)
Wu, Xiaoping; Tian, Jinfeng; Schmitter, Sebastian; Vaughan, J Tommy; Uğurbil, Kâmil; Van de Moortele, Pierre-François
2016-06-01
We explore the advantages of using a double-ring radiofrequency (RF) array and slice orientation to design parallel transmission (pTx) multiband (MB) pulses for simultaneous multislice (SMS) imaging with whole-brain coverage at 7 Tesla (T). A double-ring head array with 16 elements split evenly in two rings stacked in the z-direction was modeled and compared with two single-ring arrays consisting of 8 or 16 elements. The array performance was evaluated by designing band-specific pTx MB pulses with local specific absorption rate (SAR) control. The impact of slice orientations was also investigated. The double-ring array consistently and significantly outperformed the other two single-ring arrays, with peak local SAR reduced by up to 40% at a fixed excitation error of 0.024. For all three arrays, exciting sagittal or coronal slices yielded better RF performance than exciting axial or oblique slices. A double-ring RF array can be used to drastically improve SAR versus excitation fidelity tradeoff for pTx MB pulse design for brain imaging at 7 T; therefore, it is preferable against single-ring RF array designs when pursuing various biomedical applications of pTx SMS imaging. In comparing the stripline arrays, coronal and sagittal slices are more advantageous than axial and oblique slices for pTx MB pulses. Magn Reson Med 75:2464-2472, 2016. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.
Algorithms for computational fluid dynamics n parallel processors
International Nuclear Information System (INIS)
Van de Velde, E.F.
1986-01-01
A study of parallel algorithms for the numerical solution of partial differential equations arising in computational fluid dynamics is presented. The actual implementation on parallel processors of shared and nonshared memory design is discussed. The performance of these algorithms is analyzed in terms of machine efficiency, communication time, bottlenecks and software development costs. For elliptic equations, a parallel preconditioned conjugate gradient method is described, which has been used to solve pressure equations discretized with high order finite elements on irregular grids. A parallel full multigrid method and a parallel fast Poisson solver are also presented. Hyperbolic conservation laws were discretized with parallel versions of finite difference methods like the Lax-Wendroff scheme and with the Random Choice method. Techniques are developed for comparing the behavior of an algorithm on different architectures as a function of problem size and local computational effort. Effective use of these advanced architecture machines requires the use of machine dependent programming. It is shown that the portability problems can be minimized by introducing high level operations on vectors and matrices structured into program libraries
Energy Technology Data Exchange (ETDEWEB)
NONE
2000-09-01
Research and development has been performed on a general purpose parallel processing software that can be utilized for value solving methods, such as the finite element method, finite volume method and finite difference method. The achievements of the research and development may be summarized as follows: this parallel platform is parallelized in the concept of the domain division method for the elements (calculation cells), and is applicable to any of the finite element method, finite volume method and finite difference method; a researcher who has developed a program can easily perform the parallelization work to have the parallelizing performance displayed; the platform can be utilized in agreement with several parallel levels that are required by the user; with regard to the parallelization efficiency in large-size problems, it has become possible to execute at an efficiency of higher than 70% for the solver parts by using 32 processors of SR8000 at the computation center of the Agency of Industrial Science and Technology; the rigidity matrix preparing part shows an efficiency close to 100%W; and the developed parallel platform is under continued evaluation at the Machine Technology Research Institute and the Material Engineering Research Institute. (NEDO)
Caltagirone, Jean-Paul
2014-01-01
This book presents the fundamental principles of mechanics to re-establish the equations of Discrete Mechanics. It introduces physics and thermodynamics associated to the physical modeling. The development and the complementarity of sciences lead to review today the old concepts that were the basis for the development of continuum mechanics. The differential geometry is used to review the conservation laws of mechanics. For instance, this formalism requires a different location of vector and scalar quantities in space. The equations of Discrete Mechanics form a system of equations where the H
International Nuclear Information System (INIS)
Lee, T.D.
1985-01-01
This paper reviews the role of time throughout all phases of mechanics: classical mechanics, non-relativistic quantum mechanics, and relativistic quantum theory. As an example of the relativistic quantum field theory, the case of a massless scalar field interacting with an arbitrary external current is discussed. The comparison between the new discrete theory and the usual continuum formalism is presented. An example is given of a two-dimensional random lattice and its duel. The author notes that there is no evidence that the discrete mechanics is more appropriate than the usual continuum mechanics
New non-structured discretizations for fluid flows with reinforced incompressibility
International Nuclear Information System (INIS)
Heib, S.
2003-01-01
This work deals with the discretization of Stokes and Navier-Stokes equations modeling the flow of incompressible fluids on 2-D or 3-D non-structured meshes. Triangles and tetrahedrons are used for 2-D and 3-D meshes, respectively. The developments and calculations are performed with the code Priceles (fast CEA-EdF industrial platform for large Eddy simulation). This code allows to perform simulations both on structured and non-structured meshes. A finite-volume resolution method is used: a finite difference volume (FDV) method is used for the structured meshes and a finite element volume (FEV) method is used for the non-structured meshes. The finite element used in the beginning of this work has several defects. Starting from this situation, the discretization is improved by adding modifications to this element and the new elements introduced are analyzed theoretically. In parallel to these analyses, the new discretizations are implemented in order to test them numerically and to confirm the theoretical analyses. The first chapter presents the physical and mathematical modeling used in this work. The second chapter treats of the discretization of Stokes equations and presents the FEV resolution method. Chapter 3 presents a first attempt of improvement of this finite element and leads to the proposal of a new element which is presented in details. The problem encountered with the new discretization leads to a modification presented in chapter 4. This new discretization gives all the expected convergence results and sometimes shows super-convergence properties. Chapter 5 deals with the study and discretization of the Navier-Stokes equations. The study of the filtered Navier-Stokes equations, used for large Eddy simulations, requires to give a particular attention to the discretization of the diffusive terms. Then, the convective terms are considered. The effects of the convective terms in the initial discretization and in the improved method are compared. The use of
Kordy, M. A.; Wannamaker, P. E.; Maris, V.; Cherkaev, E.; Hill, G. J.
2014-12-01
We have developed an algorithm for 3D simulation and inversion of magnetotelluric (MT) responses using deformable hexahedral finite elements that permits incorporation of topography. Direct solvers parallelized on symmetric multiprocessor (SMP), single-chassis workstations with large RAM are used for the forward solution, parameter jacobians, and model update. The forward simulator, jacobians calculations, as well as synthetic and real data inversion are presented. We use first-order edge elements to represent the secondary electric field (E), yielding accuracy O(h) for E and its curl (magnetic field). For very low frequency or small material admittivity, the E-field requires divergence correction. Using Hodge decomposition, correction may be applied after the forward solution is calculated. It allows accurate E-field solutions in dielectric air. The system matrix factorization is computed using the MUMPS library, which shows moderately good scalability through 12 processor cores but limited gains beyond that. The factored matrix is used to calculate the forward response as well as the jacobians of field and MT responses using the reciprocity theorem. Comparison with other codes demonstrates accuracy of our forward calculations. We consider a popular conductive/resistive double brick structure and several topographic models. In particular, the ability of finite elements to represent smooth topographic slopes permits accurate simulation of refraction of electromagnetic waves normal to the slopes at high frequencies. Run time tests indicate that for meshes as large as 150x150x60 elements, MT forward response and jacobians can be calculated in ~2.5 hours per frequency. For inversion, we implemented data space Gauss-Newton method, which offers reduction in memory requirement and a significant speedup of the parameter step versus model space approach. For dense matrix operations we use tiling approach of PLASMA library, which shows very good scalability. In synthetic
DEFF Research Database (Denmark)
Sitchinava, Nodar; Zeh, Norbert
2012-01-01
We present the parallel buffer tree, a parallel external memory (PEM) data structure for batched search problems. This data structure is a non-trivial extension of Arge's sequential buffer tree to a private-cache multiprocessor environment and reduces the number of I/O operations by the number of...... in the optimal OhOf(psortN + K/PB) parallel I/O complexity, where K is the size of the output reported in the process and psortN is the parallel I/O complexity of sorting N elements using P processors....
International Nuclear Information System (INIS)
Eraslan, A.H.
1975-02-01
A far-field mathematical model is presented for numerical simulation of short-time (within tidal cycle) transient, two-dimensional temperature distributions in large coastal and offshore regions resulting from the condenser cooling water discharges of power plants. The Eulerian FLIDE (fluid-in-discrete-element) formulation employs the integral forms of the conservation principles for mass and thermal energy in variable-sized discrete elements that span the specific flow region. The contributions of vertical variations of the velocity components and temperature are rigorously incorporated in the development of depth-averaged, two-dimensional energy transport fluxes by spatially integrating the conservation equations over the enclosure surfaces of the discrete elements. The general mathematical formulation considers completely arbitrary, transient oceanic flow conditions, which include periodic tidal, geostrophic, and wind-induced currents, as locally specified inputs to the model. The thermal impact of a hypothetical, multiunit generating station in a coastal region is analyzed where the oceanic flow conditions are assumed to be strictly periodic tidal currents within any appreciable net drift of sufficient duration to remove the heated effluent. The numerical simulation indicates that the periodic flow conditions cause considerable variations in the temperature distributions during the day and the tidal cycles, which result in severe recirculation and re-entrainment of the heated water between the intakes and the discharges of the different units. This leads to a gradual, long-term increase of the temperatures in the immediate vicinity of the discharge structures and also in the far-field zone. (U.S.)
Kordy, M.; Wannamaker, P.; Maris, V.; Cherkaev, E.; Hill, G.
2016-01-01
Following the creation described in Part I of a deformable edge finite-element simulator for 3-D magnetotelluric (MT) responses using direct solvers, in Part II we develop an algorithm named HexMT for 3-D regularized inversion of MT data including topography. Direct solvers parallelized on large-RAM, symmetric multiprocessor (SMP) workstations are used also for the Gauss-Newton model update. By exploiting the data-space approach, the computational cost of the model update becomes much less in both time and computer memory than the cost of the forward simulation. In order to regularize using the second norm of the gradient, we factor the matrix related to the regularization term and apply its inverse to the Jacobian, which is done using the MKL PARDISO library. For dense matrix multiplication and factorization related to the model update, we use the PLASMA library which shows very good scalability across processor cores. A synthetic test inversion using a simple hill model shows that including topography can be important; in this case depression of the electric field by the hill can cause false conductors at depth or mask the presence of resistive structure. With a simple model of two buried bricks, a uniform spatial weighting for the norm of model smoothing recovered more accurate locations for the tomographic images compared to weightings which were a function of parameter Jacobians. We implement joint inversion for static distortion matrices tested using the Dublin secret model 2, for which we are able to reduce nRMS to ˜1.1 while avoiding oscillatory convergence. Finally we test the code on field data by inverting full impedance and tipper MT responses collected around Mount St Helens in the Cascade volcanic chain. Among several prominent structures, the north-south trending, eruption-controlling shear zone is clearly imaged in the inversion.
Vectorization and parallelization of the finite strip method for dynamic Mindlin plate problems
Chen, Hsin-Chu; He, Ai-Fang
1993-01-01
The finite strip method is a semi-analytical finite element process which allows for a discrete analysis of certain types of physical problems by discretizing the domain of the problem into finite strips. This method decomposes a single large problem into m smaller independent subproblems when m harmonic functions are employed, thus yielding natural parallelism at a very high level. In this paper we address vectorization and parallelization strategies for the dynamic analysis of simply-supported Mindlin plate bending problems and show how to prevent potential conflicts in memory access during the assemblage process. The vector and parallel implementations of this method and the performance results of a test problem under scalar, vector, and vector-concurrent execution modes on the Alliant FX/80 are also presented.
Parker, R Gary
1988-01-01
This book treats the fundamental issues and algorithmic strategies emerging as the core of the discipline of discrete optimization in a comprehensive and rigorous fashion. Following an introductory chapter on computational complexity, the basic algorithmic results for the two major models of polynomial algorithms are introduced--models using matroids and linear programming. Further chapters treat the major non-polynomial algorithms: branch-and-bound and cutting planes. The text concludes with a chapter on heuristic algorithms.Several appendixes are included which review the fundamental ideas o
Gong, Yongmei; Zwinger, Thomas; Åström, Jan; Gladstone, Rupert; Schellenberger, Thomas; Altena, Bas; Moore, John
2017-04-01
The outlet glacier at Basin 3, Austfonna ice-cap entered its active surge phase in autumn 2012. We assess the evolution of the basal friction during the surge through inverse modelling of basal friction coefficients using recent velocity observation from 2012 to 2014 in a continuum ice dynamic model Elmer/ice. The obtained basal friction coefficient distributions at different time instances are further used as a boundary condition in a discrete element model (HiDEM) that is capable of computing fracturing of ice. The inverted basal friction coefficient evolution shows a gradual 'unplugging' of the stagnant frontal area and northwards and inland expansion of the fast flowing region in the southern basin. The validation between the modeled crevasses distribution and the satellite observation in August 2013 shows a good agreement in shear zones inland and at the frontal area. Crevasse distributions of the summer before and after the glacier reached its maximum velocity in January 2013 (August 2012 and August 2014, respectively) are also evaluated. Previous studies suggest the triggering and development of the surge are linked to surface melt water penetrating through ice to form an efficient basal hydrology system thereby triggering a hydro- thermodynamic feedback. This preliminary offline coupling between a continuum ice dynamic model and a discrete element model will give a hint on future model development of linking supra-glacial to sub-glacial hydrology system.
Discrete gradients in discrete classical mechanics
International Nuclear Information System (INIS)
Renna, L.
1987-01-01
A simple model of discrete classical mechanics is given where, starting from the continuous Hamilton equations, discrete equations of motion are established together with a proper discrete gradient definition. The conservation laws of the total discrete momentum, angular momentum, and energy are demonstrated
Space-Time Discrete KPZ Equation
Cannizzaro, G.; Matetski, K.
2018-03-01
We study a general family of space-time discretizations of the KPZ equation and show that they converge to its solution. The approach we follow makes use of basic elements of the theory of regularity structures (Hairer in Invent Math 198(2):269-504, 2014) as well as its discrete counterpart (Hairer and Matetski in Discretizations of rough stochastic PDEs, 2015. arXiv:1511.06937). Since the discretization is in both space and time and we allow non-standard discretization for the product, the methods mentioned above have to be suitably modified in order to accommodate the structure of the models under study.
Micro-mechanical Simulations of Soils using Massively Parallel Supercomputers
Directory of Open Access Journals (Sweden)
David W. Washington
2004-06-01
Full Text Available In this research a computer program, Trubal version 1.51, based on the Discrete Element Method was converted to run on a Connection Machine (CM-5,a massively parallel supercomputer with 512 nodes, to expedite the computational times of simulating Geotechnical boundary value problems. The dynamic memory algorithm in Trubal program did not perform efficiently in CM-2 machine with the Single Instruction Multiple Data (SIMD architecture. This was due to the communication overhead involving global array reductions, global array broadcast and random data movement. Therefore, a dynamic memory algorithm in Trubal program was converted to a static memory arrangement and Trubal program was successfully converted to run on CM-5 machines. The converted program was called "TRUBAL for Parallel Machines (TPM." Simulating two physical triaxial experiments and comparing simulation results with Trubal simulations validated the TPM program. With a 512 nodes CM-5 machine TPM produced a nine-fold speedup demonstrating the inherent parallelism within algorithms based on the Discrete Element Method.
Firth, Jean M
1992-01-01
The analysis of signals and systems using transform methods is a very important aspect of the examination of processes and problems in an increasingly wide range of applications. Whereas the initial impetus in the development of methods appropriate for handling discrete sets of data occurred mainly in an electrical engineering context (for example in the design of digital filters), the same techniques are in use in such disciplines as cardiology, optics, speech analysis and management, as well as in other branches of science and engineering. This text is aimed at a readership whose mathematical background includes some acquaintance with complex numbers, linear differen tial equations, matrix algebra, and series. Specifically, a familiarity with Fourier series (in trigonometric and exponential forms) is assumed, and an exposure to the concept of a continuous integral transform is desirable. Such a background can be expected, for example, on completion of the first year of a science or engineering degree cour...
Massively parallel mathematical sieves
Energy Technology Data Exchange (ETDEWEB)
Montry, G.R.
1989-01-01
The Sieve of Eratosthenes is a well-known algorithm for finding all prime numbers in a given subset of integers. A parallel version of the Sieve is described that produces computational speedups over 800 on a hypercube with 1,024 processing elements for problems of fixed size. Computational speedups as high as 980 are achieved when the problem size per processor is fixed. The method of parallelization generalizes to other sieves and will be efficient on any ensemble architecture. We investigate two highly parallel sieves using scattered decomposition and compare their performance on a hypercube multiprocessor. A comparison of different parallelization techniques for the sieve illustrates the trade-offs necessary in the design and implementation of massively parallel algorithms for large ensemble computers.
Crockett, Thomas W.
1995-01-01
This article provides a broad introduction to the subject of parallel rendering, encompassing both hardware and software systems. The focus is on the underlying concepts and the issues which arise in the design of parallel rendering algorithms and systems. We examine the different types of parallelism and how they can be applied in rendering applications. Concepts from parallel computing, such as data decomposition, task granularity, scalability, and load balancing, are considered in relation to the rendering problem. We also explore concepts from computer graphics, such as coherence and projection, which have a significant impact on the structure of parallel rendering algorithms. Our survey covers a number of practical considerations as well, including the choice of architectural platform, communication and memory requirements, and the problem of image assembly and display. We illustrate the discussion with numerous examples from the parallel rendering literature, representing most of the principal rendering methods currently used in computer graphics.
1982-01-01
Parallel Computations focuses on parallel computation, with emphasis on algorithms used in a variety of numerical and physical applications and for many different types of parallel computers. Topics covered range from vectorization of fast Fourier transforms (FFTs) and of the incomplete Cholesky conjugate gradient (ICCG) algorithm on the Cray-1 to calculation of table lookups and piecewise functions. Single tridiagonal linear systems and vectorized computation of reactive flow are also discussed.Comprised of 13 chapters, this volume begins by classifying parallel computers and describing techn
Energy Technology Data Exchange (ETDEWEB)
Smith, Jovanca J.; Bishop, Joseph E.
2013-11-01
This report summarizes the work performed by the graduate student Jovanca Smith during a summer internship in the summer of 2012 with the aid of mentor Joe Bishop. The projects were a two-part endeavor that focused on the use of the numerical model called the Lattice Discrete Particle Model (LDPM). The LDPM is a discrete meso-scale model currently used at Northwestern University and the ERDC to model the heterogeneous quasi-brittle material, concrete. In the first part of the project, LDPM was compared to the Karagozian and Case Concrete Model (K&C) used in Presto, an explicit dynamics finite-element code, developed at Sandia National Laboratories. In order to make this comparison, a series of quasi-static numerical experiments were performed, namely unconfined uniaxial compression tests on four varied cube specimen sizes, three-point bending notched experiments on three proportional specimen sizes, and six triaxial compression tests on a cylindrical specimen. The second part of this project focused on the application of LDPM to simulate projectile perforation on an ultra high performance concrete called CORTUF. This application illustrates the strengths of LDPM over traditional continuum models.
Energy Technology Data Exchange (ETDEWEB)
Liu, Peiyuan [Univ. of Colorado, Boulder, CO (United States); Brown, Timothy [Univ. of Colorado, Boulder, CO (United States); Fullmer, William D. [Univ. of Colorado, Boulder, CO (United States); Hauser, Thomas [Univ. of Colorado, Boulder, CO (United States); Hrenya, Christine [Univ. of Colorado, Boulder, CO (United States); Grout, Ray [National Renewable Energy Lab. (NREL), Golden, CO (United States); Sitaraman, Hariswaran [National Renewable Energy Lab. (NREL), Golden, CO (United States)
2016-01-29
Five benchmark problems are developed and simulated with the computational fluid dynamics and discrete element model code MFiX. The benchmark problems span dilute and dense regimes, consider statistically homogeneous and inhomogeneous (both clusters and bubbles) particle concentrations and a range of particle and fluid dynamic computational loads. Several variations of the benchmark problems are also discussed to extend the computational phase space to cover granular (particles only), bidisperse and heat transfer cases. A weak scaling analysis is performed for each benchmark problem and, in most cases, the scalability of the code appears reasonable up to approx. 103 cores. Profiling of the benchmark problems indicate that the most substantial computational time is being spent on particle-particle force calculations, drag force calculations and interpolating between discrete particle and continuum fields. Hardware performance analysis was also carried out showing significant Level 2 cache miss ratios and a rather low degree of vectorization. These results are intended to serve as a baseline for future developments to the code as well as a preliminary indicator of where to best focus performance optimizations.
Limit sets for the discrete spectrum of complex Jacobi matrices
International Nuclear Information System (INIS)
Golinskii, L B; Egorova, I E
2005-01-01
The discrete spectrum of complex Jacobi matrices that are compact perturbations of the discrete Laplacian is studied. The precise stabilization rate (in the sense of order) of the matrix elements ensuring the finiteness of the discrete spectrum is found. An example of a Jacobi matrix with discrete spectrum having a unique limit point is constructed. These results are discrete analogues of Pavlov's well-known results on Schroedinger operators with complex potential on a half-axis.
Balanced, parallel operation of flashlamps
International Nuclear Information System (INIS)
Carder, B.M.; Merritt, B.T.
1979-01-01
A new energy store, the Compensated Pulsed Alternator (CPA), promises to be a cost effective substitute for capacitors to drive flashlamps that pump large Nd:glass lasers. Because the CPA is large and discrete, it will be necessary that it drive many parallel flashlamp circuits, presenting a problem in equal current distribution. Current division to +- 20% between parallel flashlamps has been achieved, but this is marginal for laser pumping. A method is presented here that provides equal current sharing to about 1%, and it includes fused protection against short circuit faults. The method was tested with eight parallel circuits, including both open-circuit and short-circuit fault tests
Discrete integrable systems and deformations of associative algebras
International Nuclear Information System (INIS)
Konopelchenko, B G
2009-01-01
Interrelations between discrete deformations of the structure constants for associative algebras and discrete integrable systems are reviewed. Theory of deformations for associative algebras is presented. Closed left ideal generated by the elements representing the multiplication table plays a central role in this theory. Deformations of the structure constants are generated by the deformation driving algebra and governed by the central system of equations. It is demonstrated that many discrete equations such as discrete Boussinesq equation, discrete WDVV equation, discrete Schwarzian KP and BKP equations, discrete Hirota-Miwa equations for KP and BKP hierarchies are particular realizations of the central system. An interaction between the theories of discrete integrable systems and discrete deformations of associative algebras is reciprocal and fruitful. An interpretation of the Menelaus relation (discrete Schwarzian KP equation), discrete Hirota-Miwa equation for KP hierarchy, consistency around the cube as the associativity conditions and the concept of gauge equivalence, for instance, between the Menelaus and KP configurations are particular examples.
Neutron transport solver parallelization using a Domain Decomposition method
International Nuclear Information System (INIS)
Van Criekingen, S.; Nataf, F.; Have, P.
2008-01-01
A domain decomposition (DD) method is investigated for the parallel solution of the second-order even-parity form of the time-independent Boltzmann transport equation. The spatial discretization is performed using finite elements, and the angular discretization using spherical harmonic expansions (P N method). The main idea developed here is due to P.L. Lions. It consists in having sub-domains exchanging not only interface point flux values, but also interface flux 'derivative' values. (The word 'derivative' is here used with quotes, because in the case considered here, it in fact consists in the Ω.∇ operator, with Ω the angular variable vector and ∇ the spatial gradient operator.) A parameter α is introduced, as proportionality coefficient between point flux and 'derivative' values. This parameter can be tuned - so far heuristically - to optimize the method. (authors)
PARALLEL MOVING MECHANICAL SYSTEMS
Directory of Open Access Journals (Sweden)
Florian Ion Tiberius Petrescu
2014-09-01
Full Text Available Normal 0 false false false EN-US X-NONE X-NONE MicrosoftInternetExplorer4 Moving mechanical systems parallel structures are solid, fast, and accurate. Between parallel systems it is to be noticed Stewart platforms, as the oldest systems, fast, solid and precise. The work outlines a few main elements of Stewart platforms. Begin with the geometry platform, kinematic elements of it, and presented then and a few items of dynamics. Dynamic primary element on it means the determination mechanism kinetic energy of the entire Stewart platforms. It is then in a record tail cinematic mobile by a method dot matrix of rotation. If a structural mottoelement consists of two moving elements which translates relative, drive train and especially dynamic it is more convenient to represent the mottoelement as a single moving components. We have thus seven moving parts (the six motoelements or feet to which is added mobile platform 7 and one fixed.
Discrete Curvatures and Discrete Minimal Surfaces
Sun, Xiang
2012-01-01
This thesis presents an overview of some approaches to compute Gaussian and mean curvature on discrete surfaces and discusses discrete minimal surfaces. The variety of applications of differential geometry in visualization and shape design leads
Parallel Numerical Simulations of Water Reservoirs
Torres, Pedro; Mangiavacchi, Norberto
2010-11-01
The study of the water flow and scalar transport in water reservoirs is important for the determination of the water quality during the initial stages of the reservoir filling and during the life of the reservoir. For this scope, a parallel 2D finite element code for solving the incompressible Navier-Stokes equations coupled with scalar transport was implemented using the message-passing programming model, in order to perform simulations of hidropower water reservoirs in a computer cluster environment. The spatial discretization is based on the MINI element that satisfies the Babuska-Brezzi (BB) condition, which provides sufficient conditions for a stable mixed formulation. All the distributed data structures needed in the different stages of the code, such as preprocessing, solving and post processing, were implemented using the PETSc library. The resulting linear systems for the velocity and the pressure fields were solved using the projection method, implemented by an approximate block LU factorization. In order to increase the parallel performance in the solution of the linear systems, we employ the static condensation method for solving the intermediate velocity at vertex and centroid nodes separately. We compare performance results of the static condensation method with the approach of solving the complete system. In our tests the static condensation method shows better performance for large problems, at the cost of an increased memory usage. Performance results for other intensive parts of the code in a computer cluster are also presented.
Discrete mathematics in the high school curriculum
Anderson, I.; Asch, van A.G.; van Lint, J.H.
2004-01-01
In this paper we present some topics from the field of discrete mathematics which might be suitable for the high school curriculum. These topics yield both easy to understand challenging problems and important applications of discrete mathematics. We choose elements from number theory and various
Parallel Solver for H(div) Problems Using Hybridization and AMG
Energy Technology Data Exchange (ETDEWEB)
Lee, Chak S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2016-01-15
In this paper, a scalable parallel solver is proposed for H(div) problems discretized by arbitrary order finite elements on general unstructured meshes. The solver is based on hybridization and algebraic multigrid (AMG). Unlike some previously studied H(div) solvers, the hybridization solver does not require discrete curl and gradient operators as additional input from the user. Instead, only some element information is needed in the construction of the solver. The hybridization results in a H1-equivalent symmetric positive definite system, which is then rescaled and solved by AMG solvers designed for H1 problems. Weak and strong scaling of the method are examined through several numerical tests. Our numerical results show that the proposed solver provides a promising alternative to ADS, a state-of-the-art solver [12], for H(div) problems. In fact, it outperforms ADS for higher order elements.
Parallel Newton-Krylov-Schwarz algorithms for the transonic full potential equation
Cai, Xiao-Chuan; Gropp, William D.; Keyes, David E.; Melvin, Robin G.; Young, David P.
1996-01-01
We study parallel two-level overlapping Schwarz algorithms for solving nonlinear finite element problems, in particular, for the full potential equation of aerodynamics discretized in two dimensions with bilinear elements. The overall algorithm, Newton-Krylov-Schwarz (NKS), employs an inexact finite-difference Newton method and a Krylov space iterative method, with a two-level overlapping Schwarz method as a preconditioner. We demonstrate that NKS, combined with a density upwinding continuation strategy for problems with weak shocks, is robust and, economical for this class of mixed elliptic-hyperbolic nonlinear partial differential equations, with proper specification of several parameters. We study upwinding parameters, inner convergence tolerance, coarse grid density, subdomain overlap, and the level of fill-in in the incomplete factorization, and report their effect on numerical convergence rate, overall execution time, and parallel efficiency on a distributed-memory parallel computer.
Casanova, Henri; Robert, Yves
2008-01-01
""…The authors of the present book, who have extensive credentials in both research and instruction in the area of parallelism, present a sound, principled treatment of parallel algorithms. … This book is very well written and extremely well designed from an instructional point of view. … The authors have created an instructive and fascinating text. The book will serve researchers as well as instructors who need a solid, readable text for a course on parallelism in computing. Indeed, for anyone who wants an understandable text from which to acquire a current, rigorous, and broad vi
Alternative to dead reckoning for model state quantisation when migrating to a quantised discrete
CSIR Research Space (South Africa)
Duvenhage, A
2008-06-01
Full Text Available Some progress has recently been made on migrating an existing distributed parallel discrete time simulator to a quantised discrete event architecture. The migration is done to increase the scale of the real-time simulations supported...
International Nuclear Information System (INIS)
Cutts, D.A.; Spyrou, N.M.; Stedman, J.D.
2000-01-01
Alzheimer's disease (AD) is a debilitating form of dementia which leads to impaired memory, thinking and behavior. Elemental concentrations between 'normal' and AD subjects as well as the hemispherical differences within the brain were examined. Tissue samples from both hemispheres of the frontal lobe in both AD and normal subjects were examined for their trace element concentrations using PIXE and RBS analyses. Elemental concentrations were seen to differ between AD and normal brain tissue samples. While in the normal group concentrations were found to be significantly higher in the right hemisphere than in the left the converse was tru in AD. A change in elemental concentrations may indicate possible alterations in the function of the blood brain barrier. This was examined by determining regional cerebral metabolic rates of glucose (rCMRGlu) using the in vivo technique of positron emission tomography (PET). Again variations between both hemispheres and between AD and normal were found. (author)
He, Yue-Jing; Hung, Wei-Chih; Syu, Cheng-Jyun
2017-12-01
The finite-element method (FEM) and eigenmode expansion method (EEM) were adopted to analyze the guided modes and spectrum of phase-shift fiber Bragg grating at five phase-shift degrees (including zero, 1/4π, 1/2π, 3/4π, and π). In previous studies on optical fiber grating, conventional coupled-mode theory was crucial. This theory contains abstruse knowledge about physics and complex computational processes, and thus is challenging for users. Therefore, a numerical simulation method was coupled with a simple and rigorous design procedure to help beginners and users to overcome difficulty in entering the field; in addition, graphical simulation results were presented. To reduce the difference between the simulated context and the actual context, a perfectly matched layer and perfectly reflecting boundary were added to the FEM and the EEM. When the FEM was used for grid cutting, the object meshing method and the boundary meshing method proposed in this study were used to effectively enhance computational accuracy and substantially reduce the time required for simulation. In summary, users can use the simulation results in this study to easily and rapidly design an optical fiber communication system and optical sensors with spectral characteristics.
Directory of Open Access Journals (Sweden)
Jorge Mauricio Ruiz Vera
2013-03-01
Full Text Available The Derrida-Lebowitz-Speer-Spohn (DLSS equation is a fourth order in space non-linear evolution equation. This equation arises in the study of interface fluctuations in spin systems and quantum semiconductor modelling. In this paper, we present a positive preserving finite element discrtization for a coupled-equation approach to the DLSS equation. Using the available information about the physical phenomena, we are able to set the corresponding boundary conditions for the coupled system. We prove existence of a global in time discrete solution by fixed point argument. Numerical results illustrate the quantum character of the equation. Finally a test of order of convergence of the proposed discretization scheme is presented.La ecuación de Derrida-Lebowitz-Speer-Spohn (DLSS es una ecuación de evolución no lineal de cuarto orden. Esta aparece en el estudio de las fluctuaciones de interface de sistemas de espín y en la modelación de semicoductores cuánticos. En este artículo, se presenta una discretización por elementos finitos para una formulación exponencial de la ecuación DLSS abordada como un sistema acoplado de ecuaciones. Usando la información disponible acerca del fenómeno físico, se establecen las condiciones de contorno para el sistema acoplado. Se demuestra la existencia de la solución discreta global en el tiempo via un argumento de punto fijo. Los resultados numéricos ilustran el carácter cuántico de la ecuación. Finalmente se presenta un test del orden de convergencia de la discretización porpuesta.
International Nuclear Information System (INIS)
Soltz, R; Vranas, P; Blumrich, M; Chen, D; Gara, A; Giampap, M; Heidelberger, P; Salapura, V; Sexton, J; Bhanot, G
2007-01-01
The theory of the strong nuclear force, Quantum Chromodynamics (QCD), can be numerically simulated from first principles on massively-parallel supercomputers using the method of Lattice Gauge Theory. We describe the special programming requirements of lattice QCD (LQCD) as well as the optimal supercomputer hardware architectures that it suggests. We demonstrate these methods on the BlueGene massively-parallel supercomputer and argue that LQCD and the BlueGene architecture are a natural match. This can be traced to the simple fact that LQCD is a regular lattice discretization of space into lattice sites while the BlueGene supercomputer is a discretization of space into compute nodes, and that both are constrained by requirements of locality. This simple relation is both technologically important and theoretically intriguing. The main result of this paper is the speedup of LQCD using up to 131,072 CPUs on the largest BlueGene/L supercomputer. The speedup is perfect with sustained performance of about 20% of peak. This corresponds to a maximum of 70.5 sustained TFlop/s. At these speeds LQCD and BlueGene are poised to produce the next generation of strong interaction physics theoretical results
Modeling and Control of the Redundant Parallel Adjustment Mechanism on a Deployable Antenna Panel
Directory of Open Access Journals (Sweden)
Lili Tian
2016-10-01
Full Text Available With the aim of developing multiple input and multiple output (MIMO coupling systems with a redundant parallel adjustment mechanism on the deployable antenna panel, a structural control integrated design methodology is proposed in this paper. Firstly, the modal information from the finite element model of the structure of the antenna panel is extracted, and then the mathematical model is established with the Hamilton principle; Secondly, the discrete Linear Quadratic Regulator (LQR controller is added to the model in order to control the actuators and adjust the shape of the panel. Finally, the engineering practicality of the modeling and control method based on finite element analysis simulation is verified.
Institute of Scientific and Technical Information of China (English)
袁桂珍; 张涛; 刘月琴
2017-01-01
Seed metering device as a key component of the seeding machine, its working performance and reliability directly affect the overall quality of the seeding machine.Mechanical sowing machine has the advantages of simple structure, low cost, convenient maintenance.The wheel metering device as a mechanical metering device of a widely used seeding with regular shape and hardness seeds.In this paper,the Solidworks software is used to design a spoon wheel type seed metering device, and the discrete element method is used to simulate the seed sowing seeds of the seed metering device, and the working conditions of the seed metering device are obtained.Simulation results are obtained by the discrete element software: the whole working performance of the seed metering device was better when the wheel rotation speed was 10~13 r/min;the number of seeds in the seed room was 1800~2100.And appropriate vibration can improve the performance of the designed device.This paper provides a method for the design and optimization of the spoon wheel type seed metering device.%排种器作为播种机关键部件,其工作性能与可靠性直接影响播种机整体作业质量.机械式排种器具有结构简单、价格低廉、维修方便等优点,勺轮式排种器作为机械式排种器的一种,在硬度较大、较规则种子播种作业中得到广泛应用.为此,应用SolidWorks软件设计了一种勺轮式排种器,应用离散元软件对排种器排种大豆种子进行了计算机数值模拟,得到了排种器工作性能较好的工作参数.由离散元软件计算机数值模拟结果得到:勺轮组合转速为10~13r/min,排种器种子室内种子数量在1800~2100粒时,排种器整体工作性能较好;且适当的振动可提高本设计的排种器的工作性能.该研究为勺轮式排种器的设计与优化提供了一种方法.
Xu, Jian; Kim, Daniel; Otazo, Ricardo; Srichai, Monvadi B; Lim, Ruth P; Axel, Leon; Mcgorty, Kelly Anne; Niendorf, Thoralf; Sodickson, Daniel K
2013-07-01
To evaluate the feasibility and perform initial comparative evaluations of a 5-minute comprehensive whole-heart magnetic resonance imaging (MRI) protocol with four image acquisition types: perfusion (PERF), function (CINE), coronary artery imaging (CAI), and late gadolinium enhancement (LGE). This study protocol was Health Insurance Portability and Accountability Act (HIPAA)-compliant and Institutional Review Board-approved. A 5-minute comprehensive whole-heart MRI examination protocol (Accelerated) using 6-8-fold-accelerated volumetric parallel imaging was incorporated into and compared with a standard 2D clinical routine protocol (Standard). Following informed consent, 20 patients were imaged with both protocols. Datasets were reviewed for image quality using a 5-point Likert scale (0 = non-diagnostic, 4 = excellent) in blinded fashion by two readers. Good image quality with full whole-heart coverage was achieved using the accelerated protocol, particularly for CAI, although significant degradations in quality, as compared with traditional lengthy examinations, were observed for the other image types. Mean total scan time was significantly lower for the Accelerated as compared to Standard protocols (28.99 ± 4.59 min vs. 1.82 ± 0.05 min, P simplified scan prescription and high spatial and temporal resolution enabled by highly parallel imaging technology. The study also highlights technical hurdles that remain to be addressed. Although image quality remained diagnostic for most scan types, the reduced image quality of PERF, CINE, and LGE scans in the Accelerated protocol remain a concern. Copyright © 2012 Wiley Periodicals, Inc.
Botti, L.; Colombo, A.; Bassi, F.
2017-10-01
In this work we exploit agglomeration based h-multigrid preconditioners to speed-up the iterative solution of discontinuous Galerkin discretizations of the Stokes and Navier-Stokes equations. As a distinctive feature h-coarsened mesh sequences are generated by recursive agglomeration of a fine grid, admitting arbitrarily unstructured grids of complex domains, and agglomeration based discontinuous Galerkin discretizations are employed to deal with agglomerated elements of coarse levels. Both the expense of building coarse grid operators and the performance of the resulting multigrid iteration are investigated. For the sake of efficiency coarse grid operators are inherited through element-by-element L2 projections, avoiding the cost of numerical integration over agglomerated elements. Specific care is devoted to the projection of viscous terms discretized by means of the BR2 dG method. We demonstrate that enforcing the correct amount of stabilization on coarse grids levels is mandatory for achieving uniform convergence with respect to the number of levels. The numerical solution of steady and unsteady, linear and non-linear problems is considered tackling challenging 2D test cases and 3D real life computations on parallel architectures. Significant execution time gains are documented.
Parallel multiscale simulations of a brain aneurysm
Energy Technology Data Exchange (ETDEWEB)
Grinberg, Leopold [Division of Applied Mathematics, Brown University, Providence, RI 02912 (United States); Fedosov, Dmitry A. [Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, Jülich 52425 (Germany); Karniadakis, George Em, E-mail: george_karniadakis@brown.edu [Division of Applied Mathematics, Brown University, Providence, RI 02912 (United States)
2013-07-01
Cardiovascular pathologies, such as a brain aneurysm, are affected by the global blood circulation as well as by the local microrheology. Hence, developing computational models for such cases requires the coupling of disparate spatial and temporal scales often governed by diverse mathematical descriptions, e.g., by partial differential equations (continuum) and ordinary differential equations for discrete particles (atomistic). However, interfacing atomistic-based with continuum-based domain discretizations is a challenging problem that requires both mathematical and computational advances. We present here a hybrid methodology that enabled us to perform the first multiscale simulations of platelet depositions on the wall of a brain aneurysm. The large scale flow features in the intracranial network are accurately resolved by using the high-order spectral element Navier–Stokes solver NεκTαr. The blood rheology inside the aneurysm is modeled using a coarse-grained stochastic molecular dynamics approach (the dissipative particle dynamics method) implemented in the parallel code LAMMPS. The continuum and atomistic domains overlap with interface conditions provided by effective forces computed adaptively to ensure continuity of states across the interface boundary. A two-way interaction is allowed with the time-evolving boundary of the (deposited) platelet clusters tracked by an immersed boundary method. The corresponding heterogeneous solvers (NεκTαr and LAMMPS) are linked together by a computational multilevel message passing interface that facilitates modularity and high parallel efficiency. Results of multiscale simulations of clot formation inside the aneurysm in a patient-specific arterial tree are presented. We also discuss the computational challenges involved and present scalability results of our coupled solver on up to 300 K computer processors. Validation of such coupled atomistic-continuum models is a main open issue that has to be addressed in
Parallel multiscale simulations of a brain aneurysm
International Nuclear Information System (INIS)
Grinberg, Leopold; Fedosov, Dmitry A.; Karniadakis, George Em
2013-01-01
Cardiovascular pathologies, such as a brain aneurysm, are affected by the global blood circulation as well as by the local microrheology. Hence, developing computational models for such cases requires the coupling of disparate spatial and temporal scales often governed by diverse mathematical descriptions, e.g., by partial differential equations (continuum) and ordinary differential equations for discrete particles (atomistic). However, interfacing atomistic-based with continuum-based domain discretizations is a challenging problem that requires both mathematical and computational advances. We present here a hybrid methodology that enabled us to perform the first multiscale simulations of platelet depositions on the wall of a brain aneurysm. The large scale flow features in the intracranial network are accurately resolved by using the high-order spectral element Navier–Stokes solver NεκTαr. The blood rheology inside the aneurysm is modeled using a coarse-grained stochastic molecular dynamics approach (the dissipative particle dynamics method) implemented in the parallel code LAMMPS. The continuum and atomistic domains overlap with interface conditions provided by effective forces computed adaptively to ensure continuity of states across the interface boundary. A two-way interaction is allowed with the time-evolving boundary of the (deposited) platelet clusters tracked by an immersed boundary method. The corresponding heterogeneous solvers (NεκTαr and LAMMPS) are linked together by a computational multilevel message passing interface that facilitates modularity and high parallel efficiency. Results of multiscale simulations of clot formation inside the aneurysm in a patient-specific arterial tree are presented. We also discuss the computational challenges involved and present scalability results of our coupled solver on up to 300 K computer processors. Validation of such coupled atomistic-continuum models is a main open issue that has to be addressed in
Cutts, DA; Spyrou, NM; Maguire, RP; Stedman, JD; Leenders, KL
Alzheimer's disease (AD) isa debilitating form of dementia which leads to impaired memory, thinking and behavior. This work examines elemental concentrations between "normal" and AD subjects as well as the hemispherical differences within the brain. Tissue samples from both hemispheres of the
Energy Technology Data Exchange (ETDEWEB)
Deb, M.K.; Kennon, S.R.
1998-04-01
A cooperative R&D effort between industry and the US government, this project, under the HPPP (High Performance Parallel Processing) initiative of the Dept. of Energy, started the investigations into parallel object-oriented (OO) numerics. The basic goal was to research and utilize the emerging technologies to create a physics-independent computational kernel for applications using adaptive finite element method. The industrial team included Computational Mechanics Co., Inc. (COMCO) of Austin, TX (as the primary contractor), Scientific Computing Associates, Inc. (SCA) of New Haven, CT, Texaco and CONVEX. Sandia National Laboratory (Albq., NM) was the technology partner from the government side. COMCO had the responsibility of the main kernel design and development, SCA had the lead in parallel solver technology and guidance on OO technologies was Sandia`s main expertise in this venture. CONVEX and Texaco supported the partnership by hardware resource and application knowledge, respectively. As such, a minimum of fifty-percent cost-sharing was provided by the industry partnership during this project. This report describes the R&D activities and provides some details about the prototype kernel and example applications.
Boundary Layer Effect on Behavior of Discrete Models.
Eliáš, Jan
2017-02-10
The paper studies systems of rigid bodies with randomly generated geometry interconnected by normal and tangential bonds. The stiffness of these bonds determines the macroscopic elastic modulus while the macroscopic Poisson's ratio of the system is determined solely by the normal/tangential stiffness ratio. Discrete models with no directional bias have the same probability of element orientation for any direction and therefore the same mechanical properties in a statistical sense at any point and direction. However, the layers of elements in the vicinity of the boundary exhibit biased orientation, preferring elements parallel with the boundary. As a consequence, when strain occurs in this direction, the boundary layer becomes stiffer than the interior for the normal/tangential stiffness ratio larger than one, and vice versa. Nonlinear constitutive laws are typically such that the straining of an element in shear results in higher strength and ductility than straining in tension. Since the boundary layer tends, due to the bias in the elemental orientation, to involve more tension than shear at the contacts, it also becomes weaker and less ductile. The paper documents these observations and compares them to the results of theoretical analysis.
Al Jarro, Ahmed
2011-08-01
A hybrid MPI/OpenMP scheme for efficiently parallelizing the explicit marching-on-in-time (MOT)-based solution of the time-domain volume (Volterra) integral equation (TD-VIE) is presented. The proposed scheme equally distributes tested field values and operations pertinent to the computation of tested fields among the nodes using the MPI standard; while the source field values are stored in all nodes. Within each node, OpenMP standard is used to further accelerate the computation of the tested fields. Numerical results demonstrate that the proposed parallelization scheme scales well for problems involving three million or more spatial discretization elements. © 2011 IEEE.
Mimetic discretization methods
Castillo, Jose E
2013-01-01
To help solve physical and engineering problems, mimetic or compatible algebraic discretization methods employ discrete constructs to mimic the continuous identities and theorems found in vector calculus. Mimetic Discretization Methods focuses on the recent mimetic discretization method co-developed by the first author. Based on the Castillo-Grone operators, this simple mimetic discretization method is invariably valid for spatial dimensions no greater than three. The book also presents a numerical method for obtaining corresponding discrete operators that mimic the continuum differential and
Radiative transfer on discrete spaces
Preisendorfer, Rudolph W; Stark, M; Ulam, S
1965-01-01
Pure and Applied Mathematics, Volume 74: Radiative Transfer on Discrete Spaces presents the geometrical structure of natural light fields. This book describes in detail with mathematical precision the radiometric interactions of light-scattering media in terms of a few well established principles.Organized into four parts encompassing 15 chapters, this volume begins with an overview of the derivations of the practical formulas and the arrangement of formulas leading to numerical solution procedures of radiative transfer problems in plane-parallel media. This text then constructs radiative tran
Time Discretization Techniques
Gottlieb, S.; Ketcheson, David I.
2016-01-01
The time discretization of hyperbolic partial differential equations is typically the evolution of a system of ordinary differential equations obtained by spatial discretization of the original problem. Methods for this time evolution include
International Nuclear Information System (INIS)
Jejcic, A.; Maillard, J.; Maurel, G.; Silva, J.; Wolff-Bacha, F.
1997-01-01
The work in the field of parallel processing has developed as research activities using several numerical Monte Carlo simulations related to basic or applied current problems of nuclear and particle physics. For the applications utilizing the GEANT code development or improvement works were done on parts simulating low energy physical phenomena like radiation, transport and interaction. The problem of actinide burning by means of accelerators was approached using a simulation with the GEANT code. A program of neutron tracking in the range of low energies up to the thermal region has been developed. It is coupled to the GEANT code and permits in a single pass the simulation of a hybrid reactor core receiving a proton burst. Other works in this field refers to simulations for nuclear medicine applications like, for instance, development of biological probes, evaluation and characterization of the gamma cameras (collimators, crystal thickness) as well as the method for dosimetric calculations. Particularly, these calculations are suited for a geometrical parallelization approach especially adapted to parallel machines of the TN310 type. Other works mentioned in the same field refer to simulation of the electron channelling in crystals and simulation of the beam-beam interaction effect in colliders. The GEANT code was also used to simulate the operation of germanium detectors designed for natural and artificial radioactivity monitoring of environment
Discrete element weld model, phase 2
Prakash, C.; Samonds, M.; Singhal, A. K.
1987-01-01
A numerical method was developed for analyzing the tungsten inert gas (TIG) welding process. The phenomena being modeled include melting under the arc and the flow in the melt under the action of buoyancy, surface tension, and electromagnetic forces. The latter entails the calculation of the electric potential and the computation of electric current and magnetic field therefrom. Melting may occur at a single temperature or over a temperature range, and the electrical and thermal conductivities can be a function of temperature. Results of sample calculations are presented and discussed at length. A major research contribution has been the development of numerical methodology for the calculation of phase change problems in a fixed grid framework. The model has been implemented on CHAM's general purpose computer code PHOENICS. The inputs to the computer model include: geometric parameters, material properties, and weld process parameters.
Multitasking TORT Under UNICOS: Parallel Performance Models and Measurements
International Nuclear Information System (INIS)
Azmy, Y.Y.; Barnett, D.A.
1999-01-01
The existing parallel algorithms in the TORT discrete ordinates were updated to function in a UNI-COS environment. A performance model for the parallel overhead was derived for the existing algorithms. The largest contributors to the parallel overhead were identified and a new algorithm was developed. A parallel overhead model was also derived for the new algorithm. The results of the comparison of parallel performance models were compared to applications of the code to two TORT standard test problems and a large production problem. The parallel performance models agree well with the measured parallel overhead
Multitasking TORT under UNICOS: Parallel performance models and measurements
International Nuclear Information System (INIS)
Barnett, A.; Azmy, Y.Y.
1999-01-01
The existing parallel algorithms in the TORT discrete ordinates code were updated to function in a UNICOS environment. A performance model for the parallel overhead was derived for the existing algorithms. The largest contributors to the parallel overhead were identified and a new algorithm was developed. A parallel overhead model was also derived for the new algorithm. The results of the comparison of parallel performance models were compared to applications of the code to two TORT standard test problems and a large production problem. The parallel performance models agree well with the measured parallel overhead
Definable maximal discrete sets in forcing extensions
DEFF Research Database (Denmark)
Törnquist, Asger Dag; Schrittesser, David
2018-01-01
Let be a Σ11 binary relation, and recall that a set A is -discrete if no two elements of A are related by . We show that in the Sacks and Miller forcing extensions of L there is a Δ12 maximal -discrete set. We use this to answer in the negative the main question posed in [5] by showing...
McCallum, Ethan
2011-01-01
It's tough to argue with R as a high-quality, cross-platform, open source statistical software product-unless you're in the business of crunching Big Data. This concise book introduces you to several strategies for using R to analyze large datasets. You'll learn the basics of Snow, Multicore, Parallel, and some Hadoop-related tools, including how to find them, how to use them, when they work well, and when they don't. With these packages, you can overcome R's single-threaded nature by spreading work across multiple CPUs, or offloading work to multiple machines to address R's memory barrier.
Domain decomposition methods and parallel computing
International Nuclear Information System (INIS)
Meurant, G.
1991-01-01
In this paper, we show how to efficiently solve large linear systems on parallel computers. These linear systems arise from discretization of scientific computing problems described by systems of partial differential equations. We show how to get a discrete finite dimensional system from the continuous problem and the chosen conjugate gradient iterative algorithm is briefly described. Then, the different kinds of parallel architectures are reviewed and their advantages and deficiencies are emphasized. We sketch the problems found in programming the conjugate gradient method on parallel computers. For this algorithm to be efficient on parallel machines, domain decomposition techniques are introduced. We give results of numerical experiments showing that these techniques allow a good rate of convergence for the conjugate gradient algorithm as well as computational speeds in excess of a billion of floating point operations per second. (author). 5 refs., 11 figs., 2 tabs., 1 inset
A Parallel Butterfly Algorithm
Poulson, Jack; Demanet, Laurent; Maxwell, Nicholas; Ying, Lexing
2014-01-01
The butterfly algorithm is a fast algorithm which approximately evaluates a discrete analogue of the integral transform (Equation Presented.) at large numbers of target points when the kernel, K(x, y), is approximately low-rank when restricted to subdomains satisfying a certain simple geometric condition. In d dimensions with O(Nd) quasi-uniformly distributed source and target points, when each appropriate submatrix of K is approximately rank-r, the running time of the algorithm is at most O(r2Nd logN). A parallelization of the butterfly algorithm is introduced which, assuming a message latency of α and per-process inverse bandwidth of β, executes in at most (Equation Presented.) time using p processes. This parallel algorithm was then instantiated in the form of the open-source DistButterfly library for the special case where K(x, y) = exp(iΦ(x, y)), where Φ(x, y) is a black-box, sufficiently smooth, real-valued phase function. Experiments on Blue Gene/Q demonstrate impressive strong-scaling results for important classes of phase functions. Using quasi-uniform sources, hyperbolic Radon transforms, and an analogue of a three-dimensional generalized Radon transform were, respectively, observed to strong-scale from 1-node/16-cores up to 1024-nodes/16,384-cores with greater than 90% and 82% efficiency, respectively. © 2014 Society for Industrial and Applied Mathematics.
A Parallel Butterfly Algorithm
Poulson, Jack
2014-02-04
The butterfly algorithm is a fast algorithm which approximately evaluates a discrete analogue of the integral transform (Equation Presented.) at large numbers of target points when the kernel, K(x, y), is approximately low-rank when restricted to subdomains satisfying a certain simple geometric condition. In d dimensions with O(Nd) quasi-uniformly distributed source and target points, when each appropriate submatrix of K is approximately rank-r, the running time of the algorithm is at most O(r2Nd logN). A parallelization of the butterfly algorithm is introduced which, assuming a message latency of α and per-process inverse bandwidth of β, executes in at most (Equation Presented.) time using p processes. This parallel algorithm was then instantiated in the form of the open-source DistButterfly library for the special case where K(x, y) = exp(iΦ(x, y)), where Φ(x, y) is a black-box, sufficiently smooth, real-valued phase function. Experiments on Blue Gene/Q demonstrate impressive strong-scaling results for important classes of phase functions. Using quasi-uniform sources, hyperbolic Radon transforms, and an analogue of a three-dimensional generalized Radon transform were, respectively, observed to strong-scale from 1-node/16-cores up to 1024-nodes/16,384-cores with greater than 90% and 82% efficiency, respectively. © 2014 Society for Industrial and Applied Mathematics.
Directory of Open Access Journals (Sweden)
James G. Worner
2017-05-01
Full Text Available James Worner is an Australian-based writer and scholar currently pursuing a PhD at the University of Technology Sydney. His research seeks to expose masculinities lost in the shadow of Australia’s Anzac hegemony while exploring new opportunities for contemporary historiography. He is the recipient of the Doctoral Scholarship in Historical Consciousness at the university’s Australian Centre of Public History and will be hosted by the University of Bologna during 2017 on a doctoral research writing scholarship. ‘Parallel Lines’ is one of a collection of stories, The Shapes of Us, exploring liminal spaces of modern life: class, gender, sexuality, race, religion and education. It looks at lives, like lines, that do not meet but which travel in proximity, simultaneously attracted and repelled. James’ short stories have been published in various journals and anthologies.
Ultrascalable petaflop parallel supercomputer
Blumrich, Matthias A [Ridgefield, CT; Chen, Dong [Croton On Hudson, NY; Chiu, George [Cross River, NY; Cipolla, Thomas M [Katonah, NY; Coteus, Paul W [Yorktown Heights, NY; Gara, Alan G [Mount Kisco, NY; Giampapa, Mark E [Irvington, NY; Hall, Shawn [Pleasantville, NY; Haring, Rudolf A [Cortlandt Manor, NY; Heidelberger, Philip [Cortlandt Manor, NY; Kopcsay, Gerard V [Yorktown Heights, NY; Ohmacht, Martin [Yorktown Heights, NY; Salapura, Valentina [Chappaqua, NY; Sugavanam, Krishnan [Mahopac, NY; Takken, Todd [Brewster, NY
2010-07-20
A massively parallel supercomputer of petaOPS-scale includes node architectures based upon System-On-a-Chip technology, where each processing node comprises a single Application Specific Integrated Circuit (ASIC) having up to four processing elements. The ASIC nodes are interconnected by multiple independent networks that optimally maximize the throughput of packet communications between nodes with minimal latency. The multiple networks may include three high-speed networks for parallel algorithm message passing including a Torus, collective network, and a Global Asynchronous network that provides global barrier and notification functions. These multiple independent networks may be collaboratively or independently utilized according to the needs or phases of an algorithm for optimizing algorithm processing performance. The use of a DMA engine is provided to facilitate message passing among the nodes without the expenditure of processing resources at the node.
Energy Technology Data Exchange (ETDEWEB)
Han, Jong-Boo; Song, Hajun; Kim, Sung-Soo [Chungnam Nat’l Univ., Daejeon (Korea, Republic of)
2017-06-15
Flexible multibody simulations are widely used in the industry to design mechanical systems. In flexible multibody dynamics, deformation coordinates are described either relatively in the body reference frame that is floating in the space or in the inertial reference frame. Moreover, these deformation coordinates are generated based on the discretization of the body according to the finite element approach. Therefore, the formulation of the flexible multibody system always deals with a huge number of degrees of freedom and the numerical solution methods require a substantial amount of computational time. Parallel computational methods are a solution for efficient computation. However, most of the parallel computational methods are focused on the efficient solution of large-sized linear equations. For multibody analysis, we need to develop an efficient formulation that could be suitable for parallel computation. In this paper, we developed a subsystem synthesis method for a flexible multibody system and proposed efficient parallel computational schemes based on the OpenMP API in order to achieve efficient computation. Simulations of a rotating blade system, which consists of three identical blades, were carried out with two different parallel computational schemes. Actual CPU times were measured to investigate the efficiency of the proposed parallel schemes.
Modeling of brittle-viscous flow using discrete particles
Thordén Haug, Øystein; Barabasch, Jessica; Virgo, Simon; Souche, Alban; Galland, Olivier; Mair, Karen; Abe, Steffen; Urai, Janos L.
2017-04-01
range of viscosities. For identical pressure and strain rate, an order of magnitude range in viscosity can be investigated. The extensive material testing indicates that DEM particles interacting by a combination of elastic repulsion and dashpots can be used to model viscous flows. This allows us to exploit the fracturing capabilities of the discrete element methods and study systems that involve both viscous flow and brittle fracturing. However, the small viscosity range achievable using this approach does constraint the applicability for systems where larger viscosity ranges are required, such as folding of viscous layers of contrasting viscosities. References: Abe, S., Place, D., & Mora, P. (2004). A parallel implementation of the lattice solid model for the simulation of rock mechanics and earthquake dynamics. PAGEOPH, 161(11-12), 2265-2277. http://doi.org/10.1007/s00024-004-2562-x Abe, S., and J. L. Urai (2012), Discrete element modeling of boudinage: Insights on rock rheology, matrix flow, and evolution of geometry, JGR., 117, B01407, doi:10.1029/2011JB00855
Baecklund transformations for discrete Painleve equations: Discrete PII-PV
International Nuclear Information System (INIS)
Sakka, A.; Mugan, U.
2006-01-01
Transformation properties of discrete Painleve equations are investigated by using an algorithmic method. This method yields explicit transformations which relates the solutions of discrete Painleve equations, discrete P II -P V , with different values of parameters. The particular solutions which are expressible in terms of the discrete analogue of the classical special functions of discrete Painleve equations can also be obtained from these transformations
Discrete Gabor transform and discrete Zak transform
Bastiaans, M.J.; Namazi, N.M.; Matthews, K.
1996-01-01
Gabor's expansion of a discrete-time signal into a set of shifted and modulated versions of an elementary signal or synthesis window is introduced, along with the inverse operation, i.e. the Gabor transform, which uses an analysis window that is related to the synthesis window and with the help of
Discrete Mathematics Re "Tooled."
Grassl, Richard M.; Mingus, Tabitha T. Y.
1999-01-01
Indicates the importance of teaching discrete mathematics. Describes how the use of technology can enhance the teaching and learning of discrete mathematics. Explorations using Excel, Derive, and the TI-92 proved how preservice and inservice teachers experienced a new dimension in problem solving and discovery. (ASK)
International Nuclear Information System (INIS)
Gleicher, Frederick; Prinja, Anil K.
2001-01-01
An efficient multigroup model that accurately describes electronic energy loss straggling was recently presented for use in multigroup Monte Carlo and deterministic high-energy ion transport codes. The model preserves the mean energy loss per path length, using the continuous slowing down (CSD) approximation, and mean-squared energy loss per path length, using strictly down-scatter multigroup cross sections, and accurately captures the energy spectrum of an initially monoenergetic ion beam. However, the dominant CSD energy loss process coupled with the small (but non-negligible) straggling poses a significant challenge for deterministic numerical solution when incident beams are monoenergetic or have discontinuous energy spectra. Such spectra broaden very slowly with depth into the target material, and thus, the interior distributions display sharpness and discontinuities. Advanced space-energy discretization methods are consequently necessary to achieve numerical robustness. In this paper, we investigate finite element solutions to this problem using two general families of discontinuous trial functions, one linear and the other nonlinear. The two families have been numerically tested, and we show results for 1.7-GeV protons incident on a tungsten target. For benchmarking purposes, we have also performed Monte Carlo (MC) simulations. Figure 1 displays the spatially converged energy spectrum with 200 groups after the beam has penetrated two-thirds of the ion range (85 cm). We contrast results from linear (LD), bilinear (BLD), and quadratic (QD) discontinuous trail functions against those from exponential-linear (LE), exponential-bilinear (BLE), and exponential-quadratic (QE) discontinuous trail functions. It is clear that the linear and bilinear results from both families are grossly inaccurate, both showing unacceptably high numerical straggling when compared against the MC results. The nonlinear results are everywhere positive while the linear schemes display
Homogenization of discrete media
International Nuclear Information System (INIS)
Pradel, F.; Sab, K.
1998-01-01
Material such as granular media, beam assembly are easily seen as discrete media. They look like geometrical points linked together thanks to energetic expressions. Our purpose is to extend discrete kinematics to the one of an equivalent continuous material. First we explain how we build the localisation tool for periodic materials according to estimated continuum medium type (classical Cauchy, and Cosserat media). Once the bridge built between discrete and continuum media, we exhibit its application over two bidimensional beam assembly structures : the honey comb and a structural reinforced variation. The new behavior is then applied for the simple plan shear problem in a Cosserat continuum and compared with the real discrete solution. By the mean of this example, we establish the agreement of our new model with real structures. The exposed method has a longer range than mechanics and can be applied to every discrete problems like electromagnetism in which relationship between geometrical points can be summed up by an energetic function. (orig.)
International Nuclear Information System (INIS)
Aydin, Alhun; Sisman, Altug
2016-01-01
By considering the quantum-mechanically minimum allowable energy interval, we exactly count number of states (NOS) and introduce discrete density of states (DOS) concept for a particle in a box for various dimensions. Expressions for bounded and unbounded continua are analytically recovered from discrete ones. Even though substantial fluctuations prevail in discrete DOS, they're almost completely flattened out after summation or integration operation. It's seen that relative errors of analytical expressions of bounded/unbounded continua rapidly decrease for high NOS values (weak confinement or high energy conditions), while the proposed analytical expressions based on Weyl's conjecture always preserve their lower error characteristic. - Highlights: • Discrete density of states considering minimum energy difference is proposed. • Analytical DOS and NOS formulas based on Weyl conjecture are given. • Discrete DOS and NOS functions are examined for various dimensions. • Relative errors of analytical formulas are much better than the conventional ones.
Energy Technology Data Exchange (ETDEWEB)
Aydin, Alhun; Sisman, Altug, E-mail: sismanal@itu.edu.tr
2016-03-22
By considering the quantum-mechanically minimum allowable energy interval, we exactly count number of states (NOS) and introduce discrete density of states (DOS) concept for a particle in a box for various dimensions. Expressions for bounded and unbounded continua are analytically recovered from discrete ones. Even though substantial fluctuations prevail in discrete DOS, they're almost completely flattened out after summation or integration operation. It's seen that relative errors of analytical expressions of bounded/unbounded continua rapidly decrease for high NOS values (weak confinement or high energy conditions), while the proposed analytical expressions based on Weyl's conjecture always preserve their lower error characteristic. - Highlights: • Discrete density of states considering minimum energy difference is proposed. • Analytical DOS and NOS formulas based on Weyl conjecture are given. • Discrete DOS and NOS functions are examined for various dimensions. • Relative errors of analytical formulas are much better than the conventional ones.
Okuyama, Yoshifumi
2014-01-01
Discrete Control Systems establishes a basis for the analysis and design of discretized/quantized control systemsfor continuous physical systems. Beginning with the necessary mathematical foundations and system-model descriptions, the text moves on to derive a robust stability condition. To keep a practical perspective on the uncertain physical systems considered, most of the methods treated are carried out in the frequency domain. As part of the design procedure, modified Nyquist–Hall and Nichols diagrams are presented and discretized proportional–integral–derivative control schemes are reconsidered. Schemes for model-reference feedback and discrete-type observers are proposed. Although single-loop feedback systems form the core of the text, some consideration is given to multiple loops and nonlinearities. The robust control performance and stability of interval systems (with multiple uncertainties) are outlined. Finally, the monograph describes the relationship between feedback-control and discrete ev...
Discrete repulsive oscillator wavefunctions
International Nuclear Information System (INIS)
Munoz, Carlos A; Rueda-Paz, Juvenal; Wolf, Kurt Bernardo
2009-01-01
For the study of infinite discrete systems on phase space, the three-dimensional Lorentz algebra and group, so(2,1) and SO(2,1), provide a discrete model of the repulsive oscillator. Its eigenfunctions are found in the principal irreducible representation series, where the compact generator-that we identify with the position operator-has the infinite discrete spectrum of the integers Z, while the spectrum of energies is a double continuum. The right- and left-moving wavefunctions are given by hypergeometric functions that form a Dirac basis for l 2 (Z). Under contraction, the discrete system limits to the well-known quantum repulsive oscillator. Numerical computations of finite approximations raise further questions on the use of Dirac bases for infinite discrete systems.
Compatible Spatial Discretizations for Partial Differential Equations
Energy Technology Data Exchange (ETDEWEB)
Arnold, Douglas, N, ed.
2004-11-25
From May 11--15, 2004, the Institute for Mathematics and its Applications held a hot topics workshop on Compatible Spatial Discretizations for Partial Differential Equations. The numerical solution of partial differential equations (PDE) is a fundamental task in science and engineering. The goal of the workshop was to bring together a spectrum of scientists at the forefront of the research in the numerical solution of PDEs to discuss compatible spatial discretizations. We define compatible spatial discretizations as those that inherit or mimic fundamental properties of the PDE such as topology, conservation, symmetries, and positivity structures and maximum principles. A wide variety of discretization methods applied across a wide range of scientific and engineering applications have been designed to or found to inherit or mimic intrinsic spatial structure and reproduce fundamental properties of the solution of the continuous PDE model at the finite dimensional level. A profusion of such methods and concepts relevant to understanding them have been developed and explored: mixed finite element methods, mimetic finite differences, support operator methods, control volume methods, discrete differential forms, Whitney forms, conservative differencing, discrete Hodge operators, discrete Helmholtz decomposition, finite integration techniques, staggered grid and dual grid methods, etc. This workshop seeks to foster communication among the diverse groups of researchers designing, applying, and studying such methods as well as researchers involved in practical solution of large scale problems that may benefit from advancements in such discretizations; to help elucidate the relations between the different methods and concepts; and to generally advance our understanding in the area of compatible spatial discretization methods for PDE. Particular points of emphasis included: + Identification of intrinsic properties of PDE models that are critical for the fidelity of numerical
Network Science Research Laboratory (NSRL) Discrete Event Toolkit
2016-01-01
ARL-TR-7579 ● JAN 2016 US Army Research Laboratory Network Science Research Laboratory (NSRL) Discrete Event Toolkit by...Laboratory (NSRL) Discrete Event Toolkit by Theron Trout and Andrew J Toth Computational and Information Sciences Directorate, ARL...Research Laboratory (NSRL) Discrete Event Toolkit 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) Theron Trout
Parallel computation of rotating flows
DEFF Research Database (Denmark)
Lundin, Lars Kristian; Barker, Vincent A.; Sørensen, Jens Nørkær
1999-01-01
This paper deals with the simulation of 3‐D rotating flows based on the velocity‐vorticity formulation of the Navier‐Stokes equations in cylindrical coordinates. The governing equations are discretized by a finite difference method. The solution is advanced to a new time level by a two‐step process...... is that of solving a singular, large, sparse, over‐determined linear system of equations, and the iterative method CGLS is applied for this purpose. We discuss some of the mathematical and numerical aspects of this procedure and report on the performance of our software on a wide range of parallel computers. Darbe...
Parallel algorithms for 2-D cylindrical transport equations of Eigenvalue problem
International Nuclear Information System (INIS)
Wei, J.; Yang, S.
2013-01-01
In this paper, aimed at the neutron transport equations of eigenvalue problem under 2-D cylindrical geometry on unstructured grid, the discrete scheme of Sn discrete ordinate and discontinuous finite is built, and the parallel computation for the scheme is realized on MPI systems. Numerical experiments indicate that the designed parallel algorithm can reach perfect speedup, it has good practicality and scalability. (authors)
Izadi, F A; Bagirov, G
2009-01-01
With its origins stretching back several centuries, discrete calculus is now an increasingly central methodology for many problems related to discrete systems and algorithms. The topics covered here usually arise in many branches of science and technology, especially in discrete mathematics, numerical analysis, statistics and probability theory as well as in electrical engineering, but our viewpoint here is that these topics belong to a much more general realm of mathematics; namely calculus and differential equations because of the remarkable analogy of the subject to this branch of mathemati
International Nuclear Information System (INIS)
McGhee, J.M.; Roberts, R.M.; Morel, J.E.
1997-01-01
A spherical harmonics research code (DANTE) has been developed which is compatible with parallel computer architectures. DANTE provides 3-D, multi-material, deterministic, transport capabilities using an arbitrary finite element mesh. The linearized Boltzmann transport equation is solved in a second order self-adjoint form utilizing a Galerkin finite element spatial differencing scheme. The core solver utilizes a preconditioned conjugate gradient algorithm. Other distinguishing features of the code include options for discrete-ordinates and simplified spherical harmonics angular differencing, an exact Marshak boundary treatment for arbitrarily oriented boundary faces, in-line matrix construction techniques to minimize memory consumption, and an effective diffusion based preconditioner for scattering dominated problems. Algorithm efficiency is demonstrated for a massively parallel SIMD architecture (CM-5), and compatibility with MPP multiprocessor platforms or workstation clusters is anticipated
Liu, Yang
2016-03-25
A parallel plane-wave time-domain (PWTD)-accelerated explicit marching-on-in-time (MOT) scheme for solving the time domain electric field volume integral equation (TD-EFVIE) is presented. The proposed scheme leverages pulse functions and Lagrange polynomials to spatially and temporally discretize the electric flux density induced throughout the scatterers, and a finite difference scheme to compute the electric fields from the Hertz electric vector potentials radiated by the flux density. The flux density is explicitly updated during time marching by a predictor-corrector (PC) scheme and the vector potentials are efficiently computed by a scalar PWTD scheme. The memory requirement and computational complexity of the resulting explicit PWTD-PC-EFVIE solver scale as ( log ) s s O N N and ( ) s t O N N , respectively. Here, s N is the number of spatial basis functions and t N is the number of time steps. A scalable parallelization of the proposed MOT scheme on distributed- memory CPU clusters is described. The efficiency, accuracy, and applicability of the resulting (parallelized) PWTD-PC-EFVIE solver are demonstrated via its application to the analysis of transient electromagnetic wave interactions on canonical and real-life scatterers represented with up to 25 million spatial discretization elements.
Liu, Yang; Al-Jarro, Ahmed; Bagci, Hakan; Michielssen, Eric
2016-01-01
A parallel plane-wave time-domain (PWTD)-accelerated explicit marching-on-in-time (MOT) scheme for solving the time domain electric field volume integral equation (TD-EFVIE) is presented. The proposed scheme leverages pulse functions and Lagrange polynomials to spatially and temporally discretize the electric flux density induced throughout the scatterers, and a finite difference scheme to compute the electric fields from the Hertz electric vector potentials radiated by the flux density. The flux density is explicitly updated during time marching by a predictor-corrector (PC) scheme and the vector potentials are efficiently computed by a scalar PWTD scheme. The memory requirement and computational complexity of the resulting explicit PWTD-PC-EFVIE solver scale as ( log ) s s O N N and ( ) s t O N N , respectively. Here, s N is the number of spatial basis functions and t N is the number of time steps. A scalable parallelization of the proposed MOT scheme on distributed- memory CPU clusters is described. The efficiency, accuracy, and applicability of the resulting (parallelized) PWTD-PC-EFVIE solver are demonstrated via its application to the analysis of transient electromagnetic wave interactions on canonical and real-life scatterers represented with up to 25 million spatial discretization elements.
Finite Discrete Gabor Analysis
DEFF Research Database (Denmark)
Søndergaard, Peter Lempel
2007-01-01
frequency bands at certain times. Gabor theory can be formulated for both functions on the real line and for discrete signals of finite length. The two theories are largely the same because many aspects come from the same underlying theory of locally compact Abelian groups. The two types of Gabor systems...... can also be related by sampling and periodization. This thesis extends on this theory by showing new results for window construction. It also provides a discussion of the problems associated to discrete Gabor bases. The sampling and periodization connection is handy because it allows Gabor systems...... on the real line to be well approximated by finite and discrete Gabor frames. This method of approximation is especially attractive because efficient numerical methods exists for doing computations with finite, discrete Gabor systems. This thesis presents new algorithms for the efficient computation of finite...
Adaptive Discrete Hypergraph Matching.
Yan, Junchi; Li, Changsheng; Li, Yin; Cao, Guitao
2018-02-01
This paper addresses the problem of hypergraph matching using higher-order affinity information. We propose a solver that iteratively updates the solution in the discrete domain by linear assignment approximation. The proposed method is guaranteed to converge to a stationary discrete solution and avoids the annealing procedure and ad-hoc post binarization step that are required in several previous methods. Specifically, we start with a simple iterative discrete gradient assignment solver. This solver can be trapped in an -circle sequence under moderate conditions, where is the order of the graph matching problem. We then devise an adaptive relaxation mechanism to jump out this degenerating case and show that the resulting new path will converge to a fixed solution in the discrete domain. The proposed method is tested on both synthetic and real-world benchmarks. The experimental results corroborate the efficacy of our method.
Goodrich, Christopher
2015-01-01
This text provides the first comprehensive treatment of the discrete fractional calculus. Experienced researchers will find the text useful as a reference for discrete fractional calculus and topics of current interest. Students who are interested in learning about discrete fractional calculus will find this text to provide a useful starting point. Several exercises are offered at the end of each chapter and select answers have been provided at the end of the book. The presentation of the content is designed to give ample flexibility for potential use in a myriad of courses and for independent study. The novel approach taken by the authors includes a simultaneous treatment of the fractional- and integer-order difference calculus (on a variety of time scales, including both the usual forward and backwards difference operators). The reader will acquire a solid foundation in the classical topics of the discrete calculus while being introduced to exciting recent developments, bringing them to the frontiers of the...
International Nuclear Information System (INIS)
Williams, Ruth M
2006-01-01
A review is given of a number of approaches to discrete quantum gravity, with a restriction to those likely to be relevant in four dimensions. This paper is dedicated to Rafael Sorkin on the occasion of his sixtieth birthday
A non overlapping parallel domain decomposition method applied to the simplified transport equations
International Nuclear Information System (INIS)
Lathuiliere, B.; Barrault, M.; Ramet, P.; Roman, J.
2009-01-01
A reactivity computation requires to compute the highest eigenvalue of a generalized eigenvalue problem. An inverse power algorithm is used commonly. Very fine modelizations are difficult to tackle for our sequential solver, based on the simplified transport equations, in terms of memory consumption and computational time. So, we propose a non-overlapping domain decomposition method for the approximate resolution of the linear system to solve at each inverse power iteration. Our method brings to a low development effort as the inner multigroup solver can be re-use without modification, and allows us to adapt locally the numerical resolution (mesh, finite element order). Numerical results are obtained by a parallel implementation of the method on two different cases with a pin by pin discretization. This results are analyzed in terms of memory consumption and parallel efficiency. (authors)
Discrete computational structures
Korfhage, Robert R
1974-01-01
Discrete Computational Structures describes discrete mathematical concepts that are important to computing, covering necessary mathematical fundamentals, computer representation of sets, graph theory, storage minimization, and bandwidth. The book also explains conceptual framework (Gorn trees, searching, subroutines) and directed graphs (flowcharts, critical paths, information network). The text discusses algebra particularly as it applies to concentrates on semigroups, groups, lattices, propositional calculus, including a new tabular method of Boolean function minimization. The text emphasize
Circuit mismatch influence on performance of paralleling silicon carbide MOSFETs
DEFF Research Database (Denmark)
Li, Helong; Munk-Nielsen, Stig; Pham, Cam
2014-01-01
This paper focuses on circuit mismatch influence on performance of paralleling SiC MOSFETs. Power circuit mismatch and gate driver mismatch influences are analyzed in detail. Simulation and experiment results show the influence of circuit mismatch and verify the analysis. This paper aims to give...... suggestions on paralleling discrete SiC MOSFETs and designing layout of power modules with paralleled SiC MOSFETs dies....
Discrete linear canonical transform computation by adaptive method.
Zhang, Feng; Tao, Ran; Wang, Yue
2013-07-29
The linear canonical transform (LCT) describes the effect of quadratic phase systems on a wavefield and generalizes many optical transforms. In this paper, the computation method for the discrete LCT using the adaptive least-mean-square (LMS) algorithm is presented. The computation approaches of the block-based discrete LCT and the stream-based discrete LCT using the LMS algorithm are derived, and the implementation structures of these approaches by the adaptive filter system are considered. The proposed computation approaches have the inherent parallel structures which make them suitable for efficient VLSI implementations, and are robust to the propagation of possible errors in the computation process.
Parallel Algorithms for Groebner-Basis Reduction
1987-09-25
22209 ELEMENT NO. NO. NO. ACCESSION NO. 11. TITLE (Include Security Classification) * PARALLEL ALGORITHMS FOR GROEBNER -BASIS REDUCTION 12. PERSONAL...All other editions are obsolete. Productivity Engineering in the UNIXt Environment p Parallel Algorithms for Groebner -Basis Reduction Technical Report
Parallel Simulation of Three-Dimensional Free Surface Fluid Flow Problems
International Nuclear Information System (INIS)
BAER, THOMAS A.; SACKINGER, PHILIP A.; SUBIA, SAMUEL R.
1999-01-01
Simulation of viscous three-dimensional fluid flow typically involves a large number of unknowns. When free surfaces are included, the number of unknowns increases dramatically. Consequently, this class of problem is an obvious application of parallel high performance computing. We describe parallel computation of viscous, incompressible, free surface, Newtonian fluid flow problems that include dynamic contact fines. The Galerkin finite element method was used to discretize the fully-coupled governing conservation equations and a ''pseudo-solid'' mesh mapping approach was used to determine the shape of the free surface. In this approach, the finite element mesh is allowed to deform to satisfy quasi-static solid mechanics equations subject to geometric or kinematic constraints on the boundaries. As a result, nodal displacements must be included in the set of unknowns. Other issues discussed are the proper constraints appearing along the dynamic contact line in three dimensions. Issues affecting efficient parallel simulations include problem decomposition to equally distribute computational work among a SPMD computer and determination of robust, scalable preconditioners for the distributed matrix systems that must be solved. Solution continuation strategies important for serial simulations have an enhanced relevance in a parallel coquting environment due to the difficulty of solving large scale systems. Parallel computations will be demonstrated on an example taken from the coating flow industry: flow in the vicinity of a slot coater edge. This is a three dimensional free surface problem possessing a contact line that advances at the web speed in one region but transitions to static behavior in another region. As such, a significant fraction of the computational time is devoted to processing boundary data. Discussion focuses on parallel speed ups for fixed problem size, a class of problems of immediate practical importance
Homogenization of discrete media
Energy Technology Data Exchange (ETDEWEB)
Pradel, F.; Sab, K. [CERAM-ENPC, Marne-la-Vallee (France)
1998-11-01
Material such as granular media, beam assembly are easily seen as discrete media. They look like geometrical points linked together thanks to energetic expressions. Our purpose is to extend discrete kinematics to the one of an equivalent continuous material. First we explain how we build the localisation tool for periodic materials according to estimated continuum medium type (classical Cauchy, and Cosserat media). Once the bridge built between discrete and continuum media, we exhibit its application over two bidimensional beam assembly structures : the honey comb and a structural reinforced variation. The new behavior is then applied for the simple plan shear problem in a Cosserat continuum and compared with the real discrete solution. By the mean of this example, we establish the agreement of our new model with real structures. The exposed method has a longer range than mechanics and can be applied to every discrete problems like electromagnetism in which relationship between geometrical points can be summed up by an energetic function. (orig.) 7 refs.
Bayer image parallel decoding based on GPU
Hu, Rihui; Xu, Zhiyong; Wei, Yuxing; Sun, Shaohua
2012-11-01
In the photoelectrical tracking system, Bayer image is decompressed in traditional method, which is CPU-based. However, it is too slow when the images become large, for example, 2K×2K×16bit. In order to accelerate the Bayer image decoding, this paper introduces a parallel speedup method for NVIDA's Graphics Processor Unit (GPU) which supports CUDA architecture. The decoding procedure can be divided into three parts: the first is serial part, the second is task-parallelism part, and the last is data-parallelism part including inverse quantization, inverse discrete wavelet transform (IDWT) as well as image post-processing part. For reducing the execution time, the task-parallelism part is optimized by OpenMP techniques. The data-parallelism part could advance its efficiency through executing on the GPU as CUDA parallel program. The optimization techniques include instruction optimization, shared memory access optimization, the access memory coalesced optimization and texture memory optimization. In particular, it can significantly speed up the IDWT by rewriting the 2D (Tow-dimensional) serial IDWT into 1D parallel IDWT. Through experimenting with 1K×1K×16bit Bayer image, data-parallelism part is 10 more times faster than CPU-based implementation. Finally, a CPU+GPU heterogeneous decompression system was designed. The experimental result shows that it could achieve 3 to 5 times speed increase compared to the CPU serial method.
Parallel S/sub n/ iteration schemes
International Nuclear Information System (INIS)
Wienke, B.R.; Hiromoto, R.E.
1986-01-01
The iterative, multigroup, discrete ordinates (S/sub n/) technique for solving the linear transport equation enjoys widespread usage and appeal. Serial iteration schemes and numerical algorithms developed over the years provide a timely framework for parallel extension. On the Denelcor HEP, the authors investigate three parallel iteration schemes for solving the one-dimensional S/sub n/ transport equation. The multigroup representation and serial iteration methods are also reviewed. This analysis represents a first attempt to extend serial S/sub n/ algorithms to parallel environments and provides good baseline estimates on ease of parallel implementation, relative algorithm efficiency, comparative speedup, and some future directions. The authors examine ordered and chaotic versions of these strategies, with and without concurrent rebalance and diffusion acceleration. Two strategies efficiently support high degrees of parallelization and appear to be robust parallel iteration techniques. The third strategy is a weaker parallel algorithm. Chaotic iteration, difficult to simulate on serial machines, holds promise and converges faster than ordered versions of the schemes. Actual parallel speedup and efficiency are high and payoff appears substantial
DISCRETE MATHEMATICS/NUMBER THEORY
Mrs. Manju Devi*
2017-01-01
Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics such as integers, graphs, and statements do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus and analysis. Discrete objects can often be enumerated by ...
Directory of Open Access Journals (Sweden)
Prateek Sharma
2015-04-01
Full Text Available Abstract Simulation can be regarded as the emulation of the behavior of a real-world system over an interval of time. The process of simulation relies upon the generation of the history of a system and then analyzing that history to predict the outcome and improve the working of real systems. Simulations can be of various kinds but the topic of interest here is one of the most important kind of simulation which is Discrete-Event Simulation which models the system as a discrete sequence of events in time. So this paper aims at introducing about Discrete-Event Simulation and analyzing how it is beneficial to the real world systems.
Discrete systems and integrability
Hietarinta, J; Nijhoff, F W
2016-01-01
This first introductory text to discrete integrable systems introduces key notions of integrability from the vantage point of discrete systems, also making connections with the continuous theory where relevant. While treating the material at an elementary level, the book also highlights many recent developments. Topics include: Darboux and Bäcklund transformations; difference equations and special functions; multidimensional consistency of integrable lattice equations; associated linear problems (Lax pairs); connections with Padé approximants and convergence algorithms; singularities and geometry; Hirota's bilinear formalism for lattices; intriguing properties of discrete Painlevé equations; and the novel theory of Lagrangian multiforms. The book builds the material in an organic way, emphasizing interconnections between the various approaches, while the exposition is mostly done through explicit computations on key examples. Written by respected experts in the field, the numerous exercises and the thoroug...
Exarchakis, Georgios; Lücke, Jörg
2017-11-01
Sparse coding algorithms with continuous latent variables have been the subject of a large number of studies. However, discrete latent spaces for sparse coding have been largely ignored. In this work, we study sparse coding with latents described by discrete instead of continuous prior distributions. We consider the general case in which the latents (while being sparse) can take on any value of a finite set of possible values and in which we learn the prior probability of any value from data. This approach can be applied to any data generated by discrete causes, and it can be applied as an approximation of continuous causes. As the prior probabilities are learned, the approach then allows for estimating the prior shape without assuming specific functional forms. To efficiently train the parameters of our probabilistic generative model, we apply a truncated expectation-maximization approach (expectation truncation) that we modify to work with a general discrete prior. We evaluate the performance of the algorithm by applying it to a variety of tasks: (1) we use artificial data to verify that the algorithm can recover the generating parameters from a random initialization, (2) use image patches of natural images and discuss the role of the prior for the extraction of image components, (3) use extracellular recordings of neurons to present a novel method of analysis for spiking neurons that includes an intuitive discretization strategy, and (4) apply the algorithm on the task of encoding audio waveforms of human speech. The diverse set of numerical experiments presented in this letter suggests that discrete sparse coding algorithms can scale efficiently to work with realistic data sets and provide novel statistical quantities to describe the structure of the data.
Introductory discrete mathematics
Balakrishnan, V K
2010-01-01
This concise text offers an introduction to discrete mathematics for undergraduate students in computer science and mathematics. Mathematics educators consider it vital that their students be exposed to a course in discrete methods that introduces them to combinatorial mathematics and to algebraic and logical structures focusing on the interplay between computer science and mathematics. The present volume emphasizes combinatorics, graph theory with applications to some stand network optimization problems, and algorithms to solve these problems.Chapters 0-3 cover fundamental operations involv
Prateek Sharma
2015-01-01
Abstract Simulation can be regarded as the emulation of the behavior of a real-world system over an interval of time. The process of simulation relies upon the generation of the history of a system and then analyzing that history to predict the outcome and improve the working of real systems. Simulations can be of various kinds but the topic of interest here is one of the most important kind of simulation which is Discrete-Event Simulation which models the system as a discrete sequence of ev...
Geometric phases in discrete dynamical systems
Energy Technology Data Exchange (ETDEWEB)
Cartwright, Julyan H.E., E-mail: julyan.cartwright@csic.es [Instituto Andaluz de Ciencias de la Tierra, CSIC–Universidad de Granada, E-18100 Armilla, Granada (Spain); Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071 Granada (Spain); Piro, Nicolas, E-mail: nicolas.piro@epfl.ch [École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne (Switzerland); Piro, Oreste, E-mail: piro@imedea.uib-csic.es [Departamento de Física, Universitat de les Illes Balears, E-07122 Palma de Mallorca (Spain); Tuval, Idan, E-mail: ituval@imedea.uib-csic.es [Mediterranean Institute for Advanced Studies, CSIC–Universitat de les Illes Balears, E-07190 Mallorca (Spain)
2016-10-14
In order to study the behaviour of discrete dynamical systems under adiabatic cyclic variations of their parameters, we consider discrete versions of adiabatically-rotated rotators. Parallelling the studies in continuous systems, we generalize the concept of geometric phase to discrete dynamics and investigate its presence in these rotators. For the rotated sine circle map, we demonstrate an analytical relationship between the geometric phase and the rotation number of the system. For the discrete version of the rotated rotator considered by Berry, the rotated standard map, we further explore this connection as well as the role of the geometric phase at the onset of chaos. Further into the chaotic regime, we show that the geometric phase is also related to the diffusive behaviour of the dynamical variables and the Lyapunov exponent. - Highlights: • We extend the concept of geometric phase to maps. • For the rotated sine circle map, we demonstrate an analytical relationship between the geometric phase and the rotation number. • For the rotated standard map, we explore the role of the geometric phase at the onset of chaos. • We show that the geometric phase is related to the diffusive behaviour of the dynamical variables and the Lyapunov exponent.
Parallel preconditioning techniques for sparse CG solvers
Energy Technology Data Exchange (ETDEWEB)
Basermann, A.; Reichel, B.; Schelthoff, C. [Central Institute for Applied Mathematics, Juelich (Germany)
1996-12-31
Conjugate gradient (CG) methods to solve sparse systems of linear equations play an important role in numerical methods for solving discretized partial differential equations. The large size and the condition of many technical or physical applications in this area result in the need for efficient parallelization and preconditioning techniques of the CG method. In particular for very ill-conditioned matrices, sophisticated preconditioner are necessary to obtain both acceptable convergence and accuracy of CG. Here, we investigate variants of polynomial and incomplete Cholesky preconditioners that markedly reduce the iterations of the simply diagonally scaled CG and are shown to be well suited for massively parallel machines.
Parallel Programming with Intel Parallel Studio XE
Blair-Chappell , Stephen
2012-01-01
Optimize code for multi-core processors with Intel's Parallel Studio Parallel programming is rapidly becoming a "must-know" skill for developers. Yet, where to start? This teach-yourself tutorial is an ideal starting point for developers who already know Windows C and C++ and are eager to add parallelism to their code. With a focus on applying tools, techniques, and language extensions to implement parallelism, this essential resource teaches you how to write programs for multicore and leverage the power of multicore in your programs. Sharing hands-on case studies and real-world examples, the
Discrete calculus methods for counting
Mariconda, Carlo
2016-01-01
This book provides an introduction to combinatorics, finite calculus, formal series, recurrences, and approximations of sums. Readers will find not only coverage of the basic elements of the subjects but also deep insights into a range of less common topics rarely considered within a single book, such as counting with occupancy constraints, a clear distinction between algebraic and analytical properties of formal power series, an introduction to discrete dynamical systems with a thorough description of Sarkovskii’s theorem, symbolic calculus, and a complete description of the Euler-Maclaurin formulas and their applications. Although several books touch on one or more of these aspects, precious few cover all of them. The authors, both pure mathematicians, have attempted to develop methods that will allow the student to formulate a given problem in a precise mathematical framework. The aim is to equip readers with a sound strategy for classifying and solving problems by pursuing a mathematically rigorous yet ...
Discrete modelling of drapery systems
Thoeni, Klaus; Giacomini, Anna
2016-04-01
Drapery systems are an efficient and cost-effective measure in preventing and controlling rockfall hazards on rock slopes. The simplest form consists of a row of ground anchors along the top of the slope connected to a horizontal support cable from which a wire mesh is suspended down the face of the slope. Such systems are generally referred to as simple or unsecured draperies (Badger and Duffy 2012). Variations such as secured draperies, where a pattern of ground anchors is incorporated within the field of the mesh, and hybrid systems, where the upper part of an unsecured drapery is elevated to intercept rockfalls originating upslope of the installation, are becoming more and more popular. This work presents a discrete element framework for simulation of unsecured drapery systems and its variations. The numerical model is based on the classical discrete element method (DEM) and implemented into the open-source framework YADE (Šmilauer et al., 2010). The model takes all relevant interactions between block, drapery and slope into account (Thoeni et al., 2014) and was calibrated and validated based on full-scale experiments (Giacomini et al., 2012).The block is modelled as a rigid clump made of spherical particles which allows any shape to be approximated. The drapery is represented by a set of spherical particle with remote interactions. The behaviour of the remote interactions is governed by the constitutive behaviour of the wire and generally corresponds to a piecewise linear stress-strain relation (Thoeni et al., 2013). The same concept is used to model wire ropes. The rock slope is represented by rigid triangular elements where material properties (e.g., normal coefficient of restitution, friction angle) are assigned to each triangle. The capabilities of the developed model to simulate drapery systems and estimate the residual hazard involved with such systems is shown. References Badger, T.C., Duffy, J.D. (2012) Drapery systems. In: Turner, A.K., Schuster R
Parallelization of 2-D lattice Boltzmann codes
International Nuclear Information System (INIS)
Suzuki, Soichiro; Kaburaki, Hideo; Yokokawa, Mitsuo.
1996-03-01
Lattice Boltzmann (LB) codes to simulate two dimensional fluid flow are developed on vector parallel computer Fujitsu VPP500 and scalar parallel computer Intel Paragon XP/S. While a 2-D domain decomposition method is used for the scalar parallel LB code, a 1-D domain decomposition method is used for the vector parallel LB code to be vectorized along with the axis perpendicular to the direction of the decomposition. High parallel efficiency of 95.1% by the vector parallel calculation on 16 processors with 1152x1152 grid and 88.6% by the scalar parallel calculation on 100 processors with 800x800 grid are obtained. The performance models are developed to analyze the performance of the LB codes. It is shown by our performance models that the execution speed of the vector parallel code is about one hundred times faster than that of the scalar parallel code with the same number of processors up to 100 processors. We also analyze the scalability in keeping the available memory size of one processor element at maximum. Our performance model predicts that the execution time of the vector parallel code increases about 3% on 500 processors. Although the 1-D domain decomposition method has in general a drawback in the interprocessor communication, the vector parallel LB code is still suitable for the large scale and/or high resolution simulations. (author)
Parallelization of 2-D lattice Boltzmann codes
Energy Technology Data Exchange (ETDEWEB)
Suzuki, Soichiro; Kaburaki, Hideo; Yokokawa, Mitsuo
1996-03-01
Lattice Boltzmann (LB) codes to simulate two dimensional fluid flow are developed on vector parallel computer Fujitsu VPP500 and scalar parallel computer Intel Paragon XP/S. While a 2-D domain decomposition method is used for the scalar parallel LB code, a 1-D domain decomposition method is used for the vector parallel LB code to be vectorized along with the axis perpendicular to the direction of the decomposition. High parallel efficiency of 95.1% by the vector parallel calculation on 16 processors with 1152x1152 grid and 88.6% by the scalar parallel calculation on 100 processors with 800x800 grid are obtained. The performance models are developed to analyze the performance of the LB codes. It is shown by our performance models that the execution speed of the vector parallel code is about one hundred times faster than that of the scalar parallel code with the same number of processors up to 100 processors. We also analyze the scalability in keeping the available memory size of one processor element at maximum. Our performance model predicts that the execution time of the vector parallel code increases about 3% on 500 processors. Although the 1-D domain decomposition method has in general a drawback in the interprocessor communication, the vector parallel LB code is still suitable for the large scale and/or high resolution simulations. (author).
International Nuclear Information System (INIS)
Yoon, Jong Seon; Choi, Hyoung Gwon; Jeon, Byoung Jin; Jung, Hye Dong
2016-01-01
A parallel algorithm of bi-conjugate gradient method was developed based on CUDA for parallel computation of the incompressible Navier-Stokes equations. The governing equations were discretized using splitting P2P1 finite element method. Asymmetric stenotic flow problem was solved to validate the proposed algorithm, and then the parallel performance of the GPU was examined by measuring the elapsed times. Further, the GPU performance for sparse matrix-vector multiplication was also investigated with a matrix of fluid-structure interaction problem. A kernel was generated to simultaneously compute the inner product of each row of sparse matrix and a vector. In addition, the kernel was optimized to improve the performance by using both parallel reduction and memory coalescing. In the kernel construction, the effect of warp on the parallel performance of the present CUDA was also examined. The present GPU computation was more than 7 times faster than the single CPU by double precision.
Energy Technology Data Exchange (ETDEWEB)
Yoon, Jong Seon; Choi, Hyoung Gwon [Seoul Nat’l Univ. of Science and Technology, Seoul (Korea, Republic of); Jeon, Byoung Jin [Yonsei Univ., Seoul (Korea, Republic of); Jung, Hye Dong [Korea Electronics Technology Institute, Seongnam (Korea, Republic of)
2016-09-15
A parallel algorithm of bi-conjugate gradient method was developed based on CUDA for parallel computation of the incompressible Navier-Stokes equations. The governing equations were discretized using splitting P2P1 finite element method. Asymmetric stenotic flow problem was solved to validate the proposed algorithm, and then the parallel performance of the GPU was examined by measuring the elapsed times. Further, the GPU performance for sparse matrix-vector multiplication was also investigated with a matrix of fluid-structure interaction problem. A kernel was generated to simultaneously compute the inner product of each row of sparse matrix and a vector. In addition, the kernel was optimized to improve the performance by using both parallel reduction and memory coalescing. In the kernel construction, the effect of warp on the parallel performance of the present CUDA was also examined. The present GPU computation was more than 7 times faster than the single CPU by double precision.
Indian Academy of Sciences (India)
We also describe discrete-time systems in terms of difference ... A more modern alternative, especially for larger systems, is to convert ... In other words, ..... picture?) State-variable equations are also called state-space equations because the ...
Discrete Lorentzian quantum gravity
Loll, R.
2000-01-01
Just as for non-abelian gauge theories at strong coupling, discrete lattice methods are a natural tool in the study of non-perturbative quantum gravity. They have to reflect the fact that the geometric degrees of freedom are dynamical, and that therefore also the lattice theory must be formulated
Sharp, Karen Tobey
This paper cites information received from a number of sources, e.g., mathematics teachers in two-year colleges, publishers, and convention speakers, about the nature of discrete mathematics and about what topics a course in this subject should contain. Note is taken of the book edited by Ralston and Young which discusses the future of college…
Juxtaposed color halftoning relying on discrete lines.
Babaei, Vahid; Hersch, Roger D
2013-02-01
Most halftoning techniques allow screen dots to overlap. They rely on the assumption that the inks are transparent, i.e., the inks do not scatter a significant portion of the light back to the air. However, many special effect inks, such as metallic inks, iridescent inks, or pigmented inks, are not transparent. In order to create halftone images, halftone dots formed by such inks should be juxtaposed, i.e., printed side by side. We propose an efficient juxtaposed color halftoning technique for placing any desired number of colorant layers side by side without overlapping. The method uses a monochrome library of screen elements made of discrete lines with rational thicknesses. Discrete line juxtaposed color halftoning is performed efficiently by multiple accesses to the screen element library.
Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations
Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi
2017-01-01
A conservative discretization of incompressible Navier-Stokes equations over surface simplicial meshes is developed using discrete exterior calculus (DEC). Numerical experiments for flows over surfaces reveal a second order accuracy
Discrete mKdV and discrete sine-Gordon flows on discrete space curves
International Nuclear Information System (INIS)
Inoguchi, Jun-ichi; Kajiwara, Kenji; Matsuura, Nozomu; Ohta, Yasuhiro
2014-01-01
In this paper, we consider the discrete deformation of the discrete space curves with constant torsion described by the discrete mKdV or the discrete sine-Gordon equations, and show that it is formulated as the torsion-preserving equidistant deformation on the osculating plane which satisfies the isoperimetric condition. The curve is reconstructed from the deformation data by using the Sym–Tafel formula. The isoperimetric equidistant deformation of the space curves does not preserve the torsion in general. However, it is possible to construct the torsion-preserving deformation by tuning the deformation parameters. Further, it is also possible to make an arbitrary choice of the deformation described by the discrete mKdV equation or by the discrete sine-Gordon equation at each step. We finally show that the discrete deformation of discrete space curves yields the discrete K-surfaces. (paper)
Morse, H Stephen
1994-01-01
Practical Parallel Computing provides information pertinent to the fundamental aspects of high-performance parallel processing. This book discusses the development of parallel applications on a variety of equipment.Organized into three parts encompassing 12 chapters, this book begins with an overview of the technology trends that converge to favor massively parallel hardware over traditional mainframes and vector machines. This text then gives a tutorial introduction to parallel hardware architectures. Other chapters provide worked-out examples of programs using several parallel languages. Thi
Akl, Selim G
1985-01-01
Parallel Sorting Algorithms explains how to use parallel algorithms to sort a sequence of items on a variety of parallel computers. The book reviews the sorting problem, the parallel models of computation, parallel algorithms, and the lower bounds on the parallel sorting problems. The text also presents twenty different algorithms, such as linear arrays, mesh-connected computers, cube-connected computers. Another example where algorithm can be applied is on the shared-memory SIMD (single instruction stream multiple data stream) computers in which the whole sequence to be sorted can fit in the
Energy Technology Data Exchange (ETDEWEB)
Mugica R, A.; Valle G, E. del [IPN, ESFM, 07738 Mexico D.F. (Mexico)]. e-mail: mugica@esfm.ipn.mx
2003-07-01
Nowadays the numerical methods of solution to the diffusion equation by means of algorithms and computer programs result so extensive due to the great number of routines and calculations that should carry out, this rebounds directly in the execution times of this programs, being obtained results in relatively long times. This work shows the application of an acceleration method of the convergence of the classic method of those powers that it reduces notably the number of necessary iterations for to obtain reliable results, what means that the compute times they see reduced in great measure. This method is known in the literature like Wielandt method and it has incorporated to a computer program that is based on the discretization of the neutron diffusion equations in plate geometry and stationary state by polynomial nodal methods. In this work the neutron diffusion equations are described for several energy groups and their discretization by means of those called physical nodal methods, being illustrated in particular the quadratic case. It is described a model problem widely described in the literature which is solved for the physical nodal grade schemes 1, 2, 3 and 4 in three different ways: to) with the classic method of the powers, b) method of the powers with the Wielandt acceleration and c) method of the powers with the Wielandt modified acceleration. The results for the model problem as well as for two additional problems known as benchmark problems are reported. Such acceleration method can also be implemented to problems of different geometry to the proposal in this work, besides being possible to extend their application to problems in 2 or 3 dimensions. (Author)
Discrete Feature Model (DFM) User Documentation
International Nuclear Information System (INIS)
Geier, Joel
2008-06-01
geometry of discrete features and their hydrologic properties are defined as a mesh composed of triangular, finite elements. Hydrologic boundary conditions arc prescribed as a simulation sequence, which permits specification of conditions ranging from simple, steady-state flow to complex situations where both the magnitude and type of boundary conditions may vary over time
Discrete Feature Model (DFM) User Documentation
Energy Technology Data Exchange (ETDEWEB)
Geier, Joel (Clearwater Hardrock Consulting, Corvallis, OR (United States))
2008-06-15
software, the geometry of discrete features and their hydrologic properties are defined as a mesh composed of triangular, finite elements. Hydrologic boundary conditions arc prescribed as a simulation sequence, which permits specification of conditions ranging from simple, steady-state flow to complex situations where both the magnitude and type of boundary conditions may vary over time
Lumped impulses, discrete displacements and a moving load analysis
Kok, A.W.M.
1997-01-01
Finite element models are usually presented as relations between lumped forces and discrete displacements. Mostly finite element models are found by the elaboration of the method of the virtual work - which is a special case of the Galerkin's variational principle -. By application of Galerkin's
A novel two-level dynamic parallel data scheme for large 3-D SN calculations
International Nuclear Information System (INIS)
Sjoden, G.E.; Shedlock, D.; Haghighat, A.; Yi, C.
2005-01-01
We introduce a new dynamic parallel memory optimization scheme for executing large scale 3-D discrete ordinates (Sn) simulations on distributed memory parallel computers. In order for parallel transport codes to be truly scalable, they must use parallel data storage, where only the variables that are locally computed are locally stored. Even with parallel data storage for the angular variables, cumulative storage requirements for large discrete ordinates calculations can be prohibitive. To address this problem, Memory Tuning has been implemented into the PENTRAN 3-D parallel discrete ordinates code as an optimized, two-level ('large' array, 'small' array) parallel data storage scheme. Memory Tuning can be described as the process of parallel data memory optimization. Memory Tuning dynamically minimizes the amount of required parallel data in allocated memory on each processor using a statistical sampling algorithm. This algorithm is based on the integral average and standard deviation of the number of fine meshes contained in each coarse mesh in the global problem. Because PENTRAN only stores the locally computed problem phase space, optimal two-level memory assignments can be unique on each node, depending upon the parallel decomposition used (hybrid combinations of angular, energy, or spatial). As demonstrated in the two large discrete ordinates models presented (a storage cask and an OECD MOX Benchmark), Memory Tuning can save a substantial amount of memory per parallel processor, allowing one to accomplish very large scale Sn computations. (authors)
Discrete analysis of clay layer tensile strength
International Nuclear Information System (INIS)
Le, T.N.H.; Ple, O.; Villard, P.; Gourc, J.P.
2010-01-01
The Discrete Element Method is used to investigate the tensile behaviour and cracks mechanisms of a clay material submitted to bending loading. It is the case of compacted clay liners in landfill cap cover application. Such as the soil tested in this study is plastic clay, the distinct elements model was calibrated with previous data results by taking into account cohesive properties. Various contact and cohesion laws are tested to show that the numerical model is able to reproduce the failure mechanism. Numerical results are extending to simulate a landfill cap cover and comparing to experimental large scale field bending tests achieved in a real site of storage. (authors)
Discrete mathematics with applications
Koshy, Thomas
2003-01-01
This approachable text studies discrete objects and the relationsips that bind them. It helps students understand and apply the power of discrete math to digital computer systems and other modern applications. It provides excellent preparation for courses in linear algebra, number theory, and modern/abstract algebra and for computer science courses in data structures, algorithms, programming languages, compilers, databases, and computation.* Covers all recommended topics in a self-contained, comprehensive, and understandable format for students and new professionals * Emphasizes problem-solving techniques, pattern recognition, conjecturing, induction, applications of varying nature, proof techniques, algorithm development and correctness, and numeric computations* Weaves numerous applications into the text* Helps students learn by doing with a wealth of examples and exercises: - 560 examples worked out in detail - More than 3,700 exercises - More than 150 computer assignments - More than 600 writing projects*...
Discrete and computational geometry
Devadoss, Satyan L
2011-01-01
Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also fe...
2002-01-01
Discrete geometry investigates combinatorial properties of configurations of geometric objects. To a working mathematician or computer scientist, it offers sophisticated results and techniques of great diversity and it is a foundation for fields such as computational geometry or combinatorial optimization. This book is primarily a textbook introduction to various areas of discrete geometry. In each area, it explains several key results and methods, in an accessible and concrete manner. It also contains more advanced material in separate sections and thus it can serve as a collection of surveys in several narrower subfields. The main topics include: basics on convex sets, convex polytopes, and hyperplane arrangements; combinatorial complexity of geometric configurations; intersection patterns and transversals of convex sets; geometric Ramsey-type results; polyhedral combinatorics and high-dimensional convexity; and lastly, embeddings of finite metric spaces into normed spaces. Jiri Matousek is Professor of Com...
Time Discretization Techniques
Gottlieb, S.
2016-10-12
The time discretization of hyperbolic partial differential equations is typically the evolution of a system of ordinary differential equations obtained by spatial discretization of the original problem. Methods for this time evolution include multistep, multistage, or multiderivative methods, as well as a combination of these approaches. The time step constraint is mainly a result of the absolute stability requirement, as well as additional conditions that mimic physical properties of the solution, such as positivity or total variation stability. These conditions may be required for stability when the solution develops shocks or sharp gradients. This chapter contains a review of some of the methods historically used for the evolution of hyperbolic PDEs, as well as cutting edge methods that are now commonly used.
Czech Academy of Sciences Publication Activity Database
Mesiar, Radko; Li, J.; Pap, E.
2013-01-01
Roč. 54, č. 3 (2013), s. 357-364 ISSN 0888-613X R&D Projects: GA ČR GAP402/11/0378 Institutional support: RVO:67985556 Keywords : concave integral * pseudo-addition * pseudo-multiplication Subject RIV: BA - General Mathematics Impact factor: 1.977, year: 2013 http://library.utia.cas.cz/separaty/2013/E/mesiar-discrete pseudo-integrals.pdf
International Nuclear Information System (INIS)
Jalnapurkar, Sameer M; Leok, Melvin; Marsden, Jerrold E; West, Matthew
2006-01-01
This paper develops the theory of Abelian Routh reduction for discrete mechanical systems and applies it to the variational integration of mechanical systems with Abelian symmetry. The reduction of variational Runge-Kutta discretizations is considered, as well as the extent to which symmetry reduction and discretization commute. These reduced methods allow the direct simulation of dynamical features such as relative equilibria and relative periodic orbits that can be obscured or difficult to identify in the unreduced dynamics. The methods are demonstrated for the dynamics of an Earth orbiting satellite with a non-spherical J 2 correction, as well as the double spherical pendulum. The J 2 problem is interesting because in the unreduced picture, geometric phases inherent in the model and those due to numerical discretization can be hard to distinguish, but this issue does not appear in the reduced algorithm, where one can directly observe interesting dynamical structures in the reduced phase space (the cotangent bundle of shape space), in which the geometric phases have been removed. The main feature of the double spherical pendulum example is that it has a non-trivial magnetic term in its reduced symplectic form. Our method is still efficient as it can directly handle the essential non-canonical nature of the symplectic structure. In contrast, a traditional symplectic method for canonical systems could require repeated coordinate changes if one is evoking Darboux' theorem to transform the symplectic structure into canonical form, thereby incurring additional computational cost. Our method allows one to design reduced symplectic integrators in a natural way, despite the non-canonical nature of the symplectic structure
Discrete port-Hamiltonian systems
Talasila, V.; Clemente-Gallardo, J.; Schaft, A.J. van der
2006-01-01
Either from a control theoretic viewpoint or from an analysis viewpoint it is necessary to convert smooth systems to discrete systems, which can then be implemented on computers for numerical simulations. Discrete models can be obtained either by discretizing a smooth model, or by directly modeling
A paradigm for discrete physics
International Nuclear Information System (INIS)
Noyes, H.P.; McGoveran, D.; Etter, T.; Manthey, M.J.; Gefwert, C.
1987-01-01
An example is outlined for constructing a discrete physics using as a starting point the insight from quantum physics that events are discrete, indivisible and non-local. Initial postulates are finiteness, discreteness, finite computability, absolute nonuniqueness (i.e., homogeneity in the absence of specific cause) and additivity
Introduction to parallel programming
Brawer, Steven
1989-01-01
Introduction to Parallel Programming focuses on the techniques, processes, methodologies, and approaches involved in parallel programming. The book first offers information on Fortran, hardware and operating system models, and processes, shared memory, and simple parallel programs. Discussions focus on processes and processors, joining processes, shared memory, time-sharing with multiple processors, hardware, loops, passing arguments in function/subroutine calls, program structure, and arithmetic expressions. The text then elaborates on basic parallel programming techniques, barriers and race