Differential equations problem solver
Arterburn, David R
2012-01-01
REA's Problem Solvers is a series of useful, practical, and informative study guides. Each title in the series is complete step-by-step solution guide. The Differential Equations Problem Solver enables students to solve difficult problems by showing them step-by-step solutions to Differential Equations problems. The Problem Solvers cover material ranging from the elementary to the advanced and make excellent review books and textbook companions. They're perfect for undergraduate and graduate studies.The Differential Equations Problem Solver is the perfect resource for any class, any exam, and
Brouwer-Janse, M.D.
1991-01-01
Most formal problem-solving studies use verbal protocol and observational data of problem solvers working on a task. In user-centred product-design projects, observational studies of users are frequently used too. In the latter case, however, systematic control of conditions, indepth analysis and
Electric circuits problem solver
REA, Editors of
2012-01-01
Each Problem Solver is an insightful and essential study and solution guide chock-full of clear, concise problem-solving gems. All your questions can be found in one convenient source from one of the most trusted names in reference solution guides. More useful, more practical, and more informative, these study aids are the best review books and textbook companions available. Nothing remotely as comprehensive or as helpful exists in their subject anywhere. Perfect for undergraduate and graduate studies.Here in this highly useful reference is the finest overview of electric circuits currently av
Advanced calculus problem solver
REA, Editors of
2012-01-01
Each Problem Solver is an insightful and essential study and solution guide chock-full of clear, concise problem-solving gems. All your questions can be found in one convenient source from one of the most trusted names in reference solution guides. More useful, more practical, and more informative, these study aids are the best review books and textbook companions available. Nothing remotely as comprehensive or as helpful exists in their subject anywhere. Perfect for undergraduate and graduate studies.Here in this highly useful reference is the finest overview of advanced calculus currently av
Sherlock Holmes, Master Problem Solver.
Ballew, Hunter
1994-01-01
Shows the connections between Sherlock Holmes's investigative methods and mathematical problem solving, including observations, characteristics of the problem solver, importance of data, questioning the obvious, learning from experience, learning from errors, and indirect proof. (MKR)
Modern solvers for Helmholtz problems
Tang, Jok; Vuik, Kees
2017-01-01
This edited volume offers a state of the art overview of fast and robust solvers for the Helmholtz equation. The book consists of three parts: new developments and analysis in Helmholtz solvers, practical methods and implementations of Helmholtz solvers, and industrial applications. The Helmholtz equation appears in a wide range of science and engineering disciplines in which wave propagation is modeled. Examples are: seismic inversion, ultrasone medical imaging, sonar detection of submarines, waves in harbours and many more. The partial differential equation looks simple but is hard to solve. In order to approximate the solution of the problem numerical methods are needed. First a discretization is done. Various methods can be used: (high order) Finite Difference Method, Finite Element Method, Discontinuous Galerkin Method and Boundary Element Method. The resulting linear system is large, where the size of the problem increases with increasing frequency. Due to higher frequencies the seismic images need to b...
Hayes, John R.
This book, designed for a college course on general problem-solving skills, focuses on skills that can be used by anyone in solving problems that occur in everyday life. Part I considers theory and practice: understanding problems, search, and protocol analysis. Part II discusses memory and knowledge acquisition: the structure of human memory,…
Creativity for Problem Solvers
DEFF Research Database (Denmark)
Vidal, Rene Victor Valqui
2009-01-01
This paper presents some modern and interdisciplinary concepts about creativity and creative processes specially related to problem solving. Central publications related to the theme are briefly reviewed. Creative tools and approaches suitable to support problem solving are also presented. Finally......, the paper outlines the author’s experiences using creative tools and approaches to: Facilitation of problem solving processes, strategy development in organisations, design of optimisation systems for large scale and complex logistic systems, and creative design of software optimisation for complex non...
Test set for initial value problem solvers
W.M. Lioen (Walter); J.J.B. de Swart (Jacques)
1998-01-01
textabstractThe CWI test set for IVP solvers presents a collection of Initial Value Problems to test solvers for implicit differential equations. This test set can both decrease the effort for the code developer to test his software in a reliable way, and cross the bridge between the application
Problem Solvers' Conceptions about Osmosis.
Zuckerman, June T.
1994-01-01
Discusses the scheme and findings of a study designed to identify the conceptual knowledge used by high school students to solve a significant problem related to osmosis. Useful tips are provided to teachers to aid students in developing constructs that maximize understanding. (ZWH)
From 'troublemakers' to problem solvers
DEFF Research Database (Denmark)
Frandsen, Martin Severin; Pfeiffer Petersen, Lene
2012-01-01
in a disadvantaged neighbourhood in the suburbs of Copenhagen, designed and constructed colourful and imaginative dustbins to handle problems with local littering. The project was successful in creating an increased local awareness of waste management and reducing the amount of litter. However, the more important...
Fostering Creative Problem Solvers in Higher Education
DEFF Research Database (Denmark)
Zhou, Chunfang
2016-01-01
to meet such challenges. This chapter aims to illustrate how to understand: 1) complexity as the nature of professional practice; 2) creative problem solving as the core skill in professional practice; 3) creativity as interplay between persons and their environment; 4) higher education as the context......Recent studies have emphasized issues of social emergence based on thinking of societies as complex systems. The complexity of professional practice has been recognized as the root of challenges for higher education. To foster creative problem solvers is a key response of higher education in order...... of fostering creative problem solvers; and 5) some innovative strategies such as Problem-Based Learning (PBL) and building a learning environment by Information Communication Technology (ICT) as potential strategies of creativity development. Accordingly, this chapter contributes to bridge the complexity...
Finegold, M.; Mass, R.
1985-01-01
Good problem solvers and poor problem solvers in advanced physics (N=8) were significantly different in their ability in translating, planning, and physical reasoning, as well as in problem solving time; no differences in reliance on algebraic solutions and checking problems were noted. Implications for physics teaching are discussed. (DH)
Aleph Field Solver Challenge Problem Results Summary
Energy Technology Data Exchange (ETDEWEB)
Hooper, Russell [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Moore, Stan Gerald [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2015-01-01
Aleph models continuum electrostatic and steady and transient thermal fields using a finite-element method. Much work has gone into expanding the core solver capability to support enriched modeling consisting of multiple interacting fields, special boundary conditions and two-way interfacial coupling with particles modeled using Aleph's complementary particle-in-cell capability. This report provides quantitative evidence for correct implementation of Aleph's field solver via order- of-convergence assessments on a collection of problems of increasing complexity. It is intended to provide Aleph with a pedigree and to establish a basis for confidence in results for more challenging problems important to Sandia's mission that Aleph was specifically designed to address.
Metaheuristics progress as real problem solvers
Nonobe, Koji; Yagiura, Mutsunori
2005-01-01
Metaheuristics: Progress as Real Problem Solvers is a peer-reviewed volume of eighteen current, cutting-edge papers by leading researchers in the field. Included are an invited paper by F. Glover and G. Kochenberger, which discusses the concept of Metaheuristic agent processes, and a tutorial paper by M.G.C. Resende and C.C. Ribeiro discussing GRASP with path-relinking. Other papers discuss problem-solving approaches to timetabling, automated planograms, elevators, space allocation, shift design, cutting stock, flexible shop scheduling, colorectal cancer and cartography. A final group of methodology papers clarify various aspects of Metaheuristics from the computational view point.
Experiences with linear solvers for oil reservoir simulation problems
Energy Technology Data Exchange (ETDEWEB)
Joubert, W.; Janardhan, R. [Los Alamos National Lab., NM (United States); Biswas, D.; Carey, G.
1996-12-31
This talk will focus on practical experiences with iterative linear solver algorithms used in conjunction with Amoco Production Company`s Falcon oil reservoir simulation code. The goal of this study is to determine the best linear solver algorithms for these types of problems. The results of numerical experiments will be presented.
Integrating Problem Solvers from Analogous Markets in New Product Ideation
DEFF Research Database (Denmark)
Franke, Nikolaus; Poetz, Marion; Schreier, Martin
2014-01-01
Who provides better inputs to new product ideation tasks, problem solvers with expertise in the area for which new products are to be developed or problem solvers from “analogous” markets that are distant but share an analogous problem or need? Conventional wisdom appears to suggest that target...... market expertise is indispensable, which is why most managers searching for new ideas tend to stay within their own market context even when they do search outside their firms' boundaries. However, in a unique symmetric experiment that isolates the effect of market origin, we find evidence...... for the opposite: Although solutions provided by problem solvers from analogous markets show lower potential for immediate use, they demonstrate substantially higher levels of novelty. Also, compared to established novelty drivers, this effect appears highly relevant from a managerial perspective: we find...
Preston, L. A.
2017-12-01
Marine hydrokinetic (MHK) devices offer a clean, renewable alternative energy source for the future. Responsible utilization of MHK devices, however, requires that the effects of acoustic noise produced by these devices on marine life and marine-related human activities be well understood. Paracousti is a 3-D full waveform acoustic modeling suite that can accurately propagate MHK noise signals in the complex bathymetry found in the near-shore to open ocean environment and considers real properties of the seabed, water column, and air-surface interface. However, this is a deterministic simulation that assumes the environment and source are exactly known. In reality, environmental and source characteristics are often only known in a statistical sense. Thus, to fully characterize the expected noise levels within the marine environment, this uncertainty in environmental and source factors should be incorporated into the acoustic simulations. One method is to use Monte Carlo (MC) techniques where simulation results from a large number of deterministic solutions are aggregated to provide statistical properties of the output signal. However, MC methods can be computationally prohibitive since they can require tens of thousands or more simulations to build up an accurate representation of those statistical properties. An alternative method, using the technique of stochastic partial differential equations (SPDE), allows computation of the statistical properties of output signals at a small fraction of the computational cost of MC. We are developing a SPDE solver for the 3-D acoustic wave propagation problem called Paracousti-UQ to help regulators and operators assess the statistical properties of environmental noise produced by MHK devices. In this presentation, we present the SPDE method and compare statistical distributions of simulated acoustic signals in simple models to MC simulations to show the accuracy and efficiency of the SPDE method. Sandia National Laboratories
From Answer-Getters to Problem Solvers
Flynn, Mike
2017-01-01
In some math classrooms, students are taught to follow and memorize procedures to arrive at the correct solution to problems. In this article, author Mike Flynn suggests a way to move beyond answer-getting to true problem solving. He describes an instructional approach called three-act tasks in which students solve an engaging math problem in…
How to become a good problem solver.
Gurden, Dean
2016-09-14
Nurses face many problems in the workplace on a daily basis, so the ability to solve or overcome them is essential to the job. If you are a nursing student and feel you lack problem-solving skills, what kind of help can you get?
Menu-Driven Solver Of Linear-Programming Problems
Viterna, L. A.; Ferencz, D.
1992-01-01
Program assists inexperienced user in formulating linear-programming problems. A Linear Program Solver (ALPS) computer program is full-featured LP analysis program. Solves plain linear-programming problems as well as more-complicated mixed-integer and pure-integer programs. Also contains efficient technique for solution of purely binary linear-programming problems. Written entirely in IBM's APL2/PC software, Version 1.01. Packed program contains licensed material, property of IBM (copyright 1988, all rights reserved).
SolveDB: Integrating Optimization Problem Solvers Into SQL Databases
DEFF Research Database (Denmark)
Siksnys, Laurynas; Pedersen, Torben Bach
2016-01-01
for optimization problems, (2) an extensible infrastructure for integrating different solvers, and (3) query optimization techniques to achieve the best execution performance and/or result quality. Extensive experiments with the PostgreSQL-based implementation show that SolveDB is a versatile tool offering much...
Scalable Adaptive Multilevel Solvers for Multiphysics Problems
Energy Technology Data Exchange (ETDEWEB)
Xu, Jinchao [Pennsylvania State Univ., University Park, PA (United States). Dept. of Mathematics
2014-11-26
In this project, we carried out many studies on adaptive and parallel multilevel methods for numerical modeling for various applications, including Magnetohydrodynamics (MHD) and complex fluids. We have made significant efforts and advances in adaptive multilevel methods of the multiphysics problems: multigrid methods, adaptive finite element methods, and applications.
Problem Solvers: Solutions--Playing Basketball
Smith, Jeffrey
2014-01-01
In this article, fourth grade Upper Allen Elementary School (Mechanicsburg, Pennsylvania) teacher Jeffrey Smith describes his exploration of the Playing Basketball activity. Herein he describes how he found the problem to be an effective way to review concepts associated with the measurement of elapsed time with his students. Additionally, it…
The Human Mind As General Problem Solver
Gurr, Henry
2011-10-01
Since leaving U Cal Irvine Neutrino Research, I have been a University Physics Teacher, and an Informal Researcher Of Human Functionality. My talk will share what I discovered about the best ways to learn, many of which are regularities that are to be expected from the Neuronal Network Properties announced in the publications of physicist John Joseph Hopfield. Hopfield's Model of mammalian brain-body, provides solid instructive understanding of how best Learn, Solve Problems, Live! With it we understand many otherwise puzzling features of our intellect! Examples Why 1) Analogies and metaphors powerful in class instruction, ditto poems. 2) Best learning done in physical (Hands-On) situations with tight immediate dynamical feedback such as seen in learning to ride bike, drive car, speak language, etc. 3) Some of the best learning happens in seeming random exploration, bump around, trial and error. 4) Scientific discoveries happen, with no apparent effort, at odd moments. 5) Important discoveries DEPEND on considerable frustrating effort, then Flash of Insight AHA EURIKA.
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.
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.
Mathematical Tasks without Words and Word Problems: Perceptions of Reluctant Problem Solvers
Holbert, Sydney Margaret
2013-01-01
This qualitative research study used a multiple, holistic case study approach (Yin, 2009) to explore the perceptions of reluctant problem solvers related to mathematical tasks without words and word problems. Participants were given a choice of working a mathematical task without words or a word problem during four problem-solving sessions. Data…
Cartesian Mesh Linearized Euler Equations Solver for Aeroacoustic Problems around Full Aircraft
Directory of Open Access Journals (Sweden)
Yuma Fukushima
2015-01-01
Full Text Available The linearized Euler equations (LEEs solver for aeroacoustic problems has been developed on block-structured Cartesian mesh to address complex geometry. Taking advantage of the benefits of Cartesian mesh, we employ high-order schemes for spatial derivatives and for time integration. On the other hand, the difficulty of accommodating curved wall boundaries is addressed by the immersed boundary method. The resulting LEEs solver is robust to complex geometry and numerically efficient in a parallel environment. The accuracy and effectiveness of the present solver are validated by one-dimensional and three-dimensional test cases. Acoustic scattering around a sphere and noise propagation from the JT15D nacelle are computed. The results show good agreement with analytical, computational, and experimental results. Finally, noise propagation around fuselage-wing-nacelle configurations is computed as a practical example. The results show that the sound pressure level below the over-the-wing nacelle (OWN configuration is much lower than that of the conventional DLR-F6 aircraft configuration due to the shielding effect of the OWN configuration.
Teaching problem solving: Don't forget the problem solver(s)
Ranade, Saidas M.; Corrales, Angela
2013-05-01
The importance of intrapersonal and interpersonal intelligences has long been known but educators have debated whether to and how to incorporate those topics in an already crowded engineering curriculum. In 2010, the authors used the classroom as a laboratory to observe the usefulness of including selected case studies and exercises from the fields of neurology, artificial intelligence, cognitive sciences and social psychology in a new problem-solving course. To further validate their initial findings, in 2012, the authors conducted an online survey of engineering students and engineers. The main conclusion is that engineering students will benefit from learning more about the impact of emotions, culture, diversity and cognitive biases when solving problems. Specifically, the work shows that an augmented problem-solving curriculum needs to include lessons on labelling emotions and cognitive biases, 'evidence-based' data on the importance of culture and diversity and additional practice on estimating conditional probability.
Scalable Newton-Krylov solver for very large power flow problems
Idema, R.; Lahaye, D.J.P.; Vuik, C.; Van der Sluis, L.
2010-01-01
The power flow problem is generally solved by the Newton-Raphson method with a sparse direct solver for the linear system of equations in each iteration. While this works fine for small power flow problems, we will show that for very large problems the direct solver is very slow and we present
Directory of Open Access Journals (Sweden)
Jürgen eSchmidhuber
2013-06-01
Full Text Available Most of computer science focuses on automatically solving given computational problems. I focus on automatically inventing or discovering problems in a way inspired by the playful behavior of animals and humans, to train a more and more general problem solver from scratch in an unsupervised fashion. Consider the infinite set of all computable descriptions of tasks with possibly computable solutions. The novel algorithmic framework POWERPLAY (2011 continually searches the space of possible pairs of new tasks and modifications of the current problem solver, until it finds a more powerful problem solver that provably solves all previously learned tasks plus the new one, while the unmodified predecessor does not. Wow-effects are achieved by continually making previously learned skills more efficient such that they require less time and space. New skills may (partially re-use previously learned skills. POWERPLAY's search orders candidate pairs of tasks and solver modifications by their conditional computational (time & space complexity, given the stored experience so far. The new task and its corresponding task-solving skill are those first found and validated. The computational costs of validating new tasks need not grow with task repertoire size. POWERPLAY's ongoing search for novelty keeps breaking the generalization abilities of its present solver. This is related to Goedel's sequence of increasingly powerful formal theories based on adding formerly unprovable statements to the axioms without affecting previously provable theorems. The continually increasing repertoire of problem solving procedures can be exploited by a parallel search for solutions to additional externally posed tasks. POWERPLAY may be viewed as a greedy but practical implementation of basic principles of creativity. A first experimental analysis can be found in separate papers [58, 56, 57].
Parallel time domain solvers for electrically large transient scattering problems
Liu, Yang
2014-09-26
Marching on in time (MOT)-based integral equation solvers represent an increasingly appealing avenue for analyzing transient electromagnetic interactions with large and complex structures. MOT integral equation solvers for analyzing electromagnetic scattering from perfect electrically conducting objects are obtained by enforcing electric field boundary conditions and implicitly time advance electric surface current densities by iteratively solving sparse systems of equations at all time steps. Contrary to finite difference and element competitors, these solvers apply to nonlinear and multi-scale structures comprising geometrically intricate and deep sub-wavelength features residing atop electrically large platforms. Moreover, they are high-order accurate, stable in the low- and high-frequency limits, and applicable to conducting and penetrable structures represented by highly irregular meshes. This presentation reviews some recent advances in the parallel implementations of time domain integral equation solvers, specifically those that leverage multilevel plane-wave time-domain algorithm (PWTD) on modern manycore computer architectures including graphics processing units (GPUs) and distributed memory supercomputers. The GPU-based implementation achieves at least one order of magnitude speedups compared to serial implementations while the distributed parallel implementation are highly scalable to thousands of compute-nodes. A distributed parallel PWTD kernel has been adopted to solve time domain surface/volume integral equations (TDSIE/TDVIE) for analyzing transient scattering from large and complex-shaped perfectly electrically conducting (PEC)/dielectric objects involving ten million/tens of millions of spatial unknowns.
VCODE, Ordinary Differential Equation Solver for Stiff and Non-Stiff Problems
International Nuclear Information System (INIS)
Cohen, Scott D.; Hindmarsh, Alan C.
2001-01-01
1 - Description of program or function: CVODE is a package written in ANSI standard C for solving initial value problems for ordinary differential equations. It solves both stiff and non stiff systems. In the stiff case, it includes a variety of options for treating the Jacobian of the system, including dense and band matrix solvers, and a preconditioned Krylov (iterative) solver. 2 - Method of solution: Integration is by Adams or BDF (Backward Differentiation Formula) methods, at user option. Corrector iteration is by functional iteration or Newton iteration. For the solution of linear systems within Newton iteration, users can select a dense solver, a band solver, a diagonal approximation, or a preconditioned Generalized Minimal Residual (GMRES) solver. In the dense and band cases, the user can supply a Jacobian approximation or let CVODE generate it internally. In the GMRES case, the pre-conditioner is user-supplied
Inverse problem of radiofrequency sounding of ionosphere
Velichko, E. N.; Yu. Grishentsev, A.; Korobeynikov, A. G.
2016-01-01
An algorithm for the solution of the inverse problem of vertical ionosphere sounding and a mathematical model of noise filtering are presented. An automated system for processing and analysis of spectrograms of vertical ionosphere sounding based on our algorithm is described. It is shown that the algorithm we suggest has a rather high efficiency. This is supported by the data obtained at the ionospheric stations of the so-called “AIS-M” type.
A fast direct solver for boundary value problems on locally perturbed geometries
Zhang, Yabin; Gillman, Adrianna
2018-03-01
Many applications including optimal design and adaptive discretization techniques involve solving several boundary value problems on geometries that are local perturbations of an original geometry. This manuscript presents a fast direct solver for boundary value problems that are recast as boundary integral equations. The idea is to write the discretized boundary integral equation on a new geometry as a low rank update to the discretized problem on the original geometry. Using the Sherman-Morrison formula, the inverse can be expressed in terms of the inverse of the original system applied to the low rank factors and the right hand side. Numerical results illustrate for problems where perturbation is localized the fast direct solver is three times faster than building a new solver from scratch.
Modified and fuzzified general problem solver for the 'monkey and banana' problem, 1
International Nuclear Information System (INIS)
Sano, Norihide; Takahashi, Ryoichi.
1991-01-01
The master-and-slave control system should be extensively implemented for the in-service inspection of operating nuclear power stations or the decommission of retired plants. The performance of this system depends on the intelligent slave. In this paper the degree of intelligence is approximated by the given amount of prior knowledge or suggestions. This paper aims at improving the general problem solver (GPS) by incorporating the learning process in order to solve the puzzle of the 'monkey and banana'. The monkey in this puzzle may be a reasonable alternative to represent the intelligent slave. Also, this paper deals with fuzzified problem solving since the master's command is not always crisp to the slave. (author)
Modified and fuzzified general problem solver for 'monkey and banana' problem
International Nuclear Information System (INIS)
Sano, Norihide; Takahashi, Ryoichi.
1994-01-01
Automatic operation is important for the in-service inspection of nuclear power stations of the decommission of retired plants. Master and slave control will be introduced for work-robot control. It is desirable that the slave possess problem-solving capabilities. In this paper we assume that the slave incorporates the general problem solver (GPS) algorithm. In view of having solved the 'monkey and banana' problem, the slave system is regarded as reasonable alternative which incorporates the capability of problem-solving. Basically, the GPS solves a problem by reducing the difference between the initial state and goal state, and hence the performance of GPS depends on selection of the difference to be reduced. The conventional GPS is given the order of importance of the differences in advance. In this study, the GPS was improved by making use of the rules which determine the order. When several choices are available for the given difference, a fuzzified decision to determine the necessary action is made, as demonstrated in this paper. (author)
Modified and fuzzified general problem solver for 'monkey and banana' problem, 2
International Nuclear Information System (INIS)
Sano, Norihide; Takahashi, Ryoichi.
1991-01-01
The automatic operation is important for the in-service inspection of the operating nuclear power station or the decommission of retired plants. The master and slave control will be introduced for work-robot control. It is desirable that the slave involves the capability of problem solving. This paper assumed that the slave involved the general problem solver algorithm. In view of having solved the puzzle of the 'monkey and banana', the slave system is regarded as the reasonable alternative which incorporates the capability of problem solving. Basically, the GPS solves a problem by reducing the difference between an initial state and a goal state, and hence the performance of GPS depends on selecting the difference to be reduced. The usual GPS is given in advance the ordering which indicates the importance of the differences. In this paper, the GPS was improved by making use of the rules which decide the order. When several choices are found on the given difference, the fuzzified decision to determine the action is demonstrated in this paper. (author)
A multilevel in space and energy solver for multigroup diffusion eigenvalue problems
Directory of Open Access Journals (Sweden)
Ben C. Yee
2017-09-01
Full Text Available In this paper, we present a new multilevel in space and energy diffusion (MSED method for solving multigroup diffusion eigenvalue problems. The MSED method can be described as a PI scheme with three additional features: (1 a grey (one-group diffusion equation used to efficiently converge the fission source and eigenvalue, (2 a space-dependent Wielandt shift technique used to reduce the number of PIs required, and (3 a multigrid-in-space linear solver for the linear solves required by each PI step. In MSED, the convergence of the solution of the multigroup diffusion eigenvalue problem is accelerated by performing work on lower-order equations with only one group and/or coarser spatial grids. Results from several Fourier analyses and a one-dimensional test code are provided to verify the efficiency of the MSED method and to justify the incorporation of the grey diffusion equation and the multigrid linear solver. These results highlight the potential efficiency of the MSED method as a solver for multidimensional multigroup diffusion eigenvalue problems, and they serve as a proof of principle for future work. Our ultimate goal is to implement the MSED method as an efficient solver for the two-dimensional/three-dimensional coarse mesh finite difference diffusion system in the Michigan parallel characteristics transport code. The work in this paper represents a necessary step towards that goal.
Fourier-Accelerated Nodal Solvers (FANS) for homogenization problems
Leuschner, Matthias; Fritzen, Felix
2017-11-01
Fourier-based homogenization schemes are useful to analyze heterogeneous microstructures represented by 2D or 3D image data. These iterative schemes involve discrete periodic convolutions with global ansatz functions (mostly fundamental solutions). The convolutions are efficiently computed using the fast Fourier transform. FANS operates on nodal variables on regular grids and converges to finite element solutions. Compared to established Fourier-based methods, the number of convolutions is reduced by FANS. Additionally, fast iterations are possible by assembling the stiffness matrix. Due to the related memory requirement, the method is best suited for medium-sized problems. A comparative study involving established Fourier-based homogenization schemes is conducted for a thermal benchmark problem with a closed-form solution. Detailed technical and algorithmic descriptions are given for all methods considered in the comparison. Furthermore, many numerical examples focusing on convergence properties for both thermal and mechanical problems, including also plasticity, are presented.
Implicit solvers for large-scale nonlinear problems
International Nuclear Information System (INIS)
Keyes, David E; Reynolds, Daniel R; Woodward, Carol S
2006-01-01
Computational scientists are grappling with increasingly complex, multi-rate applications that couple such physical phenomena as fluid dynamics, electromagnetics, radiation transport, chemical and nuclear reactions, and wave and material propagation in inhomogeneous media. Parallel computers with large storage capacities are paving the way for high-resolution simulations of coupled problems; however, hardware improvements alone will not prove enough to enable simulations based on brute-force algorithmic approaches. To accurately capture nonlinear couplings between dynamically relevant phenomena, often while stepping over rapid adjustments to quasi-equilibria, simulation scientists are increasingly turning to implicit formulations that require a discrete nonlinear system to be solved for each time step or steady state solution. Recent advances in iterative methods have made fully implicit formulations a viable option for solution of these large-scale problems. In this paper, we overview one of the most effective iterative methods, Newton-Krylov, for nonlinear systems and point to software packages with its implementation. We illustrate the method with an example from magnetically confined plasma fusion and briefly survey other areas in which implicit methods have bestowed important advantages, such as allowing high-order temporal integration and providing a pathway to sensitivity analyses and optimization. Lastly, we overview algorithm extensions under development motivated by current SciDAC applications
Schmidhuber, Jürgen
2013-01-01
Most of computer science focuses on automatically solving given computational problems. I focus on automatically inventing or discovering problems in a way inspired by the playful behavior of animals and humans, to train a more and more general problem solver from scratch in an unsupervised fashion. Consider the infinite set of all computable descriptions of tasks with possibly computable solutions. Given a general problem-solving architecture, at any given time, the novel algorithmic framework PowerPlay (Schmidhuber, 2011) searches the space of possible pairs of new tasks and modifications of the current problem solver, until it finds a more powerful problem solver that provably solves all previously learned tasks plus the new one, while the unmodified predecessor does not. Newly invented tasks may require to achieve a wow-effect by making previously learned skills more efficient such that they require less time and space. New skills may (partially) re-use previously learned skills. The greedy search of typical PowerPlay variants uses time-optimal program search to order candidate pairs of tasks and solver modifications by their conditional computational (time and space) complexity, given the stored experience so far. The new task and its corresponding task-solving skill are those first found and validated. This biases the search toward pairs that can be described compactly and validated quickly. The computational costs of validating new tasks need not grow with task repertoire size. Standard problem solver architectures of personal computers or neural networks tend to generalize by solving numerous tasks outside the self-invented training set; PowerPlay's ongoing search for novelty keeps breaking the generalization abilities of its present solver. This is related to Gödel's sequence of increasingly powerful formal theories based on adding formerly unprovable statements to the axioms without affecting previously provable theorems. The continually increasing
Applications of an implicit HLLC-based Godunov solver for steady state hypersonic problems
International Nuclear Information System (INIS)
Link, R.A.; Sharman, B.
2005-01-01
Over the past few years, there has been considerable activity developing research vehicles for studying hypersonic propulsion. Successful launches of the Australian Hyshot and the US Hyper-X vehicles have added a significant amount of flight test data to a field that had previously been limited to numerical simulation. A number of approaches have been proposed for hypersonics propulsion, including attached detonation wave, supersonics combustion, and shock induced combustion. Due to the high cost of developing flight hardware, CFD simulations will continue to be a key tool for investigating the feasibility of these concepts. Capturing the interactions of the vehicle body with the boundary layer and chemical reactions pushes the limits of available modelling tools and computer hardware. Explicit formulations are extremely slow in converging to a steady state; therefore, the use of implicit methods are warranted. An implicit LLC-based Godunov solver has been developed at Martec in collaboration with DRDC Valcartier to solve hypersonic problems with a minimum of CPU time and RAM storage. The solver, Chinook Implicit, is based upon the implicit formulation adopted by Batten et. al. The solver is based on a point implicit Gauss-Seidel method for unstructured grids, and includes fully implicit boundary conditions. Preliminary results for small and large scale inviscid hypersonics problems will be presented. (author)
Liu, Yang
2013-07-01
The computational complexity and memory requirements of multilevel plane wave time domain (PWTD)-accelerated marching-on-in-time (MOT)-based surface integral equation (SIE) solvers scale as O(NtNs(log 2)Ns) and O(Ns 1.5); here N t and Ns denote numbers of temporal and spatial basis functions discretizing the current [Shanker et al., IEEE Trans. Antennas Propag., 51, 628-641, 2003]. In the past, serial versions of these solvers have been successfully applied to the analysis of scattering from perfect electrically conducting as well as homogeneous penetrable targets involving up to Ns ≈ 0.5 × 106 and Nt ≈ 10 3. To solve larger problems, parallel PWTD-enhanced MOT solvers are called for. Even though a simple parallelization strategy was demonstrated in the context of electromagnetic compatibility analysis [M. Lu et al., in Proc. IEEE Int. Symp. AP-S, 4, 4212-4215, 2004], by and large, progress in this area has been slow. The lack of progress can be attributed wholesale to difficulties associated with the construction of a scalable PWTD kernel. © 2013 IEEE.
The Problem Solver and The Artisan Designer: Strategies for Utilizing Design Idea Archives
DEFF Research Database (Denmark)
Inie, Nanna; Endo, Allison; Dow, Steven
2018-01-01
This paper presents the results of an extensive qualitative study investigating how professional designers utilize personal idea archives. While we know that designers archive creative ideas in different formats and on different platforms, we know little about if and how designers utilize...... these idea archives in their daily practice. Through a series of interviews (n=20) and walkthroughs of design idea archives, we identified two archetypal strategies. The Problem Solver is concerned with the task at hand, keeps relevant ideas around, and discards them when the ideas have served their purpose...
DEFF Research Database (Denmark)
Andersen, Michael; Abel, Sarah Maria Niebe; Erleben, Kenny
2017-01-01
We address the task of computing solutions for a separating fluid-solid wall boundary condition model. We present an embarrassingly parallel, easy to implement, fluid LCP solver.We are able to use greater domain sizes than previous works have shown, due to our new solver. The solver exploits matr...
Composing problem solvers for simulation experimentation: a case study on steady state estimation.
Leye, Stefan; Ewald, Roland; Uhrmacher, Adelinde M
2014-01-01
Simulation experiments involve various sub-tasks, e.g., parameter optimization, simulation execution, or output data analysis. Many algorithms can be applied to such tasks, but their performance depends on the given problem. Steady state estimation in systems biology is a typical example for this: several estimators have been proposed, each with its own (dis-)advantages. Experimenters, therefore, must choose from the available options, even though they may not be aware of the consequences. To support those users, we propose a general scheme to aggregate such algorithms to so-called synthetic problem solvers, which exploit algorithm differences to improve overall performance. Our approach subsumes various aggregation mechanisms, supports automatic configuration from training data (e.g., via ensemble learning or portfolio selection), and extends the plugin system of the open source modeling and simulation framework James II. We show the benefits of our approach by applying it to steady state estimation for cell-biological models.
GASPACHO: a generic automatic solver using proximal algorithms for convex huge optimization problems
Goossens, Bart; Luong, Hiêp; Philips, Wilfried
2017-08-01
Many inverse problems (e.g., demosaicking, deblurring, denoising, image fusion, HDR synthesis) share various similarities: degradation operators are often modeled by a specific data fitting function while image prior knowledge (e.g., sparsity) is incorporated by additional regularization terms. In this paper, we investigate automatic algorithmic techniques for evaluating proximal operators. These algorithmic techniques also enable efficient calculation of adjoints from linear operators in a general matrix-free setting. In particular, we study the simultaneous-direction method of multipliers (SDMM) and the parallel proximal algorithm (PPXA) solvers and show that the automatically derived implementations are well suited for both single-GPU and multi-GPU processing. We demonstrate this approach for an Electron Microscopy (EM) deconvolution problem.
Telescopic Hybrid Fast Solver for 3D Elliptic Problems with Point Singularities
Paszyńska, Anna; Jopek, Konrad; Banaś, Krzysztof; Paszyński, Maciej; Gurgul, Piotr; Lenerth, Andrew; Nguyen, Donald; Pingali, Keshav; Dalcind, Lisandro; Calo, Victor M.
2015-01-01
This paper describes a telescopic solver for two dimensional h adaptive grids with point singularities. The input for the telescopic solver is an h refined two dimensional computational mesh with rectangular finite elements. The candidates for point singularities are first localized over the mesh by using a greedy algorithm. Having the candidates for point singularities, we execute either a direct solver, that performs multiple refinements towards selected point singularities and executes a parallel direct solver algorithm which has logarithmic cost with respect to refinement level. The direct solvers executed over each candidate for point singularity return local Schur complement matrices that can be merged together and submitted to iterative solver. In this paper we utilize a parallel multi-thread GALOIS solver as a direct solver. We use Incomplete LU Preconditioned Conjugated Gradients (ILUPCG) as an iterative solver. We also show that elimination of point singularities from the refined mesh reduces significantly the number of iterations to be performed by the ILUPCG iterative solver.
Telescopic Hybrid Fast Solver for 3D Elliptic Problems with Point Singularities
Paszyńska, Anna
2015-06-01
This paper describes a telescopic solver for two dimensional h adaptive grids with point singularities. The input for the telescopic solver is an h refined two dimensional computational mesh with rectangular finite elements. The candidates for point singularities are first localized over the mesh by using a greedy algorithm. Having the candidates for point singularities, we execute either a direct solver, that performs multiple refinements towards selected point singularities and executes a parallel direct solver algorithm which has logarithmic cost with respect to refinement level. The direct solvers executed over each candidate for point singularity return local Schur complement matrices that can be merged together and submitted to iterative solver. In this paper we utilize a parallel multi-thread GALOIS solver as a direct solver. We use Incomplete LU Preconditioned Conjugated Gradients (ILUPCG) as an iterative solver. We also show that elimination of point singularities from the refined mesh reduces significantly the number of iterations to be performed by the ILUPCG iterative solver.
Collier, Nathan; Dalcin, Lisandro; Calo, Victor M.
2014-01-01
SUMMARY: We compare the computational efficiency of isogeometric Galerkin and collocation methods for partial differential equations in the asymptotic regime. We define a metric to identify when numerical experiments have reached this regime. We then apply these ideas to analyze the performance of different isogeometric discretizations, which encompass C0 finite element spaces and higher-continuous spaces. We derive convergence and cost estimates in terms of the total number of degrees of freedom and then perform an asymptotic numerical comparison of the efficiency of these methods applied to an elliptic problem. These estimates are derived assuming that the underlying solution is smooth, the full Gauss quadrature is used in each non-zero knot span and the numerical solution of the discrete system is found using a direct multi-frontal solver. We conclude that under the assumptions detailed in this paper, higher-continuous basis functions provide marginal benefits.
High-resolution coupled physics solvers for analysing fine-scale nuclear reactor design problems
Mahadevan, Vijay S.; Merzari, Elia; Tautges, Timothy; Jain, Rajeev; Obabko, Aleksandr; Smith, Michael; Fischer, Paul
2014-01-01
An integrated multi-physics simulation capability for the design and analysis of current and future nuclear reactor models is being investigated, to tightly couple neutron transport and thermal-hydraulics physics under the SHARP framework. Over several years, high-fidelity, validated mono-physics solvers with proven scalability on petascale architectures have been developed independently. Based on a unified component-based architecture, these existing codes can be coupled with a mesh-data backplane and a flexible coupling-strategy-based driver suite to produce a viable tool for analysts. The goal of the SHARP framework is to perform fully resolved coupled physics analysis of a reactor on heterogeneous geometry, in order to reduce the overall numerical uncertainty while leveraging available computational resources. The coupling methodology and software interfaces of the framework are presented, along with verification studies on two representative fast sodium-cooled reactor demonstration problems to prove the usability of the SHARP framework. PMID:24982250
Collier, Nathan
2014-09-17
SUMMARY: We compare the computational efficiency of isogeometric Galerkin and collocation methods for partial differential equations in the asymptotic regime. We define a metric to identify when numerical experiments have reached this regime. We then apply these ideas to analyze the performance of different isogeometric discretizations, which encompass C0 finite element spaces and higher-continuous spaces. We derive convergence and cost estimates in terms of the total number of degrees of freedom and then perform an asymptotic numerical comparison of the efficiency of these methods applied to an elliptic problem. These estimates are derived assuming that the underlying solution is smooth, the full Gauss quadrature is used in each non-zero knot span and the numerical solution of the discrete system is found using a direct multi-frontal solver. We conclude that under the assumptions detailed in this paper, higher-continuous basis functions provide marginal benefits.
Actual problems of geo-environment and sounding systems
Burakhovich, T. K.; Kobolev, V. P.
2017-01-01
The results of the conference "Actual problems of geo-environment and sounding systems", dedicated to the memory of outstanding scientists - Vladimir Nikolaevich Shuman and Sergei Nikolaevich Kulik, who made a great contribution to the theory, methodology and geological interpretation of deep electromagnetic electromagnetic sounding of the Earth.
Seeley, Cathy L.
2016-01-01
In "Making Sense of Math," Cathy L. Seeley, former president of the National Council of Teachers of Mathematics, shares her insight into how to turn your students into flexible mathematical thinkers and problem solvers. This practical volume concentrates on the following areas: (1) Making sense of math by fostering habits of mind that…
Larger groups of passerines are more efficient problem solvers in the wild
Morand-Ferron, Julie; Quinn, John L.
2011-01-01
Group living commonly helps organisms face challenging environmental conditions. Although a known phenomenon in humans, recent findings suggest that a benefit of group living in animals generally might be increased innovative problem-solving efficiency. This benefit has never been demonstrated in a natural context, however, and the mechanisms underlying improved efficiency are largely unknown. We examined the problem-solving performance of great and blue tits at automated devices and found that efficiency increased with flock size. This relationship held when restricting the analysis to naive individuals, demonstrating that larger groups increased innovation efficiency. In addition to this effect of naive flock size, the presence of at least one experienced bird increased the frequency of solving, and larger flocks were more likely to contain experienced birds. These findings provide empirical evidence for the “pool of competence” hypothesis in nonhuman animals. The probability of success also differed consistently between individuals, a necessary condition for the pool of competence hypothesis. Solvers had a higher probability of success when foraging with a larger number of companions and when using devices located near rather than further from protective tree cover, suggesting a role for reduced predation risk on problem-solving efficiency. In contrast to traditional group living theory, individuals joining larger flocks benefited from a higher seed intake, suggesting that group living facilitated exploitation of a novel food source through improved problem-solving efficiency. Together our results suggest that both ecological and social factors, through reduced predation risk and increased pool of competence, mediate innovation in natural populations. PMID:21930936
Balsara, Dinshaw S.; Nkonga, Boniface
2017-10-01
Just as the quality of a one-dimensional approximate Riemann solver is improved by the inclusion of internal sub-structure, the quality of a multidimensional Riemann solver is also similarly improved. Such multidimensional Riemann problems arise when multiple states come together at the vertex of a mesh. The interaction of the resulting one-dimensional Riemann problems gives rise to a strongly-interacting state. We wish to endow this strongly-interacting state with physically-motivated sub-structure. The fastest way of endowing such sub-structure consists of making a multidimensional extension of the HLLI Riemann solver for hyperbolic conservation laws. Presenting such a multidimensional analogue of the HLLI Riemann solver with linear sub-structure for use on structured meshes is the goal of this work. The multidimensional MuSIC Riemann solver documented here is universal in the sense that it can be applied to any hyperbolic conservation law. The multidimensional Riemann solver is made to be consistent with constraints that emerge naturally from the Galerkin projection of the self-similar states within the wave model. When the full eigenstructure in both directions is used in the present Riemann solver, it becomes a complete Riemann solver in a multidimensional sense. I.e., all the intermediate waves are represented in the multidimensional wave model. The work also presents, for the very first time, an important analysis of the dissipation characteristics of multidimensional Riemann solvers. The present Riemann solver results in the most efficient implementation of a multidimensional Riemann solver with sub-structure. Because it preserves stationary linearly degenerate waves, it might also help with well-balancing. Implementation-related details are presented in pointwise fashion for the one-dimensional HLLI Riemann solver as well as the multidimensional MuSIC Riemann solver.
North Dakota's Centennial Quilt and Problem Solvers: Solutions: The Library Problem
Small, Marian
2010-01-01
Quilt investigations, such as the Barn quilt problem in the December 2008/January 2009 issue of "Teaching Children Mathematics" and its solutions in last month's issue, can spark interdisciplinary pursuits for teachers and exciting connections for the full range of elementary school students. This month, North Dakota's centennial quilt…
Liu, Yang; Bagci, Hakan; Michielssen, Eric
2013-01-01
numbers of temporal and spatial basis functions discretizing the current [Shanker et al., IEEE Trans. Antennas Propag., 51, 628-641, 2003]. In the past, serial versions of these solvers have been successfully applied to the analysis of scattering from
DEFF Research Database (Denmark)
Helsgaun, Keld
This report describes the implementation of an extension of the Lin-Kernighan-Helsgaun TSP solver for solving constrained traveling salesman and vehicle routing problems. The extension, which is called LKH-3, is able to solve a variety of well-known problems, including the sequential ordering...... problem (SOP), the traveling repairman problem (TRP), variants of the multiple travel-ing salesman problem (mTSP), as well as vehicle routing problems (VRPs) with capacity, time windows, pickup-and-delivery and distance constraints. The implementation of LKH-3 builds on the idea of transforming...... the problems into standard symmetric traveling salesman problems and handling constraints by means of penalty functions. Extensive testing on benchmark instances from the literature has shown that LKH-3 is effective. Best known solutions are often obtained, and in some cases, new best solutions are found...
Sound field reproduction as an equivalent acoustical scattering problem.
Fazi, Filippo Maria; Nelson, Philip A
2013-11-01
Given a continuous distribution of acoustic sources, the determination of the source strength that ensures the synthesis of a desired sound field is shown to be identical to the solution of an equivalent acoustic scattering problem. The paper begins with the presentation of the general theory that underpins sound field reproduction with secondary sources continuously arranged on the boundary of the reproduction region. The process of reproduction by a continuous source distribution is modeled by means of an integral operator (the single layer potential). It is then shown how the solution of the sound reproduction problem corresponds to that of an equivalent scattering problem. Analytical solutions are computed for two specific instances of this problem, involving, respectively, the use of a secondary source distribution in spherical and planar geometries. The results are shown to be the same as those obtained with analyses based on High Order Ambisonics and Wave Field Synthesis, respectively, thus bringing to light a fundamental analogy between these two methods of sound reproduction. Finally, it is shown how the physical optics (Kirchhoff) approximation enables the derivation of a high-frequency simplification for the problem under consideration, this in turn being related to the secondary source selection criterion reported in the literature on Wave Field Synthesis.
Experimental validation of a boundary element solver for exterior acoustic radiation problems
Visser, Rene; Nilsson, A.; Boden, H.
2003-01-01
The relation between harmonic structural vibrations and the corresponding acoustic radiation is given by the Helmholtz integral equation (HIE). To solve this integral equation a new solver (BEMSYS) based on the boundary element method (BEM) has been implemented. This numerical tool can be used for
Reimer, Ashton S.; Cheviakov, Alexei F.
2013-03-01
A Matlab-based finite-difference numerical solver for the Poisson equation for a rectangle and a disk in two dimensions, and a spherical domain in three dimensions, is presented. The solver is optimized for handling an arbitrary combination of Dirichlet and Neumann boundary conditions, and allows for full user control of mesh refinement. The solver routines utilize effective and parallelized sparse vector and matrix operations. Computations exhibit high speeds, numerical stability with respect to mesh size and mesh refinement, and acceptable error values even on desktop computers. Catalogue identifier: AENQ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENQ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License v3.0 No. of lines in distributed program, including test data, etc.: 102793 No. of bytes in distributed program, including test data, etc.: 369378 Distribution format: tar.gz Programming language: Matlab 2010a. Computer: PC, Macintosh. Operating system: Windows, OSX, Linux. RAM: 8 GB (8, 589, 934, 592 bytes) Classification: 4.3. Nature of problem: To solve the Poisson problem in a standard domain with “patchy surface”-type (strongly heterogeneous) Neumann/Dirichlet boundary conditions. Solution method: Finite difference with mesh refinement. Restrictions: Spherical domain in 3D; rectangular domain or a disk in 2D. Unusual features: Choice between mldivide/iterative solver for the solution of large system of linear algebraic equations that arise. Full user control of Neumann/Dirichlet boundary conditions and mesh refinement. Running time: Depending on the number of points taken and the geometry of the domain, the routine may take from less than a second to several hours to execute.
The block Gauss-Seidel method in sound transmission problems
Poblet-Puig, Jordi; Rodríguez Ferran, Antonio
2009-01-01
Sound transmission through partitions can be modelled as an acoustic fluid-elastic structure interaction problem. The block Gauss-Seidel iterative method is used in order to solve the finite element linear system of equations. The blocks are defined in a natural way, respecting the fluid and structural domains. The convergence criterion (spectral radius of iteration matrix smaller than one) is analysed and interpreted in physical terms by means of simple one-dimensional problems. This anal...
Energy Technology Data Exchange (ETDEWEB)
Bruno, Oscar P., E-mail: obruno@caltech.edu; Lintner, Stéphane K.
2013-11-01
We present a novel methodology for the numerical solution of problems of diffraction by infinitely thin screens in three-dimensional space. Our approach relies on new integral formulations as well as associated high-order quadrature rules. The new integral formulations involve weighted versions of the classical integral operators related to the thin-screen Dirichlet and Neumann problems as well as a generalization to the open-surface problem of the classical Calderón formulae. The high-order quadrature rules we introduce for these operators, in turn, resolve the multiple Green function and edge singularities (which occur at arbitrarily close distances from each other, and which include weakly singular as well as hypersingular kernels) and thus give rise to super-algebraically fast convergence as the discretization sizes are increased. When used in conjunction with Krylov-subspace linear algebra solvers such as GMRES, the resulting solvers produce results of high accuracy in small numbers of iterations for low and high frequencies alike. We demonstrate our methodology with a variety of numerical results for screen and aperture problems at high frequencies—including simulation of classical experiments such as the diffraction by a circular disc (featuring in particular the famous Poisson spot), evaluation of interference fringes resulting from diffraction across two nearby circular apertures, as well as solution of problems of scattering by more complex geometries consisting of multiple scatterers and cavities.
Directory of Open Access Journals (Sweden)
Jianfei Zhang
2013-01-01
Full Text Available Graphics processing unit (GPU has obtained great success in scientific computations for its tremendous computational horsepower and very high memory bandwidth. This paper discusses the efficient way to implement polynomial preconditioned conjugate gradient solver for the finite element computation of elasticity on NVIDIA GPUs using compute unified device architecture (CUDA. Sliced block ELLPACK (SBELL format is introduced to store sparse matrix arising from finite element discretization of elasticity with fewer padding zeros than traditional ELLPACK-based formats. Polynomial preconditioning methods have been investigated both in convergence and running time. From the overall performance, the least-squares (L-S polynomial method is chosen as a preconditioner in PCG solver to finite element equations derived from elasticity for its best results on different example meshes. In the PCG solver, mixed precision algorithm is used not only to reduce the overall computational, storage requirements and bandwidth but to make full use of the capacity of the GPU devices. With SBELL format and mixed precision algorithm, the GPU-based L-S preconditioned CG can get a speedup of about 7–9 to CPU-implementation.
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
An evaluation of parallel multigrid as a solver and a preconditioner for singular perturbed problems
Energy Technology Data Exchange (ETDEWEB)
Oosterlee, C.W. [Inst. for Algorithms and Scientific Computing, Sankt Augustin (Germany); Washio, T. [C& C Research Lab., Sankt Augustin (Germany)
1996-12-31
In this paper we try to achieve h-independent convergence with preconditioned GMRES and BiCGSTAB for 2D singular perturbed equations. Three recently developed multigrid methods are adopted as a preconditioner. They are also used as solution methods in order to compare the performance of the methods as solvers and as preconditioners. Two of the multigrid methods differ only in the transfer operators. One uses standard matrix- dependent prolongation operators from. The second uses {open_quotes}upwind{close_quotes} prolongation operators, developed. Both employ the Galerkin coarse grid approximation and an alternating zebra line Gauss-Seidel smoother. The third method is based on the block LU decomposition of a matrix and on an approximate Schur complement. This multigrid variant is presented in. All three multigrid algorithms are algebraic methods.
International Nuclear Information System (INIS)
Bakhos, Tania; Saibaba, Arvind K.; Kitanidis, Peter K.
2015-01-01
We consider the problem of estimating parameters in large-scale weakly nonlinear inverse problems for which the underlying governing equations is a linear, time-dependent, parabolic partial differential equation. A major challenge in solving these inverse problems using Newton-type methods is the computational cost associated with solving the forward problem and with repeated construction of the Jacobian, which represents the sensitivity of the measurements to the unknown parameters. Forming the Jacobian can be prohibitively expensive because it requires repeated solutions of the forward and adjoint time-dependent parabolic partial differential equations corresponding to multiple sources and receivers. We propose an efficient method based on a Laplace transform-based exponential time integrator combined with a flexible Krylov subspace approach to solve the resulting shifted systems of equations efficiently. Our proposed solver speeds up the computation of the forward and adjoint problems, thus yielding significant speedup in total inversion time. We consider an application from Transient Hydraulic Tomography (THT), which is an imaging technique to estimate hydraulic parameters related to the subsurface from pressure measurements obtained by a series of pumping tests. The algorithms discussed are applied to a synthetic example taken from THT to demonstrate the resulting computational gains of this proposed method
Energy Technology Data Exchange (ETDEWEB)
Bakhos, Tania, E-mail: taniab@stanford.edu [Institute for Computational and Mathematical Engineering, Stanford University (United States); Saibaba, Arvind K. [Department of Electrical and Computer Engineering, Tufts University (United States); Kitanidis, Peter K. [Institute for Computational and Mathematical Engineering, Stanford University (United States); Department of Civil and Environmental Engineering, Stanford University (United States)
2015-10-15
We consider the problem of estimating parameters in large-scale weakly nonlinear inverse problems for which the underlying governing equations is a linear, time-dependent, parabolic partial differential equation. A major challenge in solving these inverse problems using Newton-type methods is the computational cost associated with solving the forward problem and with repeated construction of the Jacobian, which represents the sensitivity of the measurements to the unknown parameters. Forming the Jacobian can be prohibitively expensive because it requires repeated solutions of the forward and adjoint time-dependent parabolic partial differential equations corresponding to multiple sources and receivers. We propose an efficient method based on a Laplace transform-based exponential time integrator combined with a flexible Krylov subspace approach to solve the resulting shifted systems of equations efficiently. Our proposed solver speeds up the computation of the forward and adjoint problems, thus yielding significant speedup in total inversion time. We consider an application from Transient Hydraulic Tomography (THT), which is an imaging technique to estimate hydraulic parameters related to the subsurface from pressure measurements obtained by a series of pumping tests. The algorithms discussed are applied to a synthetic example taken from THT to demonstrate the resulting computational gains of this proposed method.
Measuring the Level of Transfer Learning by an AP Physics Problem-Solver
National Research Council Canada - National Science Library
Klenk, Matthew; Forbus, Ken
2007-01-01
.... We approach this problem by focusing on model formulation, i.e., how to move from the unruly, broad set of concepts used in everyday life to a concise, formal vocabulary of abstractions that can be used effectively for problem solving...
Constraint-based solver for the Military unit path finding problem
CSIR Research Space (South Africa)
Leenen, L
2010-04-01
Full Text Available -based approach because it requires flexibility in modelling. The authors formulate the MUPFP as a constraint satisfaction problem and a constraint-based extension of the search algorithm. The concept demonstrator uses a provided map, for example taken from Google...
Community matrons as problem-solvers for people living with multi-co-morbid disease.
Randall, Sue; Thunhurst, Colin; Furze, Gill
2016-12-02
Working with patients in their own homes gives community matrons an advantage of seeing patients in the context of their everyday lives. This allows comprehensive assessment of need with an aim of promoting health or promoting stability for people living with chronic disease. Complex issues are resolved through problem-solving and this can result in patients being maintained in their own homes and thus in reduced unplanned hospitalisation. Data were collected from participants using semi-structured interviews and audio diaries. The sample comprised professionals: CMs (n=21), managers (n=4), former commissioners (n=2) and GPs (n=3); and patients (n=10) and their family carers (n=5). In this article, data from community matrons is discussed. Community matrons often drew on the social determinants model of health to problem solve and to create meaningful strategies that work for patients in their care. Raising awareness of the high-level skills of community matrons and promoting appreciation of the importance of a social determinants model of health is important in explaining why nurses are such a crucial element of the primary health care workforce.
Hamilton, Mark F.
1989-08-01
Four projects are discussed in this annual summary report, all of which involve basic research in nonlinear acoustics: Scattering of Sound by Sound, a theoretical study of two nonconlinear Gaussian beams which interact to produce sum and difference frequency sound; Parametric Receiving Arrays, a theoretical study of parametric reception in a reverberant environment; Nonlinear Effects in Asymmetric Sound Beams, a numerical study of two dimensional finite amplitude sound fields; and Pulsed Finite Amplitude Sound Beams, a numerical time domain solution of the KZK equation.
Robertson, William C
2003-01-01
Muddled about what makes music? Stuck on the study of harmonics? Dumbfounded by how sound gets around? Now you no longer have to struggle to teach concepts you really don t grasp yourself. Sound takes an intentionally light touch to help out all those adults science teachers, parents wanting to help with homework, home-schoolers seeking necessary scientific background to teach middle school physics with confidence. The book introduces sound waves and uses that model to explain sound-related occurrences. Starting with the basics of what causes sound and how it travels, you'll learn how musical instruments work, how sound waves add and subtract, how the human ear works, and even why you can sound like a Munchkin when you inhale helium. Sound is the fourth book in the award-winning Stop Faking It! Series, published by NSTA Press. Like the other popular volumes, it is written by irreverent educator Bill Robertson, who offers this Sound recommendation: One of the coolest activities is whacking a spinning metal rod...
Analytical Lie-algebraic solution of a 3D sound propagation problem in the ocean
Energy Technology Data Exchange (ETDEWEB)
Petrov, P.S., E-mail: petrov@poi.dvo.ru [Il' ichev Pacific Oceanological Institute, 43 Baltiyskaya str., Vladivostok, 690041 (Russian Federation); Prants, S.V., E-mail: prants@poi.dvo.ru [Il' ichev Pacific Oceanological Institute, 43 Baltiyskaya str., Vladivostok, 690041 (Russian Federation); Petrova, T.N., E-mail: petrova.tn@dvfu.ru [Far Eastern Federal University, 8 Sukhanova str., 690950, Vladivostok (Russian Federation)
2017-06-21
The problem of sound propagation in a shallow sea with variable bottom slope is considered. The sound pressure field produced by a time-harmonic point source in such inhomogeneous 3D waveguide is expressed in the form of a modal expansion. The expansion coefficients are computed using the adiabatic mode parabolic equation theory. The mode parabolic equations are solved explicitly, and the analytical expressions for the modal coefficients are obtained using a Lie-algebraic technique. - Highlights: • A group-theoretical approach is applied to a problem of sound propagation in a shallow sea with variable bottom slope. • An analytical solution of this problem is obtained in the form of modal expansion with analytical expressions of the coefficients. • Our result is the only analytical solution of the 3D sound propagation problem with no translational invariance. • This solution can be used for the validation of the numerical propagation models.
Kettering, Tracy L; Fisher, Wayne W; Kelley, Michael E; LaRue, Robert H
2018-06-06
We examined the extent to which different sounds functioned as motivating operations (MO) that evoked problem behavior during a functional analysis for two participants. Results suggested that escape from loud noises reinforced the problem behavior for one participant and escape from arguing reinforced problem behavior for the other participant. Noncontingent delivery of preferred music through sound-attenuating headphones decreased problem behavior without the use of extinction for both participants. We discuss the results in terms of the abolishing effects of the intervention. © 2018 Society for the Experimental Analysis of Behavior.
High performance simplex solver
Huangfu, Qi
2013-01-01
The dual simplex method is frequently the most efficient technique for solving linear programming (LP) problems. This thesis describes an efficient implementation of the sequential dual simplex method and the design and development of two parallel dual simplex solvers. In serial, many advanced techniques for the (dual) simplex method are implemented, including sparse LU factorization, hyper-sparse linear system solution technique, efficient approaches to updating LU factors and...
Overcoming The Problem Of English Sound System Among ...
African Journals Online (AJOL)
This paper tries to examine important issues in teaching phonetics. These are the interference problem that can affect one's speech during communication and how the teacher through the use of appropriate techniques and methods can assist the second language learner overcome these problems. Journal of Technology ...
Self-correcting Multigrid Solver
International Nuclear Information System (INIS)
Lewandowski, Jerome L.V.
2004-01-01
A new multigrid algorithm based on the method of self-correction for the solution of elliptic problems is described. The method exploits information contained in the residual to dynamically modify the source term (right-hand side) of the elliptic problem. It is shown that the self-correcting solver is more efficient at damping the short wavelength modes of the algebraic error than its standard equivalent. When used in conjunction with a multigrid method, the resulting solver displays an improved convergence rate with no additional computational work
Global existence and decay of solutions of the Cauchy problem in thermoelasticity with second sound
Kasimov, Aslan R.
2013-06-04
We consider the one-dimensional Cauchy problem in non-linear thermoelasticity with second sound, where the heat conduction is modelled by Cattaneo\\'s law. After presenting decay estimates for solutions to the linearized problem, including refined estimates for data in weighted Lebesgue-spaces, we prove a global existence theorem for small data together with improved decay estimates, in particular for derivatives of the solutions. © 2013 Taylor & Francis.
Global existence and decay of solutions of the Cauchy problem in thermoelasticity with second sound
Kasimov, Aslan R.; Racke, Reinhard; Said-Houari, Belkacem
2013-01-01
We consider the one-dimensional Cauchy problem in non-linear thermoelasticity with second sound, where the heat conduction is modelled by Cattaneo's law. After presenting decay estimates for solutions to the linearized problem, including refined estimates for data in weighted Lebesgue-spaces, we prove a global existence theorem for small data together with improved decay estimates, in particular for derivatives of the solutions. © 2013 Taylor & Francis.
Cantor, Alida; DeLauer, Verna; Martin, Deborah; Rogan, John
2015-01-01
Management of "wicked problems", messy real-world problems that defy resolution, requires thinkers who can transcend disciplinary boundaries, work collaboratively, and handle complexity and obstacles. This paper explores how educators can train undergraduates in these skills through applied community-based research, using the example of…
Foley, Greg
2014-01-01
A problem that illustrates two ways of computing the break-even radius of insulation is outlined. The problem is suitable for students who are taking an introductory module in heat transfer or transport phenomena and who have some previous knowledge of the numerical solution of non- linear algebraic equations. The potential for computer algebra,…
Directory of Open Access Journals (Sweden)
Taufik Nur Hidayat
2017-10-01
Full Text Available The study is to classify the problem triggers in consecutive interpreting especially in listening. The objectives of the research are to find out the relationship between listening skills and sound problem by comparing the test results of English student and non-English student and prove that students’ problem triggers are closely related to the writing and reading performances which are caused by listening skill problems such as domain in comprehension, similar word, etc. The method used in the research is descriptive qualitative. The participants are English Department and non English student. Technique of collecting data in the research uses questionnaire, test, and interview. The biggest problem faced by non-English student group is numbering and proper names. It is 34 % which occupy in first rank. Whereas the percentage of English student in comprehension is 27%, then the numbering and proper names, the last is similar word which has 20%. Meanwhile, the test result of English group is 84.5 and non-English group is 60. It represent the background knowledge factors are also play an important role in doing the test. In conclusion, there is relationship between students’ problem triggers, writing and reading performances, especially homophone errors. So, the hypothesis is accepted and it strengthens a currently underdeveloped theory that sounds problem play an important role in listening.
A Test Set for stiff Initial Value Problem Solvers in the open source software R: Package deTestSet
Mazzia, F.; Cash, J.R.; Soetaert, K.
2012-01-01
In this paper we present the R package deTestSet that includes challenging test problems written as ordinary differential equations (ODEs), differential algebraic equations (DAEs) of index up to 3 and implicit differential equations (IDES). In addition it includes 6 new codes to solve initial value
Thevenot, Catherine; Castel, Caroline; Fanget, Muriel; Fayol, Michel
2010-01-01
The authors used the operand-recognition paradigm (C. Thevenot, M. Fanget, & M. Fayol, 2007) in order to study the strategies used by adults to solve subtraction problems. This paradigm capitalizes on the fact that algorithmic procedures degrade the memory traces of the operands. Therefore, greater difficulty in recognizing them is expected…
Ergü l, Ö zgü r; Feki, Saber; Al-Jarro, Ahmed; Clo, Alain M.; Bagci, Hakan
2014-01-01
-level approach, utilizing the OpenACC directive-based parallel programming model, is used to minimize two often-faced challenges in GPU programming: developer productivity and code portability. The MOT-TDVIE solver code, originally developed for CPUs
Cafesat: A modern sat solver for scala
Blanc Régis
2013-01-01
We present CafeSat a SAT solver written in the Scala programming language. CafeSat is a modern solver based on DPLL and featuring many state of the art techniques and heuristics. It uses two watched literals for Boolean constraint propagation conict driven learning along with clause deletion a restarting strategy and the VSIDS heuristics for choosing the branching literal. CafeSat is both sound and complete. In order to achieve reasonable performance low level and hand tuned data structures a...
Parallel Symmetric Eigenvalue Problem Solvers
2015-05-01
Research” and the use of copyright material. Approved by Major Professor(s): Approved by: Head of the Departmental Graduate Program Date Alicia Marie... matrix . . . . . . . . . . . . . . . . . 106 8.15 Sparsity patterns for the Nastran benchmark of order 1.5 million . . . . 108 8.16 Sparsity patterns...magnitude eigenvalues of a given matrix pencil (A,B) along with their associated eigenvectors. Computing the smallest eigenvalues is more difficult
Comparing direct and iterative equation solvers in a large structural analysis software system
Poole, E. L.
1991-01-01
Two direct Choleski equation solvers and two iterative preconditioned conjugate gradient (PCG) equation solvers used in a large structural analysis software system are described. The two direct solvers are implementations of the Choleski method for variable-band matrix storage and sparse matrix storage. The two iterative PCG solvers include the Jacobi conjugate gradient method and an incomplete Choleski conjugate gradient method. The performance of the direct and iterative solvers is compared by solving several representative structural analysis problems. Some key factors affecting the performance of the iterative solvers relative to the direct solvers are identified.
Gerretsen, E.
2000-01-01
Prediction models for the airborne and impact sound transmission in buildings have recently been established (EN 12354- 1&2:1999). However, these models do not cover technical installations and machinery as a source of sound in buildings. Yet these can cause unacceptable sound levels and it is
Halldane, J. F.
1972-01-01
Technology is considered as a culture for changing a physical world and technology assessment questions the inherent cultural capability to modify power and material in support of living organisms. A comprehensive goal-parameter-synthesis-criterion specification is presented as a basis for a rational assessment of technology. The thesis queries the purpose of the assessed problems, the factors considered, the relationships between factors, and the values assigned those factors to accomplish the appropriate purpose. Stationary and sequential evaluation of enviro-organismic systems are delegated to the responsible personalities involved in design; from promoter/designer through contractor to occupant. Discussion includes design goals derived from organismic factors, definitions of human responses which establish viable criteria and relevant correlation models, linking stimulus parameters, and parallel problem-discipline centered design organization. A consistent concept of impedance, as a degradation in the performance of a specified parameter, is introduced to overcome the arbitrary inoperative connotations of terms like noise, discomfort, and glare. Applications of the evaluative specification are illustrated through design problems related to auditory impedance and sound distribution.
A Novel Interactive MINLP Solver for CAPE Applications
DEFF Research Database (Denmark)
Henriksen, Jens Peter; Støy, S.; Russel, Boris Mariboe
2000-01-01
This paper presents an interactive MINLP solver that is particularly suitable for solution of process synthesis, design and analysis problems. The interactive MINLP solver is based on the decomposition based MINLP algorithms, where a NLP sub-problem is solved in the innerloop and a MILP master pr...
Thakur, Chetan Singh; Wang, Runchun M; Afshar, Saeed; Hamilton, Tara J; Tapson, Jonathan C; Shamma, Shihab A; van Schaik, André
2015-01-01
The human auditory system has the ability to segregate complex auditory scenes into a foreground component and a background, allowing us to listen to specific speech sounds from a mixture of sounds. Selective attention plays a crucial role in this process, colloquially known as the "cocktail party effect." It has not been possible to build a machine that can emulate this human ability in real-time. Here, we have developed a framework for the implementation of a neuromorphic sound segregation algorithm in a Field Programmable Gate Array (FPGA). This algorithm is based on the principles of temporal coherence and uses an attention signal to separate a target sound stream from background noise. Temporal coherence implies that auditory features belonging to the same sound source are coherently modulated and evoke highly correlated neural response patterns. The basis for this form of sound segregation is that responses from pairs of channels that are strongly positively correlated belong to the same stream, while channels that are uncorrelated or anti-correlated belong to different streams. In our framework, we have used a neuromorphic cochlea as a frontend sound analyser to extract spatial information of the sound input, which then passes through band pass filters that extract the sound envelope at various modulation rates. Further stages include feature extraction and mask generation, which is finally used to reconstruct the targeted sound. Using sample tonal and speech mixtures, we show that our FPGA architecture is able to segregate sound sources in real-time. The accuracy of segregation is indicated by the high signal-to-noise ratio (SNR) of the segregated stream (90, 77, and 55 dB for simple tone, complex tone, and speech, respectively) as compared to the SNR of the mixture waveform (0 dB). This system may be easily extended for the segregation of complex speech signals, and may thus find various applications in electronic devices such as for sound segregation and
Ergül, Özgür
2014-04-01
Graphics processing units (GPUs) are gradually becoming mainstream in high-performance computing, as their capabilities for enhancing performance of a large spectrum of scientific applications to many fold when compared to multi-core CPUs have been clearly identified and proven. In this paper, implementation and performance-tuning details for porting an explicit marching-on-in-time (MOT)-based time-domain volume-integral-equation (TDVIE) solver onto GPUs are described in detail. To this end, a high-level approach, utilizing the OpenACC directive-based parallel programming model, is used to minimize two often-faced challenges in GPU programming: developer productivity and code portability. The MOT-TDVIE solver code, originally developed for CPUs, is annotated with compiler directives to port it to GPUs in a fashion similar to how OpenMP targets multi-core CPUs. In contrast to CUDA and OpenCL, where significant modifications to CPU-based codes are required, this high-level approach therefore requires minimal changes to the codes. In this work, we make use of two available OpenACC compilers, CAPS and PGI. Our experience reveals that different annotations of the code are required for each of the compilers, due to different interpretations of the fairly new standard by the compiler developers. Both versions of the OpenACC accelerated code achieved significant performance improvements, with up to 30× speedup against the sequential CPU code using recent hardware technology. Moreover, we demonstrated that the GPU-accelerated fully explicit MOT-TDVIE solver leveraged energy-consumption gains of the order of 3× against its CPU counterpart. © 2014 IEEE.
Music algorithm for imaging of a sound-hard arc in limited-view inverse scattering problem
Park, Won-Kwang
2017-07-01
MUltiple SIgnal Classification (MUSIC) algorithm for a non-iterative imaging of sound-hard arc in limited-view inverse scattering problem is considered. In order to discover mathematical structure of MUSIC, we derive a relationship between MUSIC and an infinite series of Bessel functions of integer order. This structure enables us to examine some properties of MUSIC in limited-view problem. Numerical simulations are performed to support the identified structure of MUSIC.
Benchmarking optimization solvers for structural topology optimization
DEFF Research Database (Denmark)
Rojas Labanda, Susana; Stolpe, Mathias
2015-01-01
solvers in IPOPT and FMINCON, and the sequential quadratic programming method in SNOPT, are benchmarked on the library using performance profiles. Whenever possible the methods are applied to both the nested and the Simultaneous Analysis and Design (SAND) formulations of the problem. The performance...
On a construction of fast direct solvers
Czech Academy of Sciences Publication Activity Database
Práger, Milan
2003-01-01
Roč. 48, č. 3 (2003), s. 225-236 ISSN 0862-7940 Institutional research plan: CEZ:AV0Z1019905; CEZ:AV0Z1019905 Keywords : Poisson equation * boundary value problem * fast direct solver Subject RIV: BA - General Mathematics
DEFF Research Database (Denmark)
Bjørner, Nikolaj; Dung, Phan Anh; Fleckenstein, Lars
2015-01-01
vZ is a part of the SMT solver Z3. It allows users to pose and solve optimization problems modulo theories. Many SMT applications use models to provide satisfying assignments, and a growing number of these build on top of Z3 to get optimal assignments with respect to objective functions. vZ provi...
Two-dimensional time dependent Riemann solvers for neutron transport
International Nuclear Information System (INIS)
Brunner, Thomas A.; Holloway, James Paul
2005-01-01
A two-dimensional Riemann solver is developed for the spherical harmonics approximation to the time dependent neutron transport equation. The eigenstructure of the resulting equations is explored, giving insight into both the spherical harmonics approximation and the Riemann solver. The classic Roe-type Riemann solver used here was developed for one-dimensional problems, but can be used in multidimensional problems by treating each face of a two-dimensional computation cell in a locally one-dimensional way. Several test problems are used to explore the capabilities of both the Riemann solver and the spherical harmonics approximation. The numerical solution for a simple line source problem is compared to the analytic solution to both the P 1 equation and the full transport solution. A lattice problem is used to test the method on a more challenging problem
Directory of Open Access Journals (Sweden)
В. А. Куликов
2017-03-01
Full Text Available Electrical methods of exploration are widely applied in prospecting and estimation of ore mineral resources. It is not always that geoelectrical models obtained in the course of interpretation of different types of electric and electromagnetic sounding are in line with each other. This leads to difficulties in geological interpretation of electrical exploration results. In single cases a geological model can be built that with great precision satisfies data from different electrical explorations, for instance, results of geometric and inductive electromagnetic soundings. For this purpose an algorithm of combined inversion of electrotomographic and audio-megnetotellurgic sounding data has been developed and implemented by A.E.Kaminskii in software ZondRes2D. Advantage of combined inversion has been shown for investigation of sections up till 400-500 m deep on synthetic models and actual field data.
Parallel sparse direct solver for integrated circuit simulation
Chen, Xiaoming; Yang, Huazhong
2017-01-01
This book describes algorithmic methods and parallelization techniques to design a parallel sparse direct solver which is specifically targeted at integrated circuit simulation problems. The authors describe a complete flow and detailed parallel algorithms of the sparse direct solver. They also show how to improve the performance by simple but effective numerical techniques. The sparse direct solver techniques described can be applied to any SPICE-like integrated circuit simulator and have been proven to be high-performance in actual circuit simulation. Readers will benefit from the state-of-the-art parallel integrated circuit simulation techniques described in this book, especially the latest parallel sparse matrix solution techniques. · Introduces complicated algorithms of sparse linear solvers, using concise principles and simple examples, without complex theory or lengthy derivations; · Describes a parallel sparse direct solver that can be adopted to accelerate any SPICE-like integrated circuit simulato...
Ferencz, Donald C.; Viterna, Larry A.
1991-01-01
ALPS is a computer program which can be used to solve general linear program (optimization) problems. ALPS was designed for those who have minimal linear programming (LP) knowledge and features a menu-driven scheme to guide the user through the process of creating and solving LP formulations. Once created, the problems can be edited and stored in standard DOS ASCII files to provide portability to various word processors or even other linear programming packages. Unlike many math-oriented LP solvers, ALPS contains an LP parser that reads through the LP formulation and reports several types of errors to the user. ALPS provides a large amount of solution data which is often useful in problem solving. In addition to pure linear programs, ALPS can solve for integer, mixed integer, and binary type problems. Pure linear programs are solved with the revised simplex method. Integer or mixed integer programs are solved initially with the revised simplex, and the completed using the branch-and-bound technique. Binary programs are solved with the method of implicit enumeration. This manual describes how to use ALPS to create, edit, and solve linear programming problems. Instructions for installing ALPS on a PC compatible computer are included in the appendices along with a general introduction to linear programming. A programmers guide is also included for assistance in modifying and maintaining the program.
В. А. Куликов; А. Е. Каминский; А. Г. Яковлев
2017-01-01
Electrical methods of exploration are widely applied in prospecting and estimation of ore mineral resources. It is not always that geoelectrical models obtained in the course of interpretation of different types of electric and electromagnetic sounding are in line with each other. This leads to difficulties in geological interpretation of electrical exploration results. In single cases a geological model can be built that with great precision satisfies data from different electrical...
1987-07-01
fields (see also Chapter 4 of Ref. 22). Like our investigation, theirs is based on the Khokhlov-Zabolotskaya-Kuznetsov ( KZK ) equa- tion [23,24...25,26], also based on the KZK e(iualiou, is limited to weakly nonlinear systems. However, the practical case of a focused circular source with gain of...iment. The demonstrated abihty of the KZK equation to accurately model focused sound fields from reahstic sources [i.e., having abrupt edges and
On Cafesat: A Modern SAT Solver for Scala
Blanc, Régis William
2013-01-01
We present CafeSat, a SAT solver written in the Scala programming language. CafeSat is a modern solver based on DPLL and featuring many state-of-the-art techniques and heuristics. It uses two-watched literals for Boolean constraint propagation, conflict-driven learning along with clause deletion, a restarting strategy, and the VSIDS heuristics for choosing the branching literal. CafeSat is both sound and complete. In order to achieve reasonnable performances, low level and hand-tuned data ...
Comparison of open-source linear programming solvers.
Energy Technology Data Exchange (ETDEWEB)
Gearhart, Jared Lee; Adair, Kristin Lynn; Durfee, Justin David.; Jones, Katherine A.; Martin, Nathaniel; Detry, Richard Joseph
2013-10-01
When developing linear programming models, issues such as budget limitations, customer requirements, or licensing may preclude the use of commercial linear programming solvers. In such cases, one option is to use an open-source linear programming solver. A survey of linear programming tools was conducted to identify potential open-source solvers. From this survey, four open-source solvers were tested using a collection of linear programming test problems and the results were compared to IBM ILOG CPLEX Optimizer (CPLEX) [1], an industry standard. The solvers considered were: COIN-OR Linear Programming (CLP) [2], [3], GNU Linear Programming Kit (GLPK) [4], lp_solve [5] and Modular In-core Nonlinear Optimization System (MINOS) [6]. As no open-source solver outperforms CPLEX, this study demonstrates the power of commercial linear programming software. CLP was found to be the top performing open-source solver considered in terms of capability and speed. GLPK also performed well but cannot match the speed of CLP or CPLEX. lp_solve and MINOS were considerably slower and encountered issues when solving several test problems.
Directory of Open Access Journals (Sweden)
Mehmet DEMİREZEN
2006-10-01
Full Text Available The Fossilized pronunciation errors constitute a great problem in the mastery of L2in second or foreign language learning and teaching (Odlin 1989; Demirezen, 2003;Demirezen, 2004; Johnson, 2001. One of such errors, which is committed by a greatmajority of Turkish teachers of English and student teachers, is the acquisition of ƒËƒÁƒÍ andƒËƒµƒÍ vowel sounds of the English language. There has been no specific material or lessonplan encountered so far in the literature to rehabilitate the pronunciation difficulty, createdby ƒËƒÁƒÍ and ƒËƒµƒÍ vowel sounds of the English language. Therefore, this article aims toprovide pronunciation teaching material and a sample lesson on two difficult sounds forTurks, like ƒËƒÁƒÍ and ƒËƒµƒÍ, to the Turkish teachers-on-the-job and student teachers ofEnglish.
van der Schoot, M.; Bakker Arkema, A.H.; Horsley, T.M.; van Lieshout, E.C.D.M.
2009-01-01
This study examined the effects of consistency (relational term consistent vs. inconsistent with required arithmetic operation) and markedness (relational term unmarked ['more than'] vs. marked ['less than']) on word problem solving in 10-12 years old children differing in problem-solving skill. The
Mathematical programming solver based on local search
Gardi, Frédéric; Darlay, Julien; Estellon, Bertrand; Megel, Romain
2014-01-01
This book covers local search for combinatorial optimization and its extension to mixed-variable optimization. Although not yet understood from the theoretical point of view, local search is the paradigm of choice for tackling large-scale real-life optimization problems. Today's end-users demand interactivity with decision support systems. For optimization software, this means obtaining good-quality solutions quickly. Fast iterative improvement methods, like local search, are suited to satisfying such needs. Here the authors show local search in a new light, in particular presenting a new kind of mathematical programming solver, namely LocalSolver, based on neighborhood search. First, an iconoclast methodology is presented to design and engineer local search algorithms. The authors' concern about industrializing local search approaches is of particular interest for practitioners. This methodology is applied to solve two industrial problems with high economic stakes. Software based on local search induces ex...
Use of Tabu Search in a Solver to Map Complex Networks onto Emulab Testbeds
National Research Council Canada - National Science Library
MacDonald, Jason E
2007-01-01
The University of Utah's solver for the testbed mapping problem uses a simulated annealing metaheuristic algorithm to map a researcher's experimental network topology onto available testbed resources...
Evolving effective incremental SAT solvers with GP
Bader, Mohamed; Poli, R.
2008-01-01
Hyper-Heuristics could simply be defined as heuristics to choose other heuristics, and it is a way of combining existing heuristics to generate new ones. In a Hyper-Heuristic framework, the framework is used for evolving effective incremental (Inc*) solvers for SAT. We test the evolved heuristics (IncHH) against other known local search heuristics on a variety of benchmark SAT problems.
Turovets, Sergei; Volkov, Vasily; Zherdetsky, Aleksej; Prakonina, Alena; Malony, Allen D
2014-01-01
The Electrical Impedance Tomography (EIT) and electroencephalography (EEG) forward problems in anisotropic inhomogeneous media like the human head belongs to the class of the three-dimensional boundary value problems for elliptic equations with mixed derivatives. We introduce and explore the performance of several new promising numerical techniques, which seem to be more suitable for solving these problems. The proposed numerical schemes combine the fictitious domain approach together with the finite-difference method and the optimally preconditioned Conjugate Gradient- (CG-) type iterative method for treatment of the discrete model. The numerical scheme includes the standard operations of summation and multiplication of sparse matrices and vector, as well as FFT, making it easy to implement and eligible for the effective parallel implementation. Some typical use cases for the EIT/EEG problems are considered demonstrating high efficiency of the proposed numerical technique.
International Nuclear Information System (INIS)
Turinsky, P.J.; Al-Chalabi, R.M.K.; Engrand, P.; Sarsour, H.N.; Faure, F.X.; Guo, W.
1994-06-01
NESTLE is a FORTRAN77 code that solves the few-group neutron diffusion equation utilizing the Nodal Expansion Method (NEM). NESTLE can solve the eigenvalue (criticality); eigenvalue adjoint; external fixed-source steady-state; or external fixed-source. or eigenvalue initiated transient problems. The code name NESTLE originates from the multi-problem solution capability, abbreviating Nodal Eigenvalue, Steady-state, Transient, Le core Evaluator. The eigenvalue problem allows criticality searches to be completed, and the external fixed-source steady-state problem can search to achieve a specified power level. Transient problems model delayed neutrons via precursor groups. Several core properties can be input as time dependent. Two or four energy groups can be utilized, with all energy groups being thermal groups (i.e. upscatter exits) if desired. Core geometries modelled include Cartesian and Hexagonal. Three, two and one dimensional models can be utilized with various symmetries. The non-linear iterative strategy associated with the NEM method is employed. An advantage of the non-linear iterative strategy is that NSTLE can be utilized to solve either the nodal or Finite Difference Method representation of the few-group neutron diffusion equation
International Nuclear Information System (INIS)
Koteras, J.R.
1996-01-01
The prediction of stresses and displacements around tunnels buried deep within the earth is an important class of geomechanics problems. The material behavior immediately surrounding the tunnel is typically nonlinear. The surrounding mass, even if it is nonlinear, can usually be characterized by a simple linear elastic model. The finite element method is best suited for modeling nonlinear materials of limited volume, while the boundary element method is well suited for modeling large volumes of linear elastic material. A computational scheme that couples the finite element and boundary element methods would seem particularly useful for geomechanics problems. A variety of coupling schemes have been proposed, but they rely on direct solution methods. Direct solution techniques have large storage requirements that become cumbersome for large-scale three-dimensional problems. An alternative to direct solution methods is iterative solution techniques. A scheme has been developed for coupling the finite element and boundary element methods that uses an iterative solution method. This report shows that this coupling scheme is valid for problems where nonlinear material behavior occurs in the finite element region
Hamilton, Mark F.
1990-12-01
This report discusses five projects all of which involve basic theoretical research in nonlinear acoustics: (1) pulsed finite amplitude sound beams are studied with a recently developed time domain computer algorithm that solves the KZK nonlinear parabolic wave equation; (2) nonlinear acoustic wave propagation in a liquid layer is a study of harmonic generation and acoustic soliton information in a liquid between a rigid and a free surface; (3) nonlinear effects in asymmetric cylindrical sound beams is a study of source asymmetries and scattering of sound by sound at high intensity; (4) effects of absorption on the interaction of sound beams is a completed study of the role of absorption in second harmonic generation and scattering of sound by sound; and (5) parametric receiving arrays is a completed study of parametric reception in a reverberant environment.
Parallel iterative solvers and preconditioners using approximate hierarchical methods
Energy Technology Data Exchange (ETDEWEB)
Grama, A.; Kumar, V.; Sameh, A. [Univ. of Minnesota, Minneapolis, MN (United States)
1996-12-31
In this paper, we report results of the performance, convergence, and accuracy of a parallel GMRES solver for Boundary Element Methods. The solver uses a hierarchical approximate matrix-vector product based on a hybrid Barnes-Hut / Fast Multipole Method. We study the impact of various accuracy parameters on the convergence and show that with minimal loss in accuracy, our solver yields significant speedups. We demonstrate the excellent parallel efficiency and scalability of our solver. The combined speedups from approximation and parallelism represent an improvement of several orders in solution time. We also develop fast and paralellizable preconditioners for this problem. We report on the performance of an inner-outer scheme and a preconditioner based on truncated Green`s function. Experimental results on a 256 processor Cray T3D are presented.
International Nuclear Information System (INIS)
Le Quere, P.; Weisman, C.; Paillere, H.; Vierendeels, J.; Dick, E.; Becker, R.; Braack, M.; Locke, J.
2005-01-01
Heat transfer by natural convection and conduction in enclosures occurs in numerous practical situations including the cooling of nuclear reactors. For large temperature difference, the flow becomes compressible with a strong coupling between the continuity, the momentum and the energy equations through the equation of state, and its properties (viscosity, heat conductivity) also vary with the temperature, making the Boussinesq flow approximation inappropriate and inaccurate. There are very few reference solutions in the literature on non-Boussinesq natural convection flows. We propose here a test case problem which extends the well-known De Vahl Davis differentially heated square cavity problem to the case of large temperature differences for which the Boussinesq approximation is no longer valid. The paper is split in two parts: in this first part, we propose as yet unpublished reference solutions for cases characterized by a non-dimensional temperature difference of 0.6, Ra 10 6 (constant property and variable property cases) and Ra = 10 7 (variable property case). These reference solutions were produced after a first international workshop organized by Cea and LIMSI in January 2000, in which the above authors volunteered to produce accurate numerical solutions from which the present reference solutions could be established. (authors)
International Nuclear Information System (INIS)
Anton, Luis; MartI, Jose M; Ibanez, Jose M; Aloy, Miguel A.; Mimica, Petar; Miralles, Juan A.
2010-01-01
We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization procedure relies on the characterization of the degeneracy types in terms of the normal and tangential components of the magnetic field to the wave front in the fluid rest frame. Proper expressions of the renormalized eigenvectors in conserved variables are obtained through the corresponding matrix transformations. Our work completes previous analysis that present different sets of right eigenvectors for non-degenerate and degenerate states, and can be seen as a relativistic generalization of earlier work performed in classical MHD. Based on the full wave decomposition (FWD) provided by the renormalized set of eigenvectors in conserved variables, we have also developed a linearized (Roe-type) Riemann solver. Extensive testing against one- and two-dimensional standard numerical problems allows us to conclude that our solver is very robust. When compared with a family of simpler solvers that avoid the knowledge of the full characteristic structure of the equations in the computation of the numerical fluxes, our solver turns out to be less diffusive than HLL and HLLC, and comparable in accuracy to the HLLD solver. The amount of operations needed by the FWD solver makes it less efficient computationally than those of the HLL family in one-dimensional problems. However, its relative efficiency increases in multidimensional simulations.
DEFF Research Database (Denmark)
Larsen, Ole Næsbye; Wahlberg, Magnus
2017-01-01
There is no difference in principle between the infrasonic and ultrasonic sounds, which are inaudible to humans (or other animals) and the sounds that we can hear. In all cases, sound is a wave of pressure and particle oscillations propagating through an elastic medium, such as air. This chapter...... is about the physical laws that govern how animals produce sound signals and how physical principles determine the signals’ frequency content and sound level, the nature of the sound field (sound pressure versus particle vibrations) as well as directional properties of the emitted signal. Many...... of these properties are dictated by simple physical relationships between the size of the sound emitter and the wavelength of emitted sound. The wavelengths of the signals need to be sufficiently short in relation to the size of the emitter to allow for the efficient production of propagating sound pressure waves...
ALPS - A LINEAR PROGRAM SOLVER
Viterna, L. A.
1994-01-01
Linear programming is a widely-used engineering and management tool. Scheduling, resource allocation, and production planning are all well-known applications of linear programs (LP's). Most LP's are too large to be solved by hand, so over the decades many computer codes for solving LP's have been developed. ALPS, A Linear Program Solver, is a full-featured LP analysis program. ALPS can solve plain linear programs as well as more complicated mixed integer and pure integer programs. ALPS also contains an efficient solution technique for pure binary (0-1 integer) programs. One of the many weaknesses of LP solvers is the lack of interaction with the user. ALPS is a menu-driven program with no special commands or keywords to learn. In addition, ALPS contains a full-screen editor to enter and maintain the LP formulation. These formulations can be written to and read from plain ASCII files for portability. For those less experienced in LP formulation, ALPS contains a problem "parser" which checks the formulation for errors. ALPS creates fully formatted, readable reports that can be sent to a printer or output file. ALPS is written entirely in IBM's APL2/PC product, Version 1.01. The APL2 workspace containing all the ALPS code can be run on any APL2/PC system (AT or 386). On a 32-bit system, this configuration can take advantage of all extended memory. The user can also examine and modify the ALPS code. The APL2 workspace has also been "packed" to be run on any DOS system (without APL2) as a stand-alone "EXE" file, but has limited memory capacity on a 640K system. A numeric coprocessor (80X87) is optional but recommended. The standard distribution medium for ALPS is a 5.25 inch 360K MS-DOS format diskette. IBM, IBM PC and IBM APL2 are registered trademarks of International Business Machines Corporation. MS-DOS is a registered trademark of Microsoft Corporation.
Keep Your Voice Sound: How to Prevent and Avoid Voice Problems
... Brain Listen Up! Wise Choices Avoid Voice Problems Drink 6 to 8 glasses of water a day. This helps keep your vocal folds moist and healthy. Limit intake of caffeinated or alcoholic drinks. These can dehydrate your body and make the ...
Good, L. H.; Erickson, A.
2016-02-01
Academic learning and research experiences alone cannot prepare our emerging ocean leaders to take on the challenges facing our oceans. Developing solutions that incorporate environmental and ocean sciences necessitates an interdisciplinary approach, requiring emerging leaders to be able to work in collaborative knowledge to action systems, rather than on micro-discipline islands. Professional and informal learning experiences can enhance graduate marine education by helping learners gain the communication, collaboration, and innovative problem-solving skills necessary for them to interact with peers at the interface of science and policy. These rich experiences can also provide case-based and hands-on opportunities for graduate learners to explore real-world examples of ocean science, policy, and management in action. However, academic programs are often limited in their capacity to offer such experiences as a part of a traditional curriculum. Rather than expecting learners to rely on their academic training, one approach is to encourage and support graduates to seek professional development beyond their university's walls, and think more holistically about their learning as it relates to their career interests. During this session we discuss current thinking around the professional learning needs of emerging ocean leaders, what this means for academic epistemologies, and examine initial evaluation outcomes from activities in our cross-campus consortium model in Monterey Bay, California. This innovative model includes seven regional academic institutions working together to develop an interdisciplinary ocean community and increase access to professional development opportunities to better prepare regional ocean-interested graduate students and early career researchers as future leaders.
Directory of Open Access Journals (Sweden)
Neculai Curteanu
2012-10-01
Full Text Available In this paper we point out some difficult problems of thesaurus-dictionary entry parsing, relying on the parsing technology of SCD (Segmentation-Cohesion-Dependency configurations, successfully applied on six largest thesauri -- Romanian (2, French, German (2, and Russian. \\textbf{Challenging Problems:} \\textbf{(a}~Intricate and~/~or recursive structures of the lexicographic segments met in the entries of certain thesauri; \\textbf{(b}~Cyclicity (recursive calls of some sense marker classes on marker sequences; \\textbf{(c}~Establishing the hypergraph-driven dependencies between all the atomic and non-atomic sense definitions. Classical approach to solve these parsing problems is hard mainly because of depth-first search of sense definitions and markers, the substantial complexity of entries, and the sense tree dynamic construction embodied within these parsers. \\textbf{SCD-based Parsing Solutions:} \\textbf{(a}~The SCD parsing method is a procedural tool, completely formal grammar-free, handling the recursive structure of the lexicographic segments by procedural non-recursive calls performed on the SCD parsing configurations of the entry structure. \\textbf{(b}~For dealing with cyclicity (recursive calls between secondary sense markers and the sense enumeration markers, we proposed the Enumeration Closing Condition, sometimes coupled with New{\\_}Paragraphs typographic markers transformed into numeral sense enumeration. \\textbf{(c}~These problems, their lexicographic modeling and parsing solutions are addressed to both dictionary parser programmers to experience the SCD-based parsing method, as well as to lexicographers and thesauri designers for tailoring balanced lexical-semantics granularities and sounder sense tree definitions of the dictionary entries.
Principles of underwater sound
National Research Council Canada - National Science Library
Urick, Robert J
1983-01-01
... the immediately useful help they need for sonar problem solving. Its coverage is broad-ranging from the basic concepts of sound in the sea to making performance predictions in such applications as depth sounding, fish finding, and submarine detection...
Sound a very short introduction
Goldsmith, Mike
2015-01-01
Sound is integral to how we experience the world, in the form of noise as well as music. But what is sound? What is the physical basis of pitch and harmony? And how are sound waves exploited in musical instruments? Sound: A Very Short Introduction looks at the science of sound and the behaviour of sound waves with their different frequencies. It also explores sound in different contexts, covering the audible and inaudible, sound underground and underwater, acoustic and electronic sound, and hearing in humans and animals. It concludes with the problem of sound out of place—noise and its reduction.
PCX, Interior-Point Linear Programming Solver
International Nuclear Information System (INIS)
Czyzyk, J.
2004-01-01
1 - Description of program or function: PCX solves linear programming problems using the Mehrota predictor-corrector interior-point algorithm. PCX can be called as a subroutine or used in stand-alone mode, with data supplied from an MPS file. The software incorporates modules that can be used separately from the linear programming solver, including a pre-solve routine and data structure definitions. 2 - Methods: The Mehrota predictor-corrector method is a primal-dual interior-point method for linear programming. The starting point is determined from a modified least squares heuristic. Linear systems of equations are solved at each interior-point iteration via a sparse Cholesky algorithm native to the code. A pre-solver is incorporated in the code to eliminate inefficiencies in the user's formulation of the problem. 3 - Restriction on the complexity of the problem: There are no size limitations built into the program. The size of problem solved is limited by RAM and swap space on the user's computer
Using sound to solve syntactic problems: the role of phonology in grammatical category assignments.
Kelly, M H
1992-04-01
One ubiquitous problem in language processing involves the assignment of words to the correct grammatical category, such as noun or verb. In general, semantic and syntactic cues have been cited as the principal information for grammatical category assignment, to the neglect of possible phonological cues. This neglect is unwarranted, and the following claims are made: (a) Numerous correlations between phonology and grammatical class exist, (b) some of these correlations are large and can pervade the entire lexicon of a language and hence can involve thousands of words, (c) experiments have repeatedly found that adults and children have learned these correlations, and (d) explanations for how these correlations arose can be proposed and evaluated. Implications of these phenomena for language representation and processing are discussed.
Parallel linear solvers for simulations of reactor thermal hydraulics
International Nuclear Information System (INIS)
Yan, Y.; Antal, S.P.; Edge, B.; Keyes, D.E.; Shaver, D.; Bolotnov, I.A.; Podowski, M.Z.
2011-01-01
The state-of-the-art multiphase fluid dynamics code, NPHASE-CMFD, performs multiphase flow simulations in complex domains using implicit nonlinear treatment of the governing equations and in parallel, which is a very challenging environment for the linear solver. The present work illustrates how the Portable, Extensible Toolkit for Scientific Computation (PETSc) and scalable Algebraic Multigrid (AMG) preconditioner from Hypre can be utilized to construct robust and scalable linear solvers for the Newton correction equation obtained from the discretized system of governing conservation equations in NPHASE-CMFD. The overall long-tem objective of this work is to extend the NPHASE-CMFD code into a fully-scalable solver of multiphase flow and heat transfer problems, applicable to both steady-state and stiff time-dependent phenomena in complete fuel assemblies of nuclear reactors and, eventually, the entire reactor core (such as the Virtual Reactor concept envisioned by CASL). This campaign appropriately begins with the linear algebraic equation solver, which is traditionally a bottleneck to scalability in PDE-based codes. The computational complexity of the solver is usually superlinear in problem size, whereas the rest of the code, the “physics” portion, usually has its complexity linear in the problem size. (author)
Microbes: uranium miners, money makers, problem solvers
International Nuclear Information System (INIS)
Williamson, A.L.; Payne, R.; Kerr, F.; Hall, S.; Spiers, G.A.
2010-01-01
Bioleaching, the microbial dissolution of minerals, is potentially useful in exploiting a variety of ore deposits, including the lower-grade uraniferous quartz-pebble conglomerate beds of the Quirke Syncline, Elliot Lake, Ontario. The metabolism of chemolithotropic bacterium Acidithiobacillus ferrooxidans is dependent on its ability to derive energy and reducing power from the oxidation of ferrous iron. The characteristics of this bacterium, in particular the ability to oxidize both iron and sulphur with an associated high tolerance of low acidity, allow the organism to contribute significantly to bioleaching processes. Under ideal conditions, A. ferrooxidans promotes the oxidation of iron-containing sulphide ore materials, breaking their crystal structure and promoting the dissolution of iron, base metals, as well as uranium, rare earth elements and associated elements of toxicological interest such as arsenic and selenium. The current study documents an overview of the recovery of uranium and rare earth elements to solution, plus investigates the acid generating potential of the solid residues from a series of environmentally controlled, biologically-mediated uranium ore extraction experiments. The findings will be used in the design of larger scale bioleaching experiments to further assess the potential for success of bioleaching as a metallurgical extraction technique potentially leading to minimum maintenance decommissioning strategies for the ore deposits of the Quirke Syncline. (author)
Equipping the Enterprise Interoperability Problem Solver
Oude Luttighuis, Paul; Folmer, Erwin Johan Albert; Charalabidis, Yannis
2010-01-01
The maturity of the enterprise interoperability field does not match the importance attached to it by many, both in the public as well as the private community. A host of models, paradigms, designs, standards, methods, and instruments seems to be available, but many of them are only used in rather
Microbes: uranium miners, money makers, problem solvers
Energy Technology Data Exchange (ETDEWEB)
Williamson, A.L., E-mail: awilliamson@mirarco.org [MIRARCO, Sudbury, ON (Canada); Laurentian Univ., Sudbury, ON (Canada); Payne, R.; Kerr, F. [Pele Mountain Resources Inc., Toronto, ON (Canada); Hall, S. [Laurentian Univ., Sudbury, ON (Canada); Spiers, G.A. [MIRARCO, Sudbury, ON (Canada); Laurentian Univ., Sudbury, ON (Canada)
2010-07-01
Bioleaching, the microbial dissolution of minerals, is potentially useful in exploiting a variety of ore deposits, including the lower-grade uraniferous quartz-pebble conglomerate beds of the Quirke Syncline, Elliot Lake, Ontario. The metabolism of chemolithotropic bacterium Acidithiobacillus ferrooxidans is dependent on its ability to derive energy and reducing power from the oxidation of ferrous iron. The characteristics of this bacterium, in particular the ability to oxidize both iron and sulphur with an associated high tolerance of low acidity, allow the organism to contribute significantly to bioleaching processes. Under ideal conditions, A. ferrooxidans promotes the oxidation of iron-containing sulphide ore materials, breaking their crystal structure and promoting the dissolution of iron, base metals, as well as uranium, rare earth elements and associated elements of toxicological interest such as arsenic and selenium. The current study documents an overview of the recovery of uranium and rare earth elements to solution, plus investigates the acid generating potential of the solid residues from a series of environmentally controlled, biologically-mediated uranium ore extraction experiments. The findings will be used in the design of larger scale bioleaching experiments to further assess the potential for success of bioleaching as a metallurgical extraction technique potentially leading to minimum maintenance decommissioning strategies for the ore deposits of the Quirke Syncline. (author)
Molecular biology problem solver: a laboratory guide
National Research Council Canada - National Science Library
Gerstein, Alan S
2001-01-01
... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi Chapter 1. Preparing for Success in the Laboratory Phillip P. Franciskovich . . . . . . . . . . . . . . . . . . . . . . . . 1 Chapter 2. Getting What You Need...
Refined isogeometric analysis for a preconditioned conjugate gradient solver
Garcia, Daniel
2018-02-12
Starting from a highly continuous Isogeometric Analysis (IGA) discretization, refined Isogeometric Analysis (rIGA) introduces C0 hyperplanes that act as separators for the direct LU factorization solver. As a result, the total computational cost required to solve the corresponding system of equations using a direct LU factorization solver dramatically reduces (up to a factor of 55) Garcia et al. (2017). At the same time, rIGA enriches the IGA spaces, thus improving the best approximation error. In this work, we extend the complexity analysis of rIGA to the case of iterative solvers. We build an iterative solver as follows: we first construct the Schur complements using a direct solver over small subdomains (macro-elements). We then assemble those Schur complements into a global skeleton system. Subsequently, we solve this system iteratively using Conjugate Gradients (CG) with an incomplete LU (ILU) preconditioner. For a 2D Poisson model problem with a structured mesh and a uniform polynomial degree of approximation, rIGA achieves moderate savings with respect to IGA in terms of the number of Floating Point Operations (FLOPs) and computational time (in seconds) required to solve the resulting system of linear equations. For instance, for a mesh with four million elements and polynomial degree p=3, the iterative solver is approximately 2.6 times faster (in time) when applied to the rIGA system than to the IGA one. These savings occur because the skeleton rIGA system contains fewer non-zero entries than the IGA one. The opposite situation occurs for 3D problems, and as a result, 3D rIGA discretizations provide no gains with respect to their IGA counterparts when considering iterative solvers.
T2CG1, a package of preconditioned conjugate gradient solvers for TOUGH2
International Nuclear Information System (INIS)
Moridis, G.; Pruess, K.; Antunez, E.
1994-03-01
Most of the computational work in the numerical simulation of fluid and heat flows in permeable media arises in the solution of large systems of linear equations. The simplest technique for solving such equations is by direct methods. However, because of large storage requirements and accumulation of roundoff errors, the application of direct solution techniques is limited, depending on matrix bandwidth, to systems of a few hundred to at most a few thousand simultaneous equations. T2CG1, a package of preconditioned conjugate gradient solvers, has been added to TOUGH2 to complement its direct solver and significantly increase the size of problems tractable on PCs. T2CG1 includes three different solvers: a Bi-Conjugate Gradient (BCG) solver, a Bi-Conjugate Gradient Squared (BCGS) solver, and a Generalized Minimum Residual (GMRES) solver. Results from six test problems with up to 30,000 equations show that T2CG1 (1) is significantly (and invariably) faster and requires far less memory than the MA28 direct solver, (2) it makes possible the solution of very large three-dimensional problems on PCs, and (3) that the BCGS solver is the fastest of the three in the tested problems. Sample problems are presented related to heat and fluid flow at Yucca Mountain and WIPP, environmental remediation by the Thermal Enhanced Vapor Extraction System, and geothermal resources
High-Performance Small-Scale Solvers for Moving Horizon Estimation
DEFF Research Database (Denmark)
Frison, Gianluca; Vukov, Milan; Poulsen, Niels Kjølstad
2015-01-01
implementation techniques focusing on small-scale problems. The proposed MHE solver is implemented using custom linear algebra routines and is compared against implementations using BLAS libraries. Additionally, the MHE solver is interfaced to a code generation tool for nonlinear model predictive control (NMPC...
Investigation on the Use of a Multiphase Eulerian CFD solver to simulate breaking waves
DEFF Research Database (Denmark)
Tomaselli, Pietro D.; Christensen, Erik Damgaard
2015-01-01
investigation on a CFD model capable of handling this problem. The model is based on a solver, available in the open-source CFD toolkit OpenFOAM, which combines the Eulerian multi-fluid approach for dispersed flows with a numerical interface sharpening method. The solver, enhanced with additional formulations...
Optimising a parallel conjugate gradient solver
Energy Technology Data Exchange (ETDEWEB)
Field, M.R. [O`Reilly Institute, Dublin (Ireland)
1996-12-31
This work arises from the introduction of a parallel iterative solver to a large structural analysis finite element code. The code is called FEX and it was developed at Hitachi`s Mechanical Engineering Laboratory. The FEX package can deal with a large range of structural analysis problems using a large number of finite element techniques. FEX can solve either stress or thermal analysis problems of a range of different types from plane stress to a full three-dimensional model. These problems can consist of a number of different materials which can be modelled by a range of material models. The structure being modelled can have the load applied at either a point or a surface, or by a pressure, a centrifugal force or just gravity. Alternatively a thermal load can be applied with a given initial temperature. The displacement of the structure can be constrained by having a fixed boundary or by prescribing the displacement at a boundary.
The Development of a Finite Volume Method for Modeling Sound in Coastal Ocean Environment
Energy Technology Data Exchange (ETDEWEB)
Long, Wen; Yang, Zhaoqing; Copping, Andrea E.; Jung, Ki Won; Deng, Zhiqun
2015-10-28
: As the rapid growth of marine renewable energy and off-shore wind energy, there have been concerns that the noises generated from construction and operation of the devices may interfere marine animals’ communication. In this research, a underwater sound model is developed to simulate sound prorogation generated by marine-hydrokinetic energy (MHK) devices or offshore wind (OSW) energy platforms. Finite volume and finite difference methods are developed to solve the 3D Helmholtz equation of sound propagation in the coastal environment. For finite volume method, the grid system consists of triangular grids in horizontal plane and sigma-layers in vertical dimension. A 3D sparse matrix solver with complex coefficients is formed for solving the resulting acoustic pressure field. The Complex Shifted Laplacian Preconditioner (CSLP) method is applied to efficiently solve the matrix system iteratively with MPI parallelization using a high performance cluster. The sound model is then coupled with the Finite Volume Community Ocean Model (FVCOM) for simulating sound propagation generated by human activities in a range-dependent setting, such as offshore wind energy platform constructions and tidal stream turbines. As a proof of concept, initial validation of the finite difference solver is presented for two coastal wedge problems. Validation of finite volume method will be reported separately.
Iterative solvers in forming process simulations
van den Boogaard, Antonius H.; Rietman, Bert; Huetink, Han
1998-01-01
The use of iterative solvers in implicit forming process simulations is studied. The time and memory requirements are compared with direct solvers and assessed in relation with the rest of the Newton-Raphson iteration process. It is shown that conjugate gradient{like solvers with a proper
Fast Multipole-Based Elliptic PDE Solver and Preconditioner
Ibeid, Huda
2016-01-01
extrapolated scalability. Fast multipole methods (FMM) were originally developed for accelerating N-body problems for particle-based methods in astrophysics and molecular dynamics. FMM is more than an N-body solver, however. Recent efforts to view the FMM
LAPACKrc: Fast linear algebra kernels/solvers for FPGA accelerators
International Nuclear Information System (INIS)
Gonzalez, Juan; Nunez, Rafael C
2009-01-01
We present LAPACKrc, a family of FPGA-based linear algebra solvers able to achieve more than 100x speedup per commodity processor on certain problems. LAPACKrc subsumes some of the LAPACK and ScaLAPACK functionalities, and it also incorporates sparse direct and iterative matrix solvers. Current LAPACKrc prototypes demonstrate between 40x-150x speedup compared against top-of-the-line hardware/software systems. A technology roadmap is in place to validate current performance of LAPACKrc in HPC applications, and to increase the computational throughput by factors of hundreds within the next few years.
Fast Laplace solver approach to pore-scale permeability
Arns, C. H.; Adler, P. M.
2018-02-01
We introduce a powerful and easily implemented method to calculate the permeability of porous media at the pore scale using an approximation based on the Poiseulle equation to calculate permeability to fluid flow with a Laplace solver. The method consists of calculating the Euclidean distance map of the fluid phase to assign local conductivities and lends itself naturally to the treatment of multiscale problems. We compare with analytical solutions as well as experimental measurements and lattice Boltzmann calculations of permeability for Fontainebleau sandstone. The solver is significantly more stable than the lattice Boltzmann approach, uses less memory, and is significantly faster. Permeabilities are in excellent agreement over a wide range of porosities.
Advanced Algebraic Multigrid Solvers for Subsurface Flow Simulation
Chen, Meng-Huo
2015-09-13
In this research we are particularly interested in extending the robustness of multigrid solvers to encounter complex systems related to subsurface reservoir applications for flow problems in porous media. In many cases, the step for solving the pressure filed in subsurface flow simulation becomes a bottleneck for the performance of the simulator. For solving large sparse linear system arising from MPFA discretization, we choose multigrid methods as the linear solver. The possible difficulties and issues will be addressed and the corresponding remedies will be studied. As the multigrid methods are used as the linear solver, the simulator can be parallelized (although not trivial) and the high-resolution simulation become feasible, the ultimately goal which we desire to achieve.
An efficient spectral crystal plasticity solver for GPU architectures
Malahe, Michael
2018-03-01
We present a spectral crystal plasticity (CP) solver for graphics processing unit (GPU) architectures that achieves a tenfold increase in efficiency over prior GPU solvers. The approach makes use of a database containing a spectral decomposition of CP simulations performed using a conventional iterative solver over a parameter space of crystal orientations and applied velocity gradients. The key improvements in efficiency come from reducing global memory transactions, exposing more instruction-level parallelism, reducing integer instructions and performing fast range reductions on trigonometric arguments. The scheme also makes more efficient use of memory than prior work, allowing for larger problems to be solved on a single GPU. We illustrate these improvements with a simulation of 390 million crystal grains on a consumer-grade GPU, which executes at a rate of 2.72 s per strain step.
Jennings, NR
1993-01-01
Systems composed of multiple interacting problem solvers are becoming increasingly pervasive and have been championed in some quarters as the basis of the next generation of intelligent information systems. If this technology is to fulfill its true potential then it is important that the systems which are developed have a sound theoretical grounding. One aspect of this foundation, namely the model of collaborative problem solving, is examined in this paper. A synergistic review of existing mo...
A generalized gyrokinetic Poisson solver
International Nuclear Information System (INIS)
Lin, Z.; Lee, W.W.
1995-03-01
A generalized gyrokinetic Poisson solver has been developed, which employs local operations in the configuration space to compute the polarization density response. The new technique is based on the actual physical process of gyrophase-averaging. It is useful for nonlocal simulations using general geometry equilibrium. Since it utilizes local operations rather than the global ones such as FFT, the new method is most amenable to massively parallel algorithms
PREFACE: Aerodynamic sound Aerodynamic sound
Akishita, Sadao
2010-02-01
The modern theory of aerodynamic sound originates from Lighthill's two papers in 1952 and 1954, as is well known. I have heard that Lighthill was motivated in writing the papers by the jet-noise emitted by the newly commercialized jet-engined airplanes at that time. The technology of aerodynamic sound is destined for environmental problems. Therefore the theory should always be applied to newly emerged public nuisances. This issue of Fluid Dynamics Research (FDR) reflects problems of environmental sound in present Japanese technology. The Japanese community studying aerodynamic sound has held an annual symposium since 29 years ago when the late Professor S Kotake and Professor S Kaji of Teikyo University organized the symposium. Most of the Japanese authors in this issue are members of the annual symposium. I should note the contribution of the two professors cited above in establishing the Japanese community of aerodynamic sound research. It is my pleasure to present the publication in this issue of ten papers discussed at the annual symposium. I would like to express many thanks to the Editorial Board of FDR for giving us the chance to contribute these papers. We have a review paper by T Suzuki on the study of jet noise, which continues to be important nowadays, and is expected to reform the theoretical model of generating mechanisms. Professor M S Howe and R S McGowan contribute an analytical paper, a valuable study in today's fluid dynamics research. They apply hydrodynamics to solve the compressible flow generated in the vocal cords of the human body. Experimental study continues to be the main methodology in aerodynamic sound, and it is expected to explore new horizons. H Fujita's study on the Aeolian tone provides a new viewpoint on major, longstanding sound problems. The paper by M Nishimura and T Goto on textile fabrics describes new technology for the effective reduction of bluff-body noise. The paper by T Sueki et al also reports new technology for the
A General Symbolic PDE Solver Generator: Explicit Schemes
Directory of Open Access Journals (Sweden)
K. Sheshadri
2003-01-01
Full Text Available A symbolic solver generator to deal with a system of partial differential equations (PDEs in functions of an arbitrary number of variables is presented; it can also handle arbitrary domains (geometries of the independent variables. Given a system of PDEs, the solver generates a set of explicit finite-difference methods to any specified order, and a Fourier stability criterion for each method. For a method that is stable, an iteration function is generated symbolically using the PDE and its initial and boundary conditions. This iteration function is dynamically generated for every PDE problem, and its evaluation provides a solution to the PDE problem. A C++/Fortran 90 code for the iteration function is generated using the MathCode system, which results in a performance gain of the order of a thousand over Mathematica, the language that has been used to code the solver generator. Examples of stability criteria are presented that agree with known criteria; examples that demonstrate the generality of the solver and the speed enhancement of the generated C++ and Fortran 90 codes are also presented.
Implementation and testing of a multivariate inverse radiation transport solver
International Nuclear Information System (INIS)
Mattingly, John; Mitchell, Dean J.
2012-01-01
Detection, identification, and characterization of special nuclear materials (SNM) all face the same basic challenge: to varying degrees, each must infer the presence, composition, and configuration of the SNM by analyzing a set of measured radiation signatures. Solutions to this problem implement inverse radiation transport methods. Given a set of measured radiation signatures, inverse radiation transport estimates properties of the source terms and transport media that are consistent with those signatures. This paper describes one implementation of a multivariate inverse radiation transport solver. The solver simultaneously analyzes gamma spectrometry and neutron multiplicity measurements to fit a one-dimensional radiation transport model with variable layer thicknesses using nonlinear regression. The solver's essential components are described, and its performance is illustrated by application to benchmark experiments conducted with plutonium metal. - Highlights: ► Inverse problems, specifically applied to identifying and characterizing radiation sources . ► Radiation transport. ► Analysis of gamma spectroscopy and neutron multiplicity counting measurements. ► Experimental testing of the inverse solver against measurements of plutonium.
Graph Grammar-Based Multi-Frontal Parallel Direct Solver for Two-Dimensional Isogeometric Analysis
Kuźnik, Krzysztof; Paszyński, Maciej; Calo, Victor M.
2012-01-01
at parent nodes and eliminates rows corresponding to fully assembled degrees of freedom. Finally, there are graph grammar productions responsible for root problem solution and recursive backward substitutions. Expressing the solver algorithm by graph grammar
High order Poisson Solver for unbounded flows
DEFF Research Database (Denmark)
Hejlesen, Mads Mølholm; Rasmussen, Johannes Tophøj; Chatelain, Philippe
2015-01-01
This paper presents a high order method for solving the unbounded Poisson equation on a regular mesh using a Green’s function solution. The high order convergence was achieved by formulating mollified integration kernels, that were derived from a filter regularisation of the solution field....... The method was implemented on a rectangular domain using fast Fourier transforms (FFT) to increase computational efficiency. The Poisson solver was extended to directly solve the derivatives of the solution. This is achieved either by including the differential operator in the integration kernel...... the equations of fluid mechanics as an example, but can be used in many physical problems to solve the Poisson equation on a rectangular unbounded domain. For the two-dimensional case we propose an infinitely smooth test function which allows for arbitrary high order convergence. Using Gaussian smoothing...
Motivation, Challenge, and Opportunity of Successful Solvers on an Innovation Platform
DEFF Research Database (Denmark)
Hossain, Mokter
2017-01-01
. The main motivational factors of successful solvers engaged in problem solving are money, learning, fun, sense of achievement, passion, and networking. Major challenges solvers face include unclear or insufficient problem description, lack of option for communication, language barrier, time zone...... other experts, the ability to work in a diverse environment, options of work after retirement and from distant locations, and a new source of income....
DEFF Research Database (Denmark)
Hossain, Mokter
2018-01-01
. The main motivational factors of successful solvers engaged in problem solving are money, learning, fun, sense of achievement, passion, and networking. Major challenges solvers face include unclear or insufficient problem description, lack of option for communication, language barrier, time zone...... other experts, the ability to work in a diverse environment, options of work after retirement and from distant locations, and a new source of income....
De Götzen , Amalia; Mion , Luca; Tache , Olivier
2007-01-01
International audience; We call sound algorithms the categories of algorithms that deal with digital sound signal. Sound algorithms appeared in the very infancy of computer. Sound algorithms present strong specificities that are the consequence of two dual considerations: the properties of the digital sound signal itself and its uses, and the properties of auditory perception.
Poor Hand-Pointing to Sounds in Right Brain-Damaged Patients: Not Just a Problem of Spatial-Hearing
Pavani, Francesco; Farne, Alessandro; Ladavas, Elisabetta
2005-01-01
We asked 22 right brain-damaged (RBD) patients and 11 elderly healthy controls to perform hand-pointing movements to free-field unseen sounds, while modulating two non-auditory variables: the initial position of the responding hand (left, centre or right) and the presence or absence of task-irrelevant ambient vision. RBD patients suffering from…
An Investigation of the Performance of the Colored Gauss-Seidel Solver on CPU and GPU
International Nuclear Information System (INIS)
Yoon, Jong Seon; Choi, Hyoung Gwon; Jeon, Byoung Jin
2017-01-01
The performance of the colored Gauss–Seidel solver on CPU and GPU was investigated for the two- and three-dimensional heat conduction problems by using different mesh sizes. The heat conduction equation was discretized by the finite difference method and finite element method. The CPU yielded good performance for small problems but deteriorated when the total memory required for computing was larger than the cache memory for large problems. In contrast, the GPU performed better as the mesh size increased because of the latency hiding technique. Further, GPU computation by the colored Gauss–Siedel solver was approximately 7 times that by the single CPU. Furthermore, the colored Gauss–Seidel solver was found to be approximately twice that of the Jacobi solver when parallel computing was conducted on the GPU.
An Investigation of the Performance of the Colored Gauss-Seidel Solver on CPU and GPU
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)
2017-02-15
The performance of the colored Gauss–Seidel solver on CPU and GPU was investigated for the two- and three-dimensional heat conduction problems by using different mesh sizes. The heat conduction equation was discretized by the finite difference method and finite element method. The CPU yielded good performance for small problems but deteriorated when the total memory required for computing was larger than the cache memory for large problems. In contrast, the GPU performed better as the mesh size increased because of the latency hiding technique. Further, GPU computation by the colored Gauss–Siedel solver was approximately 7 times that by the single CPU. Furthermore, the colored Gauss–Seidel solver was found to be approximately twice that of the Jacobi solver when parallel computing was conducted on the GPU.
Migration of vectorized iterative solvers to distributed memory architectures
Energy Technology Data Exchange (ETDEWEB)
Pommerell, C. [AT& T Bell Labs., Murray Hill, NJ (United States); Ruehl, R. [CSCS-ETH, Manno (Switzerland)
1994-12-31
Both necessity and opportunity motivate the use of high-performance computers for iterative linear solvers. Necessity results from the size of the problems being solved-smaller problems are often better handled by direct methods. Opportunity arises from the formulation of the iterative methods in terms of simple linear algebra operations, even if this {open_quote}natural{close_quotes} parallelism is not easy to exploit in irregularly structured sparse matrices and with good preconditioners. As a result, high-performance implementations of iterative solvers have attracted a lot of interest in recent years. Most efforts are geared to vectorize or parallelize the dominating operation-structured or unstructured sparse matrix-vector multiplication, or to increase locality and parallelism by reformulating the algorithm-reducing global synchronization in inner products or local data exchange in preconditioners. Target architectures for iterative solvers currently include mostly vector supercomputers and architectures with one or few optimized (e.g., super-scalar and/or super-pipelined RISC) processors and hierarchical memory systems. More recently, parallel computers with physically distributed memory and a better price/performance ratio have been offered by vendors as a very interesting alternative to vector supercomputers. However, programming comfort on such distributed memory parallel processors (DMPPs) still lags behind. Here the authors are concerned with iterative solvers and their changing computing environment. In particular, they are considering migration from traditional vector supercomputers to DMPPs. Application requirements force one to use flexible and portable libraries. They want to extend the portability of iterative solvers rather than reimplementing everything for each new machine, or even for each new architecture.
DEFF Research Database (Denmark)
Bendixen, Cecilie
Sound is a part of architecture, and sound is complex. Upon this, sound is invisible. How is it then possible to design visual objects that interact with the sound? This paper addresses the problem of how to get access to the complexity of sound and how to make textile material revealing the form...... goemetry by analysing the sound pattern at a specific spot. This analysis is done theoretically with algorithmic systems and practical with waves in water. The paper describes the experiments and the findings, and explains how an analysis of sound can be catched in a textile form....
Approximate Riemann solver for the two-fluid plasma model
International Nuclear Information System (INIS)
Shumlak, U.; Loverich, J.
2003-01-01
An algorithm is presented for the simulation of plasma dynamics using the two-fluid plasma model. The two-fluid plasma model is more general than the magnetohydrodynamic (MHD) model often used for plasma dynamic simulations. The two-fluid equations are derived in divergence form and an approximate Riemann solver is developed to compute the fluxes of the electron and ion fluids at the computational cell interfaces and an upwind characteristic-based solver to compute the electromagnetic fields. The source terms that couple the fluids and fields are treated implicitly to relax the stiffness. The algorithm is validated with the coplanar Riemann problem, Langmuir plasma oscillations, and the electromagnetic shock problem that has been simulated with the MHD plasma model. A numerical dispersion relation is also presented that demonstrates agreement with analytical plasma waves
Nonlinear Multigrid solver exploiting AMGe Coarse Spaces with Approximation Properties
DEFF Research Database (Denmark)
Christensen, Max la Cour; Villa, Umberto; Engsig-Karup, Allan Peter
The paper introduces a nonlinear multigrid solver for mixed finite element discretizations based on the Full Approximation Scheme (FAS) and element-based Algebraic Multigrid (AMGe). The main motivation to use FAS for unstructured problems is the guaranteed approximation property of the AMGe coarse...... properties of the coarse spaces. With coarse spaces with approximation properties, our FAS approach on unstructured meshes has the ability to be as powerful/successful as FAS on geometrically refined meshes. For comparison, Newton’s method and Picard iterations with an inner state-of-the-art linear solver...... are compared to FAS on a nonlinear saddle point problem with applications to porous media flow. It is demonstrated that FAS is faster than Newton’s method and Picard iterations for the experiments considered here. Due to the guaranteed approximation properties of our AMGe, the coarse spaces are very accurate...
Jump as Far as You Can [Problem Solvers: Problem
Bofferding, Laura; Yigit, Melike
2013-01-01
The standing long jump was an Olympic event until 1912. In 1904, Ray Ewry set the world record for the longest standing long jump, which was about 11.5 feet, or 138 inches. Although the standing long jump is no longer an Olympic event, the Norwegians still include it in their National Competition, and Arne Tvervaag set a new world record at about…
Hamiltonian Algorithm Sound Synthesis
大矢, 健一
2013-01-01
Hamiltonian Algorithm (HA) is an algorithm for searching solutions is optimization problems. This paper introduces a sound synthesis technique using Hamiltonian Algorithm and shows a simple example. "Hamiltonian Algorithm Sound Synthesis" uses phase transition effect in HA. Because of this transition effect, totally new waveforms are produced.
Multiscale Universal Interface: A concurrent framework for coupling heterogeneous solvers
Energy Technology Data Exchange (ETDEWEB)
Tang, Yu-Hang, E-mail: yuhang_tang@brown.edu [Division of Applied Mathematics, Brown University, Providence, RI (United States); Kudo, Shuhei, E-mail: shuhei-kudo@outlook.jp [Graduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe, 657-8501 (Japan); Bian, Xin, E-mail: xin_bian@brown.edu [Division of Applied Mathematics, Brown University, Providence, RI (United States); Li, Zhen, E-mail: zhen_li@brown.edu [Division of Applied Mathematics, Brown University, Providence, RI (United States); Karniadakis, George Em, E-mail: george_karniadakis@brown.edu [Division of Applied Mathematics, Brown University, Providence, RI (United States); Collaboratory on Mathematics for Mesoscopic Modeling of Materials, Pacific Northwest National Laboratory, Richland, WA 99354 (United States)
2015-09-15
Graphical abstract: - Abstract: Concurrently coupled numerical simulations using heterogeneous solvers are powerful tools for modeling multiscale phenomena. However, major modifications to existing codes are often required to enable such simulations, posing significant difficulties in practice. In this paper we present a C++ library, i.e. the Multiscale Universal Interface (MUI), which is capable of facilitating the coupling effort for a wide range of multiscale simulations. The library adopts a header-only form with minimal external dependency and hence can be easily dropped into existing codes. A data sampler concept is introduced, combined with a hybrid dynamic/static typing mechanism, to create an easily customizable framework for solver-independent data interpretation. The library integrates MPI MPMD support and an asynchronous communication protocol to handle inter-solver information exchange irrespective of the solvers' own MPI awareness. Template metaprogramming is heavily employed to simultaneously improve runtime performance and code flexibility. We validated the library by solving three different multiscale problems, which also serve to demonstrate the flexibility of the framework in handling heterogeneous models and solvers. In the first example, a Couette flow was simulated using two concurrently coupled Smoothed Particle Hydrodynamics (SPH) simulations of different spatial resolutions. In the second example, we coupled the deterministic SPH method with the stochastic Dissipative Particle Dynamics (DPD) method to study the effect of surface grafting on the hydrodynamics properties on the surface. In the third example, we consider conjugate heat transfer between a solid domain and a fluid domain by coupling the particle-based energy-conserving DPD (eDPD) method with the Finite Element Method (FEM)
Decision Engines for Software Analysis Using Satisfiability Modulo Theories Solvers
Bjorner, Nikolaj
2010-01-01
The area of software analysis, testing and verification is now undergoing a revolution thanks to the use of automated and scalable support for logical methods. A well-recognized premise is that at the core of software analysis engines is invariably a component using logical formulas for describing states and transformations between system states. The process of using this information for discovering and checking program properties (including such important properties as safety and security) amounts to automatic theorem proving. In particular, theorem provers that directly support common software constructs offer a compelling basis. Such provers are commonly called satisfiability modulo theories (SMT) solvers. Z3 is a state-of-the-art SMT solver. It is developed at Microsoft Research. It can be used to check the satisfiability of logical formulas over one or more theories such as arithmetic, bit-vectors, lists, records and arrays. The talk describes some of the technology behind modern SMT solvers, including the solver Z3. Z3 is currently mainly targeted at solving problems that arise in software analysis and verification. It has been applied to various contexts, such as systems for dynamic symbolic simulation (Pex, SAGE, Vigilante), for program verification and extended static checking (Spec#/Boggie, VCC, HAVOC), for software model checking (Yogi, SLAM), model-based design (FORMULA), security protocol code (F7), program run-time analysis and invariant generation (VS3). We will describe how it integrates support for a variety of theories that arise naturally in the context of the applications. There are several new promising avenues and the talk will touch on some of these and the challenges related to SMT solvers. Proceedings
International Nuclear Information System (INIS)
Jia, Jingfei; Kim, Hyun K.; Hielscher, Andreas H.
2015-01-01
It is well known that radiative transfer equation (RTE) provides more accurate tomographic results than its diffusion approximation (DA). However, RTE-based tomographic reconstruction codes have limited applicability in practice due to their high computational cost. In this article, we propose a new efficient method for solving the RTE forward problem with multiple light sources in an all-at-once manner instead of solving it for each source separately. To this end, we introduce here a novel linear solver called block biconjugate gradient stabilized method (block BiCGStab) that makes full use of the shared information between different right hand sides to accelerate solution convergence. Two parallelized block BiCGStab methods are proposed for additional acceleration under limited threads situation. We evaluate the performance of this algorithm with numerical simulation studies involving the Delta–Eddington approximation to the scattering phase function. The results show that the single threading block RTE solver proposed here reduces computation time by a factor of 1.5–3 as compared to the traditional sequential solution method and the parallel block solver by a factor of 1.5 as compared to the traditional parallel sequential method. This block linear solver is, moreover, independent of discretization schemes and preconditioners used; thus further acceleration and higher accuracy can be expected when combined with other existing discretization schemes or preconditioners. - Highlights: • We solve the multiple-right-hand-side problem in DOT with a block BiCGStab method. • We examine the CPU times of the block solver and the traditional sequential solver. • The block solver is faster than the sequential solver by a factor of 1.5–3.0. • Multi-threading block solvers give additional speedup under limited threads situation.
NONLINEAR MULTIGRID SOLVER EXPLOITING AMGe COARSE SPACES WITH APPROXIMATION PROPERTIES
Energy Technology Data Exchange (ETDEWEB)
Christensen, Max La Cour [Technical Univ. of Denmark, Lyngby (Denmark); Villa, Umberto E. [Univ. of Texas, Austin, TX (United States); Engsig-Karup, Allan P. [Technical Univ. of Denmark, Lyngby (Denmark); Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2016-01-22
The paper introduces a nonlinear multigrid solver for mixed nite element discretizations based on the Full Approximation Scheme (FAS) and element-based Algebraic Multigrid (AMGe). The main motivation to use FAS for unstruc- tured problems is the guaranteed approximation property of the AMGe coarse spaces that were developed recently at Lawrence Livermore National Laboratory. These give the ability to derive stable and accurate coarse nonlinear discretization problems. The previous attempts (including ones with the original AMGe method, [5, 11]), were less successful due to lack of such good approximation properties of the coarse spaces. With coarse spaces with approximation properties, our FAS approach on un- structured meshes should be as powerful/successful as FAS on geometrically re ned meshes. For comparison, Newton's method and Picard iterations with an inner state-of-the-art linear solver is compared to FAS on a nonlinear saddle point problem with applications to porous media ow. It is demonstrated that FAS is faster than Newton's method and Picard iterations for the experiments considered here. Due to the guaranteed approximation properties of our AMGe, the coarse spaces are very accurate, providing a solver with the potential for mesh-independent convergence on general unstructured meshes.
Baralea, Francesco; Minazzi, Vera
2008-10-01
The authors note that the element of sound and music has no place in the model of mental functioning bequeathed to us by Freud, which is dominated by the visual and the representational. They consider the reasons for this exclusion and its consequences, and ask whether the simple biographical explanation offered by Freud himself is acceptable. This contribution reconstructs the historical and cultural background to that exclusion, cites some relevant emblematic passages, and discusses Freud's position on music and on the aesthetic experience in general. Particular attention is devoted to the relationship between Freud and Lipps, which is important both for the originality of Lipps's thinking in the turn-of-the-century debate and for his ideas on the musical aspects of the foundations of psychic life, at which Freud 'stopped', as he himself wrote. Moreover, the shade of Lipps accompanied Freud throughout his scientific career from 1898 to 1938. Like all foundations, that of psychoanalysis was shaped by a system of inclusions and exclusions. The exclusion of the element of sound and music is understandable in view of the cultural background to the development of the concepts of the representational unconscious and infantile sexuality. While the consequences have been far reaching, the knowledge accumulated since that exclusion enables us to resume, albeit on a different basis, the composition of the 'unfinished symphony' of the relationship between psychoanalysis and music.
The impact of improved sparse linear solvers on industrial engineering applications
Energy Technology Data Exchange (ETDEWEB)
Heroux, M. [Cray Research, Inc., Eagan, MN (United States); Baddourah, M.; Poole, E.L.; Yang, Chao Wu
1996-12-31
There are usually many factors that ultimately determine the quality of computer simulation for engineering applications. Some of the most important are the quality of the analytical model and approximation scheme, the accuracy of the input data and the capability of the computing resources. However, in many engineering applications the characteristics of the sparse linear solver are the key factors in determining how complex a problem a given application code can solve. Therefore, the advent of a dramatically improved solver often brings with it dramatic improvements in our ability to do accurate and cost effective computer simulations. In this presentation we discuss the current status of sparse iterative and direct solvers in several key industrial CFD and structures codes, and show the impact that recent advances in linear solvers have made on both our ability to perform challenging simulations and the cost of those simulations. We also present some of the current challenges we have and the constraints we face in trying to improve these solvers. Finally, we discuss future requirements for sparse linear solvers on high performance architectures and try to indicate the opportunities that exist if we can develop even more improvements in linear solver capabilities.
DEFF Research Database (Denmark)
Trento, Stefano; Götzen, Amalia De
2011-01-01
This paper is an initial attempt to study the world of sound effects for motion pictures, also known as Foley sounds. Throughout several audio and audio-video tests we have compared both Foley and real sounds originated by an identical action. The main purpose was to evaluate if sound effects...
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)
Newton-Krylov-BDDC solvers for nonlinear cardiac mechanics
Pavarino, L.F.; Scacchi, S.; Zampini, Stefano
2015-01-01
The aim of this work is to design and study a Balancing Domain Decomposition by Constraints (BDDC) solver for the nonlinear elasticity system modeling the mechanical deformation of cardiac tissue. The contraction–relaxation process in the myocardium is induced by the generation and spread of the bioelectrical excitation throughout the tissue and it is mathematically described by the coupling of cardiac electro-mechanical models consisting of systems of partial and ordinary differential equations. In this study, the discretization of the electro-mechanical models is performed by Q1 finite elements in space and semi-implicit finite difference schemes in time, leading to the solution of a large-scale linear system for the bioelectrical potentials and a nonlinear system for the mechanical deformation at each time step of the simulation. The parallel mechanical solver proposed in this paper consists in solving the nonlinear system with a Newton-Krylov-BDDC method, based on the parallel solution of local mechanical problems and a coarse problem for the so-called primal unknowns. Three-dimensional parallel numerical tests on different machines show that the proposed parallel solver is scalable in the number of subdomains, quasi-optimal in the ratio of subdomain to mesh sizes, and robust with respect to tissue anisotropy.
Newton-Krylov-BDDC solvers for nonlinear cardiac mechanics
Pavarino, L.F.
2015-07-18
The aim of this work is to design and study a Balancing Domain Decomposition by Constraints (BDDC) solver for the nonlinear elasticity system modeling the mechanical deformation of cardiac tissue. The contraction–relaxation process in the myocardium is induced by the generation and spread of the bioelectrical excitation throughout the tissue and it is mathematically described by the coupling of cardiac electro-mechanical models consisting of systems of partial and ordinary differential equations. In this study, the discretization of the electro-mechanical models is performed by Q1 finite elements in space and semi-implicit finite difference schemes in time, leading to the solution of a large-scale linear system for the bioelectrical potentials and a nonlinear system for the mechanical deformation at each time step of the simulation. The parallel mechanical solver proposed in this paper consists in solving the nonlinear system with a Newton-Krylov-BDDC method, based on the parallel solution of local mechanical problems and a coarse problem for the so-called primal unknowns. Three-dimensional parallel numerical tests on different machines show that the proposed parallel solver is scalable in the number of subdomains, quasi-optimal in the ratio of subdomain to mesh sizes, and robust with respect to tissue anisotropy.
IGA-ADS: Isogeometric analysis FEM using ADS solver
Łoś, Marcin M.; Woźniak, Maciej; Paszyński, Maciej; Lenharth, Andrew; Hassaan, Muhamm Amber; Pingali, Keshav
2017-08-01
In this paper we present a fast explicit solver for solution of non-stationary problems using L2 projections with isogeometric finite element method. The solver has been implemented within GALOIS framework. It enables parallel multi-core simulations of different time-dependent problems, in 1D, 2D, or 3D. We have prepared the solver framework in a way that enables direct implementation of the selected PDE and corresponding boundary conditions. In this paper we describe the installation, implementation of exemplary three PDEs, and execution of the simulations on multi-core Linux cluster nodes. We consider three case studies, including heat transfer, linear elasticity, as well as non-linear flow in heterogeneous media. The presented package generates output suitable for interfacing with Gnuplot and ParaView visualization software. The exemplary simulations show near perfect scalability on Gilbert shared-memory node with four Intel® Xeon® CPU E7-4860 processors, each possessing 10 physical cores (for a total of 40 cores).
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 distributed-memory hierarchical solver for general sparse linear systems
Energy Technology Data Exchange (ETDEWEB)
Chen, Chao [Stanford Univ., CA (United States). Inst. for Computational and Mathematical Engineering; Pouransari, Hadi [Stanford Univ., CA (United States). Dept. of Mechanical Engineering; Rajamanickam, Sivasankaran [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Center for Computing Research; Boman, Erik G. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Center for Computing Research; Darve, Eric [Stanford Univ., CA (United States). Inst. for Computational and Mathematical Engineering and Dept. of Mechanical Engineering
2017-12-20
We present a parallel hierarchical solver for general sparse linear systems on distributed-memory machines. For large-scale problems, this fully algebraic algorithm is faster and more memory-efficient than sparse direct solvers because it exploits the low-rank structure of fill-in blocks. Depending on the accuracy of low-rank approximations, the hierarchical solver can be used either as a direct solver or as a preconditioner. The parallel algorithm is based on data decomposition and requires only local communication for updating boundary data on every processor. Moreover, the computation-to-communication ratio of the parallel algorithm is approximately the volume-to-surface-area ratio of the subdomain owned by every processor. We also provide various numerical results to demonstrate the versatility and scalability of the parallel algorithm.
DEFF Research Database (Denmark)
Grimshaw, Mark; Garner, Tom Alexander
2014-01-01
We make the case in this essay that sound that is imagined is both a perception and as much a sound as that perceived through external stimulation. To argue this, we look at the evidence from auditory science, neuroscience, and philosophy, briefly present some new conceptual thinking on sound...... that accounts for this view, and then use this to look at what the future might hold in the context of imagining sound and developing technology....
Nonlinear multigrid solvers exploiting AMGe coarse spaces with approximation properties
DEFF Research Database (Denmark)
Christensen, Max la Cour; Vassilevski, Panayot S.; Villa, Umberto
2017-01-01
discretizations on general unstructured grids for a large class of nonlinear partial differential equations, including saddle point problems. The approximation properties of the coarse spaces ensure that our FAS approach for general unstructured meshes leads to optimal mesh-independent convergence rates similar...... to those achieved by geometric FAS on a nested hierarchy of refined meshes. In the numerical results, Newton’s method and Picard iterations with state-of-the-art inner linear solvers are compared to our FAS algorithm for the solution of a nonlinear saddle point problem arising from porous media flow...
NITSOL: A Newton iterative solver for nonlinear systems
Energy Technology Data Exchange (ETDEWEB)
Pernice, M. [Univ. of Utah, Salt Lake City, UT (United States); Walker, H.F. [Utah State Univ., Logan, UT (United States)
1996-12-31
Newton iterative methods, also known as truncated Newton methods, are implementations of Newton`s method in which the linear systems that characterize Newton steps are solved approximately using iterative linear algebra methods. Here, we outline a well-developed Newton iterative algorithm together with a Fortran implementation called NITSOL. The basic algorithm is an inexact Newton method globalized by backtracking, in which each initial trial step is determined by applying an iterative linear solver until an inexact Newton criterion is satisfied. In the implementation, the user can specify inexact Newton criteria in several ways and select an iterative linear solver from among several popular {open_quotes}transpose-free{close_quotes} Krylov subspace methods. Jacobian-vector products used by the Krylov solver can be either evaluated analytically with a user-supplied routine or approximated using finite differences of function values. A flexible interface permits a wide variety of preconditioning strategies and allows the user to define a preconditioner and optionally update it periodically. We give details of these and other features and demonstrate the performance of the implementation on a representative set of test problems.
Abramovich, S.
2014-01-01
The availability of sophisticated computer programs such as "Wolfram Alpha" has made many problems found in the secondary mathematics curriculum somewhat obsolete for they can be easily solved by the software. Against this background, an interplay between the power of a modern tool of technology and educational constraints it presents is…
Matlab Geochemistry: An open source geochemistry solver based on MRST
McNeece, C. J.; Raynaud, X.; Nilsen, H.; Hesse, M. A.
2017-12-01
The study of geological systems often requires the solution of complex geochemical relations. To address this need we present an open source geochemical solver based on the Matlab Reservoir Simulation Toolbox (MRST) developed by SINTEF. The implementation supports non-isothermal multicomponent aqueous complexation, surface complexation, ion exchange, and dissolution/precipitation reactions. The suite of tools available in MRST allows for rapid model development, in particular the incorporation of geochemical calculations into transport simulations of multiple phases, complex domain geometry and geomechanics. Different numerical schemes and additional physics can be easily incorporated into the existing tools through the object-oriented framework employed by MRST. The solver leverages the automatic differentiation tools available in MRST to solve arbitrarily complex geochemical systems with any choice of species or element concentration as input. Four mathematical approaches enable the solver to be quite robust: 1) the choice of chemical elements as the basis components makes all entries in the composition matrix positive thus preserving convexity, 2) a log variable transformation is used which transfers the nonlinearity to the convex composition matrix, 3) a priori bounds on variables are calculated from the structure of the problem, constraining Netwon's path and 4) an initial guess is calculated implicitly by sequentially adding model complexity. As a benchmark we compare the model to experimental and semi-analytic solutions of the coupled salinity-acidity transport system. Together with the reservoir simulation capabilities of MRST the solver offers a promising tool for geochemical simulations in reservoir domains for applications in a diversity of fields from enhanced oil recovery to radionuclide storage.
A robust multilevel simultaneous eigenvalue solver
Costiner, Sorin; Taasan, Shlomo
1993-01-01
Multilevel (ML) algorithms for eigenvalue problems are often faced with several types of difficulties such as: the mixing of approximated eigenvectors by the solution process, the approximation of incomplete clusters of eigenvectors, the poor representation of solution on coarse levels, and the existence of close or equal eigenvalues. Algorithms that do not treat appropriately these difficulties usually fail, or their performance degrades when facing them. These issues motivated the development of a robust adaptive ML algorithm which treats these difficulties, for the calculation of a few eigenvectors and their corresponding eigenvalues. The main techniques used in the new algorithm include: the adaptive completion and separation of the relevant clusters on different levels, the simultaneous treatment of solutions within each cluster, and the robustness tests which monitor the algorithm's efficiency and convergence. The eigenvectors' separation efficiency is based on a new ML projection technique generalizing the Rayleigh Ritz projection, combined with a technique, the backrotations. These separation techniques, when combined with an FMG formulation, in many cases lead to algorithms of O(qN) complexity, for q eigenvectors of size N on the finest level. Previously developed ML algorithms are less focused on the mentioned difficulties. Moreover, algorithms which employ fine level separation techniques are of O(q(sub 2)N) complexity and usually do not overcome all these difficulties. Computational examples are presented where Schrodinger type eigenvalue problems in 2-D and 3-D, having equal and closely clustered eigenvalues, are solved with the efficiency of the Poisson multigrid solver. A second order approximation is obtained in O(qN) work, where the total computational work is equivalent to only a few fine level relaxations per eigenvector.
Accelerated Cyclic Reduction: A Distributed-Memory Fast Solver for Structured Linear Systems
Chávez, Gustavo
2017-12-15
We present Accelerated Cyclic Reduction (ACR), a distributed-memory fast solver for rank-compressible block tridiagonal linear systems arising from the discretization of elliptic operators, developed here for three dimensions. Algorithmic synergies between Cyclic Reduction and hierarchical matrix arithmetic operations result in a solver that has O(kNlogN(logN+k2)) arithmetic complexity and O(k Nlog N) memory footprint, where N is the number of degrees of freedom and k is the rank of a block in the hierarchical approximation, and which exhibits substantial concurrency. We provide a baseline for performance and applicability by comparing with the multifrontal method with and without hierarchical semi-separable matrices, with algebraic multigrid and with the classic cyclic reduction method. Over a set of large-scale elliptic systems with features of nonsymmetry and indefiniteness, the robustness of the direct solvers extends beyond that of the multigrid solver, and relative to the multifrontal approach ACR has lower or comparable execution time and size of the factors, with substantially lower numerical ranks. ACR exhibits good strong and weak scaling in a distributed context and, as with any direct solver, is advantageous for problems that require the solution of multiple right-hand sides. Numerical experiments show that the rank k patterns are of O(1) for the Poisson equation and of O(n) for the indefinite Helmholtz equation. The solver is ideal in situations where low-accuracy solutions are sufficient, or otherwise as a preconditioner within an iterative method.
Accelerated Cyclic Reduction: A Distributed-Memory Fast Solver for Structured Linear Systems
Chá vez, Gustavo; Turkiyyah, George; Zampini, Stefano; Ltaief, Hatem; Keyes, David E.
2017-01-01
We present Accelerated Cyclic Reduction (ACR), a distributed-memory fast solver for rank-compressible block tridiagonal linear systems arising from the discretization of elliptic operators, developed here for three dimensions. Algorithmic synergies between Cyclic Reduction and hierarchical matrix arithmetic operations result in a solver that has O(kNlogN(logN+k2)) arithmetic complexity and O(k Nlog N) memory footprint, where N is the number of degrees of freedom and k is the rank of a block in the hierarchical approximation, and which exhibits substantial concurrency. We provide a baseline for performance and applicability by comparing with the multifrontal method with and without hierarchical semi-separable matrices, with algebraic multigrid and with the classic cyclic reduction method. Over a set of large-scale elliptic systems with features of nonsymmetry and indefiniteness, the robustness of the direct solvers extends beyond that of the multigrid solver, and relative to the multifrontal approach ACR has lower or comparable execution time and size of the factors, with substantially lower numerical ranks. ACR exhibits good strong and weak scaling in a distributed context and, as with any direct solver, is advantageous for problems that require the solution of multiple right-hand sides. Numerical experiments show that the rank k patterns are of O(1) for the Poisson equation and of O(n) for the indefinite Helmholtz equation. The solver is ideal in situations where low-accuracy solutions are sufficient, or otherwise as a preconditioner within an iterative method.
Parallelization of the preconditioned IDR solver for modern multicore computer systems
Bessonov, O. A.; Fedoseyev, A. I.
2012-10-01
This paper present the analysis, parallelization and optimization approach for the large sparse matrix solver CNSPACK for modern multicore microprocessors. CNSPACK is an advanced solver successfully used for coupled solution of stiff problems arising in multiphysics applications such as CFD, semiconductor transport, kinetic and quantum problems. It employs iterative IDR algorithm with ILU preconditioning (user chosen ILU preconditioning order). CNSPACK has been successfully used during last decade for solving problems in several application areas, including fluid dynamics and semiconductor device simulation. However, there was a dramatic change in processor architectures and computer system organization in recent years. Due to this, performance criteria and methods have been revisited, together with involving the parallelization of the solver and preconditioner using Open MP environment. Results of the successful implementation for efficient parallelization are presented for the most advances computer system (Intel Core i7-9xx or two-processor Xeon 55xx/56xx).
Domain decomposition solvers for nonlinear multiharmonic finite element equations
Copeland, D. M.
2010-01-01
In many practical applications, for instance, in computational electromagnetics, the excitation is time-harmonic. Switching from the time domain to the frequency domain allows us to replace the expensive time-integration procedure by the solution of a simple elliptic equation for the amplitude. This is true for linear problems, but not for nonlinear problems. However, due to the periodicity of the solution, we can expand the solution in a Fourier series. Truncating this Fourier series and approximating the Fourier coefficients by finite elements, we arrive at a large-scale coupled nonlinear system for determining the finite element approximation to the Fourier coefficients. The construction of fast solvers for such systems is very crucial for the efficiency of this multiharmonic approach. In this paper we look at nonlinear, time-harmonic potential problems as simple model problems. We construct and analyze almost optimal solvers for the Jacobi systems arising from the Newton linearization of the large-scale coupled nonlinear system that one has to solve instead of performing the expensive time-integration procedure. © 2010 de Gruyter.
Directory of Open Access Journals (Sweden)
Robert SZABO
2011-12-01
Full Text Available The dispersion relations, appearing in the analysis of the stability of a gas flow in a straight acoustically-lined duct with respect to perturbations produced by a time harmonic source, beside the wave number and complex frequency contain the solution of a boundary value problem of the Pridmore-Brown equation depending on the wave number and frequency. For this reason, in practice the dispersion relations are rarely simple enough for carried out the zeros. The determination of zeros of these dispersion relations is crucial for the prediction of the perturbation attenuation or amplification. In this paper an approximation of the dispersion relations is given. Our approach preserves the general character of the mean flow, the general Pridmore-Brown equation and it’s only in the shear flow that we replace the exact solution of the boundary value problem with its Taylor polynomial approximate. In this way new approximate dispersion relations are obtained which zero’s can be found by computer.
DEFF Research Database (Denmark)
Knakkergaard, Martin
2016-01-01
This article discusses the change in premise that digitally produced sound brings about and how digital technologies more generally have changed our relationship to the musical artifact, not simply in degree but in kind. It demonstrates how our acoustical conceptions are thoroughly challenged...... by the digital production of sound and, by questioning the ontological basis for digital sound, turns our understanding of the core term substance upside down....
Fuchs, H. V.; Möser, M.
Sound absorption indicates the transformation of sound energy into heat. It is, for instance, employed to design the acoustics in rooms. The noise emitted by machinery and plants shall be reduced before arriving at a workplace; auditoria such as lecture rooms or concert halls require a certain reverberation time. Such design goals are realised by installing absorbing components at the walls with well-defined absorption characteristics, which are adjusted for corresponding demands. Sound absorbers also play an important role in acoustic capsules, ducts and screens to avoid sound immission from noise intensive environments into the neighbourhood.
Domain decomposed preconditioners with Krylov subspace methods as subdomain solvers
Energy Technology Data Exchange (ETDEWEB)
Pernice, M. [Univ. of Utah, Salt Lake City, UT (United States)
1994-12-31
Domain decomposed preconditioners for nonsymmetric partial differential equations typically require the solution of problems on the subdomains. Most implementations employ exact solvers to obtain these solutions. Consequently work and storage requirements for the subdomain problems grow rapidly with the size of the subdomain problems. Subdomain solves constitute the single largest computational cost of a domain decomposed preconditioner, and improving the efficiency of this phase of the computation will have a significant impact on the performance of the overall method. The small local memory available on the nodes of most message-passing multicomputers motivates consideration of the use of an iterative method for solving subdomain problems. For large-scale systems of equations that are derived from three-dimensional problems, memory considerations alone may dictate the need for using iterative methods for the subdomain problems. In addition to reduced storage requirements, use of an iterative solver on the subdomains allows flexibility in specifying the accuracy of the subdomain solutions. Substantial savings in solution time is possible if the quality of the domain decomposed preconditioner is not degraded too much by relaxing the accuracy of the subdomain solutions. While some work in this direction has been conducted for symmetric problems, similar studies for nonsymmetric problems appear not to have been pursued. This work represents a first step in this direction, and explores the effectiveness of performing subdomain solves using several transpose-free Krylov subspace methods, GMRES, transpose-free QMR, CGS, and a smoothed version of CGS. Depending on the difficulty of the subdomain problem and the convergence tolerance used, a reduction in solution time is possible in addition to the reduced memory requirements. The domain decomposed preconditioner is a Schur complement method in which the interface operators are approximated using interface probing.
A high-performance Riccati based solver for tree-structured quadratic programs
DEFF Research Database (Denmark)
Frison, Gianluca; Kouzoupis, Dimitris; Diehl, Moritz
2017-01-01
the online solution of such problems challenging and the development of tailored solvers crucial. In this paper, an interior point method is presented that can solve Quadratic Programs (QPs) arising in multi-stage MPC efficiently by means of a tree-structured Riccati recursion and a high-performance linear...... algebra library. A performance comparison with code-generated and general purpose sparse QP solvers shows that the computation times can be significantly reduced for all problem sizes that are practically relevant in embedded MPC applications. The presented implementation is freely available as part...
Collier, Nathan; Pardo, David; Dalcí n, Lisandro D.; Paszyński, Maciej R.; Calo, Victor M.
2012-01-01
We study the performance of direct solvers on linear systems of equations resulting from isogeometric analysis. The problem of choice is the canonical Laplace equation in three dimensions. From this study we conclude that for a fixed number of unknowns and polynomial degree of approximation, a higher degree of continuity k drastically increases the CPU time and RAM needed to solve the problem when using a direct solver. This paper presents numerical results detailing the phenomenon as well as a theoretical analysis that explains the underlying cause. © 2011 Elsevier B.V.
Collier, Nathan
2012-03-01
We study the performance of direct solvers on linear systems of equations resulting from isogeometric analysis. The problem of choice is the canonical Laplace equation in three dimensions. From this study we conclude that for a fixed number of unknowns and polynomial degree of approximation, a higher degree of continuity k drastically increases the CPU time and RAM needed to solve the problem when using a direct solver. This paper presents numerical results detailing the phenomenon as well as a theoretical analysis that explains the underlying cause. © 2011 Elsevier B.V.
A Parallel Algebraic Multigrid Solver on Graphics Processing Units
Haase, Gundolf
2010-01-01
The paper presents a multi-GPU implementation of the preconditioned conjugate gradient algorithm with an algebraic multigrid preconditioner (PCG-AMG) for an elliptic model problem on a 3D unstructured grid. An efficient parallel sparse matrix-vector multiplication scheme underlying the PCG-AMG algorithm is presented for the many-core GPU architecture. A performance comparison of the parallel solver shows that a singe Nvidia Tesla C1060 GPU board delivers the performance of a sixteen node Infiniband cluster and a multi-GPU configuration with eight GPUs is about 100 times faster than a typical server CPU core. © 2010 Springer-Verlag.
Modelo de selección de cartera con Solver
Directory of Open Access Journals (Sweden)
P. Fogués Zornoza
2012-04-01
Full Text Available In this paper, we present an example of linear optimization in the context of degrees in Economics or Business Administration and Management. We show techniques that enable students to go deep and investigate in real problems that have been modelled using the Excel platform. The model shown here has been developed by a student and it consists in minimizing the absolute deviations over the average expected return of a portfolio of securities, using the solver tool that it is included in this software.
Using SPARK as a Solver for Modelica
Energy Technology Data Exchange (ETDEWEB)
Wetter, Michael; Wetter, Michael; Haves, Philip; Moshier, Michael A.; Sowell, Edward F.
2008-06-30
Modelica is an object-oriented acausal modeling language that is well positioned to become a de-facto standard for expressing models of complex physical systems. To simulate a model expressed in Modelica, it needs to be translated into executable code. For generating run-time efficient code, such a translation needs to employ algebraic formula manipulations. As the SPARK solver has been shown to be competitive for generating such code but currently cannot be used with the Modelica language, we report in this paper how SPARK's symbolic and numerical algorithms can be implemented in OpenModelica, an open-source implementation of a Modelica modeling and simulation environment. We also report benchmark results that show that for our air flow network simulation benchmark, the SPARK solver is competitive with Dymola, which is believed to provide the best solver for Modelica.
New iterative solvers for the NAG Libraries
Energy Technology Data Exchange (ETDEWEB)
Salvini, S.; Shaw, G. [Numerical Algorithms Group Ltd., Oxford (United Kingdom)
1996-12-31
The purpose of this paper is to introduce the work which has been carried out at NAG Ltd to update the iterative solvers for sparse systems of linear equations, both symmetric and unsymmetric, in the NAG Fortran 77 Library. Our current plans to extend this work and include it in our other numerical libraries in our range are also briefly mentioned. We have added to the Library the new Chapter F11, entirely dedicated to sparse linear algebra. At Mark 17, the F11 Chapter includes sparse iterative solvers, preconditioners, utilities and black-box routines for sparse symmetric (both positive-definite and indefinite) linear systems. Mark 18 will add solvers, preconditioners, utilities and black-boxes for sparse unsymmetric systems: the development of these has already been completed.
s-Step Krylov Subspace Methods as Bottom Solvers for Geometric Multigrid
Energy Technology Data Exchange (ETDEWEB)
Williams, Samuel [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Lijewski, Mike [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Almgren, Ann [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Straalen, Brian Van [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Carson, Erin [Univ. of California, Berkeley, CA (United States); Knight, Nicholas [Univ. of California, Berkeley, CA (United States); Demmel, James [Univ. of California, Berkeley, CA (United States)
2014-08-14
Geometric multigrid solvers within adaptive mesh refinement (AMR) applications often reach a point where further coarsening of the grid becomes impractical as individual sub domain sizes approach unity. At this point the most common solution is to use a bottom solver, such as BiCGStab, to reduce the residual by a fixed factor at the coarsest level. Each iteration of BiCGStab requires multiple global reductions (MPI collectives). As the number of BiCGStab iterations required for convergence grows with problem size, and the time for each collective operation increases with machine scale, bottom solves in large-scale applications can constitute a significant fraction of the overall multigrid solve time. In this paper, we implement, evaluate, and optimize a communication-avoiding s-step formulation of BiCGStab (CABiCGStab for short) as a high-performance, distributed-memory bottom solver for geometric multigrid solvers. This is the first time s-step Krylov subspace methods have been leveraged to improve multigrid bottom solver performance. We use a synthetic benchmark for detailed analysis and integrate the best implementation into BoxLib in order to evaluate the benefit of a s-step Krylov subspace method on the multigrid solves found in the applications LMC and Nyx on up to 32,768 cores on the Cray XE6 at NERSC. Overall, we see bottom solver improvements of up to 4.2x on synthetic problems and up to 2.7x in real applications. This results in as much as a 1.5x improvement in solver performance in real applications.
Berkhoff, Arthur P.
2008-01-01
A sound generator, particularly a loudspeaker, configured to emit sound, comprising a rigid element (2) enclosing a plurality of air compartments (3), wherein the rigid element (2) has a back side (B) comprising apertures (4), and a front side (F) that is closed, wherein the generator is provided
Berkhoff, Arthur P.
2010-01-01
A sound generator, particularly a loudspeaker, configured to emit sound, comprising a rigid element (2) enclosing a plurality of air compartments (3), wherein the rigid element (2) has a back side (B) comprising apertures (4), and a front side (F) that is closed, wherein the generator is provided
Berkhoff, Arthur P.
2007-01-01
A sound generator, particularly a loudspeaker, configured to emit sound, comprising a rigid element (2) enclosing a plurality of air compartments (3), wherein the rigid element (2) has a back side (B) comprising apertures (4), and a front side (F) that is closed, wherein the generator is provided
Fast Multipole-Based Elliptic PDE Solver and Preconditioner
Ibeid, Huda
2016-12-07
Exascale systems are predicted to have approximately one billion cores, assuming Gigahertz cores. Limitations on affordable network topologies for distributed memory systems of such massive scale bring new challenges to the currently dominant parallel programing model. Currently, there are many efforts to evaluate the hardware and software bottlenecks of exascale designs. It is therefore of interest to model application performance and to understand what changes need to be made to ensure extrapolated scalability. Fast multipole methods (FMM) were originally developed for accelerating N-body problems for particle-based methods in astrophysics and molecular dynamics. FMM is more than an N-body solver, however. Recent efforts to view the FMM as an elliptic PDE solver have opened the possibility to use it as a preconditioner for even a broader range of applications. In this thesis, we (i) discuss the challenges for FMM on current parallel computers and future exascale architectures, with a focus on inter-node communication, and develop a performance model that considers the communication patterns of the FMM for spatially quasi-uniform distributions, (ii) employ this performance model to guide performance and scaling improvement of FMM for all-atom molecular dynamics simulations of uniformly distributed particles, and (iii) demonstrate that, beyond its traditional use as a solver in problems for which explicit free-space kernel representations are available, the FMM has applicability as a preconditioner in finite domain elliptic boundary value problems, by equipping it with boundary integral capability for satisfying conditions at finite boundaries and by wrapping it in a Krylov method for extensibility to more general operators. Compared with multilevel methods, FMM is capable of comparable algebraic convergence rates down to the truncation error of the discretized PDE, and it has superior multicore and distributed memory scalability properties on commodity
An Extensive Evaluation of Portfolio Approaches for Constraint Satisfaction Problems
Directory of Open Access Journals (Sweden)
Roberto Amadini
2016-06-01
Full Text Available In the context of Constraint Programming, a portfolio approach exploits the complementary strengths of a portfolio of different constraint solvers. The goal is to predict and run the best solver(s of the portfolio for solving a new, unseen problem. In this work we reproduce, simulate, and evaluate the performance of different portfolio approaches on extensive benchmarks of Constraint Satisfaction Problems. Empirical results clearly show the benefits of portfolio solvers in terms of both solved instances and solving time.
Energy Technology Data Exchange (ETDEWEB)
Bordner, J.; Saied, F. [Univ. of Illinois, Urbana, IL (United States)
1996-12-31
GLab3D is an enhancement of an interactive environment (MGLab) for experimenting with iterative solvers and multigrid algorithms. It is implemented in MATLAB. The new version has built-in 3D elliptic pde`s and several iterative methods and preconditioners that were not available in the original version. A sparse direct solver option has also been included. The multigrid solvers have also been extended to 3D. The discretization and pde domains are restricted to standard finite differences on the unit square/cube. The power of this software studies in the fact that no programming is needed to solve, for example, the convection-diffusion equation in 3D with TFQMR and a customized V-cycle preconditioner, for a variety of problem sizes and mesh Reynolds, numbers. In addition to the graphical user interface, some sample drivers are included to show how experiments can be composed using the underlying suite of problems and solvers.
Fast Multipole-Based Preconditioner for Sparse Iterative Solvers
Ibeid, Huda; Yokota, Rio; Keyes, David E.
2014-01-01
Among optimal hierarchical algorithms for the computational solution of elliptic problems, the Fast Multipole Method (FMM) stands out for its adaptability to emerging architectures, having high arithmetic intensity, tunable accuracy, and relaxed global synchronization requirements. We demonstrate that, beyond its traditional use as a solver in problems for which explicit free-space kernel representations are available, the FMM has applicability as a preconditioner in finite domain elliptic boundary value problems, by equipping it with boundary integral capability for finite boundaries and by wrapping it in a Krylov method for extensibility to more general operators. Compared with multilevel methods, it is capable of comparable algebraic convergence rates down to the truncation error of the discretized PDE, and it has superior multicore and distributed memory scalability properties on commodity architecture supercomputers.
Fast Multipole-Based Preconditioner for Sparse Iterative Solvers
Ibeid, Huda
2014-05-04
Among optimal hierarchical algorithms for the computational solution of elliptic problems, the Fast Multipole Method (FMM) stands out for its adaptability to emerging architectures, having high arithmetic intensity, tunable accuracy, and relaxed global synchronization requirements. We demonstrate that, beyond its traditional use as a solver in problems for which explicit free-space kernel representations are available, the FMM has applicability as a preconditioner in finite domain elliptic boundary value problems, by equipping it with boundary integral capability for finite boundaries and by wrapping it in a Krylov method for extensibility to more general operators. Compared with multilevel methods, it is capable of comparable algebraic convergence rates down to the truncation error of the discretized PDE, and it has superior multicore and distributed memory scalability properties on commodity architecture supercomputers.
DEFF Research Database (Denmark)
Møller, Martin Bo; Olsen, Martin
2017-01-01
Sound zones, i.e. spatially confined regions of individual audio content, can be created by appropriate filtering of the desired audio signals reproduced by an array of loudspeakers. The challenge of designing filters for sound zones is twofold: First, the filtered responses should generate...... an acoustic separation between the control regions. Secondly, the pre- and post-ringing as well as spectral deterioration introduced by the filters should be minimized. The tradeoff between acoustic separation and filter ringing is the focus of this paper. A weighted L2-norm penalty is introduced in the sound...
Application of alternating decision trees in selecting sparse linear solvers
Bhowmick, Sanjukta; Eijkhout, Victor; Freund, Yoav; Fuentes, Erika; Keyes, David E.
2010-01-01
The solution of sparse linear systems, a fundamental and resource-intensive task in scientific computing, can be approached through multiple algorithms. Using an algorithm well adapted to characteristics of the task can significantly enhance the performance, such as reducing the time required for the operation, without compromising the quality of the result. However, the best solution method can vary even across linear systems generated in course of the same PDE-based simulation, thereby making solver selection a very challenging problem. In this paper, we use a machine learning technique, Alternating Decision Trees (ADT), to select efficient solvers based on the properties of sparse linear systems and runtime-dependent features, such as the stages of simulation. We demonstrate the effectiveness of this method through empirical results over linear systems drawn from computational fluid dynamics and magnetohydrodynamics applications. The results also demonstrate that using ADT can resolve the problem of over-fitting, which occurs when limited amount of data is available. © 2010 Springer Science+Business Media LLC.
Iterative linear solvers in a 2D radiation-hydrodynamics code: Methods and performance
International Nuclear Information System (INIS)
Baldwin, C.; Brown, P.N.; Falgout, R.; Graziani, F.; Jones, J.
1999-01-01
Computer codes containing both hydrodynamics and radiation play a central role in simulating both astrophysical and inertial confinement fusion (ICF) phenomena. A crucial aspect of these codes is that they require an implicit solution of the radiation diffusion equations. The authors present in this paper the results of a comparison of five different linear solvers on a range of complex radiation and radiation-hydrodynamics problems. The linear solvers used are diagonally scaled conjugate gradient, GMRES with incomplete LU preconditioning, conjugate gradient with incomplete Cholesky preconditioning, multigrid, and multigrid-preconditioned conjugate gradient. These problems involve shock propagation, opacities varying over 5--6 orders of magnitude, tabular equations of state, and dynamic ALE (Arbitrary Lagrangian Eulerian) meshes. They perform a problem size scalability study by comparing linear solver performance over a wide range of problem sizes from 1,000 to 100,000 zones. The fundamental question they address in this paper is: Is it more efficient to invert the matrix in many inexpensive steps (like diagonally scaled conjugate gradient) or in fewer expensive steps (like multigrid)? In addition, what is the answer to this question as a function of problem size and is the answer problem dependent? They find that the diagonally scaled conjugate gradient method performs poorly with the growth of problem size, increasing in both iteration count and overall CPU time with the size of the problem and also increasing for larger time steps. For all problems considered, the multigrid algorithms scale almost perfectly (i.e., the iteration count is approximately independent of problem size and problem time step). For pure radiation flow problems (i.e., no hydrodynamics), they see speedups in CPU time of factors of ∼15--30 for the largest problems, when comparing the multigrid solvers relative to diagonal scaled conjugate gradient
Extending the Finite Domain Solver of GNU Prolog
Bloemen, Vincent; Diaz, Daniel; van der Bijl, Machiel; Abreu, Salvador; Ströder, Thomas; Swift, Terrance
This paper describes three significant extensions for the Finite Domain solver of GNU Prolog. First, the solver now supports negative integers. Second, the solver detects and prevents integer overflows from occurring. Third, the internal representation of sparse domains has been redesigned to
DEFF Research Database (Denmark)
Crocker, Malcolm J.; Jacobsen, Finn
1998-01-01
This chapter is an overview, intended for readers with no special knowledge about this particular topic. The chapter deals with all aspects of sound intensity and its measurement from the fundamental theoretical background to practical applications of the measurement technique.......This chapter is an overview, intended for readers with no special knowledge about this particular topic. The chapter deals with all aspects of sound intensity and its measurement from the fundamental theoretical background to practical applications of the measurement technique....
DEFF Research Database (Denmark)
Crocker, M.J.; Jacobsen, Finn
1997-01-01
This chapter is an overview, intended for readers with no special knowledge about this particular topic. The chapter deals with all aspects of sound intensity and its measurement from the fundamental theoretical background to practical applications of the measurement technique.......This chapter is an overview, intended for readers with no special knowledge about this particular topic. The chapter deals with all aspects of sound intensity and its measurement from the fundamental theoretical background to practical applications of the measurement technique....
High-performance small-scale solvers for linear Model Predictive Control
DEFF Research Database (Denmark)
Frison, Gianluca; Sørensen, Hans Henrik Brandenborg; Dammann, Bernd
2014-01-01
, with the two main research areas of explicit MPC and tailored on-line MPC. State-of-the-art solvers in this second class can outperform optimized linear-algebra libraries (BLAS) only for very small problems, and do not explicitly exploit the hardware capabilities, relying on compilers for that. This approach...
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
Balancing Energy and Performance in Dense Linear System Solvers for Hybrid ARM+GPU platforms
Directory of Open Access Journals (Sweden)
Juan P. Silva
2016-04-01
Full Text Available The high performance computing community has traditionally focused uniquely on the reduction of execution time, though in the last years, the optimization of energy consumption has become a main issue. A reduction of energy usage without a degradation of performance requires the adoption of energy-efficient hardware platforms accompanied by the development of energy-aware algorithms and computational kernels. The solution of linear systems is a key operation for many scientific and engineering problems. Its relevance has motivated an important amount of work, and consequently, it is possible to find high performance solvers for a wide variety of hardware platforms. In this work, we aim to develop a high performance and energy-efficient linear system solver. In particular, we develop two solvers for a low-power CPU-GPU platform, the NVIDIA Jetson TK1. These solvers implement the Gauss-Huard algorithm yielding an efficient usage of the target hardware as well as an efficient memory access. The experimental evaluation shows that the novel proposal reports important savings in both time and energy-consumption when compared with the state-of-the-art solvers of the platform.
Lin, John J. H.; Lin, Sunny S. J.
2018-01-01
To deepen our understanding of those aspects of problems that cause the most difficulty for solvers, this study integrated eye-tracking with handwriting devices to investigate problem solvers' online processes while solving geometry problems. We are interested in whether the difference between successful and unsuccessful solvers can be identified…
Yihaa Roodhiyah, Lisa’; Tjong, Tiffany; Nurhasan; Sutarno, D.
2018-04-01
The late research, linear matrices of vector finite element in two dimensional(2-D) magnetotelluric (MT) responses modeling was solved by non-sparse direct solver in TE mode. Nevertheless, there is some weakness which have to be improved especially accuracy in the low frequency (10-3 Hz-10-5 Hz) which is not achieved yet and high cost computation in dense mesh. In this work, the solver which is used is sparse direct solver instead of non-sparse direct solverto overcome the weaknesses of solving linear matrices of vector finite element metod using non-sparse direct solver. Sparse direct solver will be advantageous in solving linear matrices of vector finite element method because of the matrix properties which is symmetrical and sparse. The validation of sparse direct solver in solving linear matrices of vector finite element has been done for a homogen half-space model and vertical contact model by analytical solution. Thevalidation result of sparse direct solver in solving linear matrices of vector finite element shows that sparse direct solver is more stable than non-sparse direct solver in computing linear problem of vector finite element method especially in low frequency. In the end, the accuracy of 2D MT responses modelling in low frequency (10-3 Hz-10-5 Hz) has been reached out under the efficient allocation memory of array and less computational time consuming.
A Direct Elliptic Solver Based on Hierarchically Low-Rank Schur Complements
Chávez, Gustavo
2017-03-17
A parallel fast direct solver for rank-compressible block tridiagonal linear systems is presented. Algorithmic synergies between Cyclic Reduction and Hierarchical matrix arithmetic operations result in a solver with O(Nlog2N) arithmetic complexity and O(NlogN) memory footprint. We provide a baseline for performance and applicability by comparing with well-known implementations of the $$\\\\mathcal{H}$$ -LU factorization and algebraic multigrid within a shared-memory parallel environment that leverages the concurrency features of the method. Numerical experiments reveal that this method is comparable with other fast direct solvers based on Hierarchical Matrices such as $$\\\\mathcal{H}$$ -LU and that it can tackle problems where algebraic multigrid fails to converge.
Wavelet-Based Poisson Solver for Use in Particle-in-Cell Simulations
Terzic, Balsa; Mihalcea, Daniel; Pogorelov, Ilya V
2005-01-01
We report on a successful implementation of a wavelet-based Poisson solver for use in 3D particle-in-cell simulations. One new aspect of our algorithm is its ability to treat the general (inhomogeneous) Dirichlet boundary conditions. The solver harnesses advantages afforded by the wavelet formulation, such as sparsity of operators and data sets, existence of effective preconditioners, and the ability simultaneously to remove numerical noise and further compress relevant data sets. Having tested our method as a stand-alone solver on two model problems, we merged it into IMPACT-T to obtain a fully functional serial PIC code. We present and discuss preliminary results of application of the new code to the modelling of the Fermilab/NICADD and AES/JLab photoinjectors.
Wavelet-based Poisson Solver for use in Particle-In-Cell Simulations
International Nuclear Information System (INIS)
Terzic, B.; Mihalcea, D.; Bohn, C.L.; Pogorelov, I.V.
2005-01-01
We report on a successful implementation of a wavelet based Poisson solver for use in 3D particle-in-cell (PIC) simulations. One new aspect of our algorithm is its ability to treat the general(inhomogeneous) Dirichlet boundary conditions (BCs). The solver harnesses advantages afforded by the wavelet formulation, such as sparsity of operators and data sets, existence of effective preconditioners, and the ability simultaneously to remove numerical noise and further compress relevant data sets. Having tested our method as a stand-alone solver on two model problems, we merged it into IMPACT-T to obtain a fully functional serial PIC code. We present and discuss preliminary results of application of the new code to the modeling of the Fermilab/NICADD and AES/JLab photoinjectors
Algorithms for parallel flow solvers on message passing architectures
Vanderwijngaart, Rob F.
1995-01-01
The purpose of this project has been to identify and test suitable technologies for implementation of fluid flow solvers -- possibly coupled with structures and heat equation solvers -- on MIMD parallel computers. In the course of this investigation much attention has been paid to efficient domain decomposition strategies for ADI-type algorithms. Multi-partitioning derives its efficiency from the assignment of several blocks of grid points to each processor in the parallel computer. A coarse-grain parallelism is obtained, and a near-perfect load balance results. In uni-partitioning every processor receives responsibility for exactly one block of grid points instead of several. This necessitates fine-grain pipelined program execution in order to obtain a reasonable load balance. Although fine-grain parallelism is less desirable on many systems, especially high-latency networks of workstations, uni-partition methods are still in wide use in production codes for flow problems. Consequently, it remains important to achieve good efficiency with this technique that has essentially been superseded by multi-partitioning for parallel ADI-type algorithms. Another reason for the concentration on improving the performance of pipeline methods is their applicability in other types of flow solver kernels with stronger implied data dependence. Analytical expressions can be derived for the size of the dynamic load imbalance incurred in traditional pipelines. From these it can be determined what is the optimal first-processor retardation that leads to the shortest total completion time for the pipeline process. Theoretical predictions of pipeline performance with and without optimization match experimental observations on the iPSC/860 very well. Analysis of pipeline performance also highlights the effect of uncareful grid partitioning in flow solvers that employ pipeline algorithms. If grid blocks at boundaries are not at least as large in the wall-normal direction as those
Diffusion of Zonal Variables Using Node-Centered Diffusion Solver
Energy Technology Data Exchange (ETDEWEB)
Yang, T B
2007-08-06
Tom Kaiser [1] has done some preliminary work to use the node-centered diffusion solver (originally developed by T. Palmer [2]) in Kull for diffusion of zonal variables such as electron temperature. To avoid numerical diffusion, Tom used a scheme developed by Shestakov et al. [3] and found their scheme could, in the vicinity of steep gradients, decouple nearest-neighbor zonal sub-meshes leading to 'alternating-zone' (red-black mode) errors. Tom extended their scheme to couple the sub-meshes with appropriate chosen artificial diffusion and thereby solved the 'alternating-zone' problem. Because the choice of the artificial diffusion coefficient could be very delicate, it is desirable to use a scheme that does not require the artificial diffusion but still able to avoid both numerical diffusion and the 'alternating-zone' problem. In this document we present such a scheme.
Gurr, Henry
2014-03-01
Princeton Physicist J. J. Hopfield's Mathematical Model of the Mammalian Brain, (Similar To Ising Glass Model of a crystal of magnetic spin particles) says our Brain-Work for Memory, Perception, Language, Thinking, etc, (Even the AHA-EUREKA-Flash Of Insight Type Problem Solving), is achieved by our massively inter-connected CNS Neurons ... working together ... MINIMIZING an analog of physical energy ... thus yielding Optimal Solutions: These ``best'' answers, correspond to highest mental coherence, for most facets organism response, beit mental (eg: perception, memory, ideas, thinking, etc) or physical-muscular-actions (eg speaking, tool using, trail following, etc). Our brain is this way, because living creature, MUST be evolved, so they will find & use the best actions, for survival!!! Our human heritage, is to instantly compute near optimal future plans, (mental & physical-muscular), and be able to accomplish plans reliably & efficiently. If you know of book or articles in these topic areas, please email to HenryG--USCA.edu How to work well, with your own ``self'', called mind-body, will follow!! Conjectures: Who is the ``I'' that appears to make decisions? Am ``I'' the master of my domain? Is there an ``I'' or am ``I'' merely an illusion of reality.
Riemann solvers and undercompressive shocks of convex FPU chains
International Nuclear Information System (INIS)
Herrmann, Michael; Rademacher, Jens D M
2010-01-01
We consider FPU-type atomic chains with general convex potentials. The naive continuum limit in the hyperbolic space–time scaling is the p-system of mass and momentum conservation. We systematically compare Riemann solutions to the p-system with numerical solutions to discrete Riemann problems in FPU chains, and argue that the latter can be described by modified p-system Riemann solvers. We allow the flux to have a turning point, and observe a third type of elementary wave (conservative shocks) in the atomistic simulations. These waves are heteroclinic travelling waves and correspond to non-classical, undercompressive shocks of the p-system. We analyse such shocks for fluxes with one or more turning points. Depending on the convexity properties of the flux we propose FPU-Riemann solvers. Our numerical simulations confirm that Lax shocks are replaced by so-called dispersive shocks. For convex–concave flux we provide numerical evidence that convex FPU chains follow the p-system in generating conservative shocks that are supersonic. For concave–convex flux, however, the conservative shocks of the p-system are subsonic and do not appear in FPU-Riemann solutions
Computational cost estimates for parallel shared memory isogeometric multi-frontal solvers
Woźniak, Maciej
2014-06-01
In this paper we present computational cost estimates for parallel shared memory isogeometric multi-frontal solvers. The estimates show that the ideal isogeometric shared memory parallel direct solver scales as O( p2log(N/p)) for one dimensional problems, O(Np2) for two dimensional problems, and O(N4/3p2) for three dimensional problems, where N is the number of degrees of freedom, and p is the polynomial order of approximation. The computational costs of the shared memory parallel isogeometric direct solver are compared with those corresponding to the sequential isogeometric direct solver, being the latest equal to O(N p2) for the one dimensional case, O(N1.5p3) for the two dimensional case, and O(N2p3) for the three dimensional case. The shared memory version significantly reduces both the scalability in terms of N and p. Theoretical estimates are compared with numerical experiments performed with linear, quadratic, cubic, quartic, and quintic B-splines, in one and two spatial dimensions. © 2014 Elsevier Ltd. All rights reserved.
A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments
International Nuclear Information System (INIS)
Fisicaro, G.; Goedecker, S.; Genovese, L.; Andreussi, O.; Marzari, N.
2016-01-01
The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes
A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments.
Fisicaro, G; Genovese, L; Andreussi, O; Marzari, N; Goedecker, S
2016-01-07
The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes.
Computational cost estimates for parallel shared memory isogeometric multi-frontal solvers
Woźniak, Maciej; Kuźnik, Krzysztof M.; Paszyński, Maciej R.; Calo, Victor M.; Pardo, D.
2014-01-01
In this paper we present computational cost estimates for parallel shared memory isogeometric multi-frontal solvers. The estimates show that the ideal isogeometric shared memory parallel direct solver scales as O( p2log(N/p)) for one dimensional problems, O(Np2) for two dimensional problems, and O(N4/3p2) for three dimensional problems, where N is the number of degrees of freedom, and p is the polynomial order of approximation. The computational costs of the shared memory parallel isogeometric direct solver are compared with those corresponding to the sequential isogeometric direct solver, being the latest equal to O(N p2) for the one dimensional case, O(N1.5p3) for the two dimensional case, and O(N2p3) for the three dimensional case. The shared memory version significantly reduces both the scalability in terms of N and p. Theoretical estimates are compared with numerical experiments performed with linear, quadratic, cubic, quartic, and quintic B-splines, in one and two spatial dimensions. © 2014 Elsevier Ltd. All rights reserved.
A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments
Energy Technology Data Exchange (ETDEWEB)
Fisicaro, G., E-mail: giuseppe.fisicaro@unibas.ch; Goedecker, S. [Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel (Switzerland); Genovese, L. [University of Grenoble Alpes, CEA, INAC-SP2M, L-Sim, F-38000 Grenoble (France); Andreussi, O. [Institute of Computational Science, Università della Svizzera Italiana, Via Giuseppe Buffi 13, CH-6904 Lugano (Switzerland); Theory and Simulations of Materials (THEOS) and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, Station 12, CH-1015 Lausanne (Switzerland); Marzari, N. [Theory and Simulations of Materials (THEOS) and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, Station 12, CH-1015 Lausanne (Switzerland)
2016-01-07
The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes.
Asynchronous Parallelization of a CFD Solver
Abdi, Daniel S.; Bitsuamlak, Girma T.
2015-01-01
The article of record as published may be found at http://dx.doi.org/10.1155/2015/295393 A Navier-Stokes equations solver is parallelized to run on a cluster of computers using the domain decomposition method. Two approaches of communication and computation are investigated, namely, synchronous and asynchronous methods. Asynchronous communication between subdomains is not commonly used inCFDcodes; however, it has a potential to alleviate scaling bottlenecks incurred due to process...
Chemical Mechanism Solvers in Air Quality Models
Directory of Open Access Journals (Sweden)
John C. Linford
2011-09-01
Full Text Available The solution of chemical kinetics is one of the most computationally intensivetasks in atmospheric chemical transport simulations. Due to the stiff nature of the system,implicit time stepping algorithms which repeatedly solve linear systems of equations arenecessary. This paper reviews the issues and challenges associated with the construction ofefficient chemical solvers, discusses several families of algorithms, presents strategies forincreasing computational efficiency, and gives insight into implementing chemical solverson accelerated computer architectures.
DEFF Research Database (Denmark)
Explorations and analysis of soundscapes have, since Canadian R. Murray Schafer's work during the early 1970's, developed into various established research - and artistic disciplines. The interest in sonic environments is today present within a broad range of contemporary art projects and in arch......Explorations and analysis of soundscapes have, since Canadian R. Murray Schafer's work during the early 1970's, developed into various established research - and artistic disciplines. The interest in sonic environments is today present within a broad range of contemporary art projects...... and in architectural design. Aesthetics, psychoacoustics, perception, and cognition are all present in this expanding field embracing such categories as soundscape composition, sound art, sonic art, sound design, sound studies and auditory culture. Of greatest significance to the overall field is the investigation...
DEFF Research Database (Denmark)
Mortensen, Peder Duelund; Hornyanszky, Elisabeth Dalholm; Larsen, Jacob Norvig
2013-01-01
Præsentation af projektresultater fra Interreg forskningen Sound Settlements om udvikling af bæredygtighed i det almene boligbyggerier i København, Malmø, Helsingborg og Lund samt europæiske eksempler på best practice......Præsentation af projektresultater fra Interreg forskningen Sound Settlements om udvikling af bæredygtighed i det almene boligbyggerier i København, Malmø, Helsingborg og Lund samt europæiske eksempler på best practice...
International Nuclear Information System (INIS)
Wambach, J.
1991-01-01
Nuclei, like more familiar mechanical systems, undergo simple vibrational motion. Among these vibrations, sound modes are of particular interest since they reveal important information on the effective interactions among the constituents and, through extrapolation, on the bulk behaviour of nuclear and neutron matter. Sound wave propagation in nuclei shows strong quantum effects familiar from other quantum systems. Microscopic theory suggests that the restoring forces are caused by the complex structure of the many-Fermion wavefunction and, in some cases, have no classical analogue. The damping of the vibrational amplitude is strongly influenced by phase coherence among the particles participating in the motion. (author)
International Nuclear Information System (INIS)
Nelson, E.M.
1993-12-01
Some two-dimensional finite element electromagnetic field solvers are described and tested. For TE and TM modes in homogeneous cylindrical waveguides and monopole modes in homogeneous axisymmetric structures, the solvers find approximate solutions to a weak formulation of the wave equation. Second-order isoparametric lagrangian triangular elements represent the field. For multipole modes in axisymmetric structures, the solver finds approximate solutions to a weak form of the curl-curl formulation of Maxwell's equations. Second-order triangular edge elements represent the radial (ρ) and axial (z) components of the field, while a second-order lagrangian basis represents the azimuthal (φ) component of the field weighted by the radius ρ. A reduced set of basis functions is employed for elements touching the axis. With this basis the spurious modes of the curl-curl formulation have zero frequency, so spurious modes are easily distinguished from non-static physical modes. Tests on an annular ring, a pillbox and a sphere indicate the solutions converge rapidly as the mesh is refined. Computed eigenvalues with relative errors of less than a few parts per million are obtained. Boundary conditions for symmetric, periodic and symmetric-periodic structures are discussed and included in the field solver. Boundary conditions for structures with inversion symmetry are also discussed. Special corner elements are described and employed to improve the accuracy of cylindrical waveguide and monopole modes with singular fields at sharp corners. The field solver is applied to three problems: (1) cross-field amplifier slow-wave circuits, (2) a detuned disk-loaded waveguide linear accelerator structure and (3) a 90 degrees overmoded waveguide bend. The detuned accelerator structure is a critical application of this high accuracy field solver. To maintain low long-range wakefields, tight design and manufacturing tolerances are required
DEFF Research Database (Denmark)
Mortensen, Peder Duelund; Hornyanszky, Elisabeth Dalholm; Larsen, Jacob Norvig
2013-01-01
Præsentation af projektresultater fra Interreg forskningen Sound Settlements om udvikling af bæredygtighed i det almene boligbyggerier i København, Malmø, Helsingborg og Lund samt europæiske eksempler på best practice...
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 4; Issue 6. Second Sound - The Role of Elastic Waves. R Srinivasan. General Article Volume 4 Issue 6 June 1999 pp 15-19. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/reso/004/06/0015-0019 ...
A wavelet-based PWTD algorithm-accelerated time domain surface integral equation solver
Liu, Yang
2015-10-26
© 2015 IEEE. The multilevel plane-wave time-domain (PWTD) algorithm allows for fast and accurate analysis of transient scattering from, and radiation by, electrically large and complex structures. When used in tandem with marching-on-in-time (MOT)-based surface integral equation (SIE) solvers, it reduces the computational and memory costs of transient analysis from equation and equation to equation and equation, respectively, where Nt and Ns denote the number of temporal and spatial unknowns (Ergin et al., IEEE Trans. Antennas Mag., 41, 39-52, 1999). In the past, PWTD-accelerated MOT-SIE solvers have been applied to transient problems involving half million spatial unknowns (Shanker et al., IEEE Trans. Antennas Propag., 51, 628-641, 2003). Recently, a scalable parallel PWTD-accelerated MOT-SIE solver that leverages a hiearchical parallelization strategy has been developed and successfully applied to the transient problems involving ten million spatial unknowns (Liu et. al., in URSI Digest, 2013). We further enhanced the capabilities of this solver by implementing a compression scheme based on local cosine wavelet bases (LCBs) that exploits the sparsity in the temporal dimension (Liu et. al., in URSI Digest, 2014). Specifically, the LCB compression scheme was used to reduce the memory requirement of the PWTD ray data and computational cost of operations in the PWTD translation stage.
Seo, Jongmin; Schiavazzi, Daniele; Marsden, Alison
2017-11-01
Cardiovascular simulations are increasingly used in clinical decision making, surgical planning, and disease diagnostics. Patient-specific modeling and simulation typically proceeds through a pipeline from anatomic model construction using medical image data to blood flow simulation and analysis. To provide confidence intervals on simulation predictions, we use an uncertainty quantification (UQ) framework to analyze the effects of numerous uncertainties that stem from clinical data acquisition, modeling, material properties, and boundary condition selection. However, UQ poses a computational challenge requiring multiple evaluations of the Navier-Stokes equations in complex 3-D models. To achieve efficiency in UQ problems with many function evaluations, we implement and compare a range of iterative linear solver and preconditioning techniques in our flow solver. We then discuss applications to patient-specific cardiovascular simulation and how the problem/boundary condition formulation in the solver affects the selection of the most efficient linear solver. Finally, we discuss performance improvements in the context of uncertainty propagation. Support from National Institute of Health (R01 EB018302) is greatly appreciated.
Improving mathematical problem solving : A computerized approach
Harskamp, EG; Suhre, CJM
Mathematics teachers often experience difficulties in teaching students to become skilled problem solvers. This paper evaluates the effectiveness of two interactive computer programs for high school mathematics problem solving. Both programs present students with problems accompanied by instruction
POSSOL, 2-D Poisson Equation Solver for Nonuniform Grid
International Nuclear Information System (INIS)
Orvis, W.J.
1988-01-01
1 - Description of program or function: POSSOL is a two-dimensional Poisson equation solver for problems with arbitrary non-uniform gridding in Cartesian coordinates. It is an adaptation of the uniform grid PWSCRT routine developed by Schwarztrauber and Sweet at the National Center for Atmospheric Research (NCAR). 2 - Method of solution: POSSOL will solve the Helmholtz equation on an arbitrary, non-uniform grid on a rectangular domain allowing only one type of boundary condition on any one side. It can also be used to handle more than one type of boundary condition on a side by means of a capacitance matrix technique. There are three types of boundary conditions that can be applied: fixed, derivative, or periodic
Domain Decomposition Solvers for Frequency-Domain Finite Element Equations
Copeland, Dylan; Kolmbauer, Michael; Langer, Ulrich
2010-01-01
The paper is devoted to fast iterative solvers for frequency-domain finite element equations approximating linear and nonlinear parabolic initial boundary value problems with time-harmonic excitations. Switching from the time domain to the frequency domain allows us to replace the expensive time-integration procedure by the solution of a simple linear elliptic system for the amplitudes belonging to the sine- and to the cosine-excitation or a large nonlinear elliptic system for the Fourier coefficients in the linear and nonlinear case, respectively. The fast solution of the corresponding linear and nonlinear system of finite element equations is crucial for the competitiveness of this method. © 2011 Springer-Verlag Berlin Heidelberg.
Domain Decomposition Solvers for Frequency-Domain Finite Element Equations
Copeland, Dylan
2010-10-05
The paper is devoted to fast iterative solvers for frequency-domain finite element equations approximating linear and nonlinear parabolic initial boundary value problems with time-harmonic excitations. Switching from the time domain to the frequency domain allows us to replace the expensive time-integration procedure by the solution of a simple linear elliptic system for the amplitudes belonging to the sine- and to the cosine-excitation or a large nonlinear elliptic system for the Fourier coefficients in the linear and nonlinear case, respectively. The fast solution of the corresponding linear and nonlinear system of finite element equations is crucial for the competitiveness of this method. © 2011 Springer-Verlag Berlin Heidelberg.
A General Symbolic PDE Solver Generator: Beyond Explicit Schemes
Directory of Open Access Journals (Sweden)
K. Sheshadri
2003-01-01
Full Text Available This paper presents an extension of our Mathematica- and MathCode-based symbolic-numeric framework for solving a variety of partial differential equation (PDE problems. The main features of our earlier work, which implemented explicit finite-difference schemes, include the ability to handle (1 arbitrary number of dependent variables, (2 arbitrary dimensionality, and (3 arbitrary geometry, as well as (4 developing finite-difference schemes to any desired order of approximation. In the present paper, extensions of this framework to implicit schemes and the method of lines are discussed. While C++ code is generated, using the MathCode system for the implicit method, Modelica code is generated for the method of lines. The latter provides a preliminary PDE support for the Modelica language. Examples illustrating the various aspects of the solver generator are presented.
GPU accelerated FDTD solver and its application in MRI.
Chi, J; Liu, F; Jin, J; Mason, D G; Crozier, S
2010-01-01
The finite difference time domain (FDTD) method is a popular technique for computational electromagnetics (CEM). The large computational power often required, however, has been a limiting factor for its applications. In this paper, we will present a graphics processing unit (GPU)-based parallel FDTD solver and its successful application to the investigation of a novel B1 shimming scheme for high-field magnetic resonance imaging (MRI). The optimized shimming scheme exhibits considerably improved transmit B(1) profiles. The GPU implementation dramatically shortened the runtime of FDTD simulation of electromagnetic field compared with its CPU counterpart. The acceleration in runtime has made such investigation possible, and will pave the way for other studies of large-scale computational electromagnetic problems in modern MRI which were previously impractical.
Jump as Far as You Can [Problem Solvers: Solutions
Yigit, Melike; Bofferding, Laura; Warnock, Miranda
2014-01-01
The How Far Do You Think You Can Jump? activity (see EJ1174770) was completed in three different contexts: an after-school mathematics enrichment program at Woodland and Country Schools in Weston, Massachusetts; a small-group pull-out of second graders at Wren Elementary in Piedmont, South Carolina; and a family math night in Lafayette, Indiana.…
Critical Thinking and the Development of Innovative Problem Solvers
National Research Council Canada - National Science Library
Drew, Christopher T
2005-01-01
.... This capability can be trained by making Critical Thinking the focus of officer education. Critical Thinking is the general cognitive skill of developing the best solution when there is not a single correct answer...
A TFETI domain decomposition solver for elastoplastic problems
Czech Academy of Sciences Publication Activity Database
Čermák, M.; Kozubek, T.; Sysala, Stanislav; Valdman, J.
2014-01-01
Roč. 231, č. 1 (2014), s. 634-653 ISSN 0096-3003 Institutional support: RVO:68145535 Keywords : elastoplasticity * Total FETI domain decomposition method * Finite element method * Semismooth Newton method Subject RIV: BA - General Mathematics Impact factor: 1.551, year: 2014 http://ac.els-cdn.com/S0096300314000253/1-s2.0-S0096300314000253-main.pdf?_tid=33a29cf4-996a-11e3-8c5a-00000aacb360&acdnat=1392816896_4584697dc26cf934dcf590c63f0dbab7
Nonlinear Chance Constrained Problems: Optimality Conditions, Regularization and Solvers
Czech Academy of Sciences Publication Activity Database
Adam, Lukáš; Branda, Martin
2016-01-01
Roč. 170, č. 2 (2016), s. 419-436 ISSN 0022-3239 R&D Projects: GA ČR GA15-00735S Institutional support: RVO:67985556 Keywords : Chance constrained programming * Optimality conditions * Regularization * Algorithms * Free MATLAB codes Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 1.289, year: 2016 http://library.utia.cas.cz/separaty/2016/MTR/adam-0460909.pdf
Parallel time domain solvers for electrically large transient scattering problems
Liu, Yang; Yucel, Abdulkadir; Bagcý , Hakan; Michielssen, Eric
2014-01-01
scattering from perfect electrically conducting objects are obtained by enforcing electric field boundary conditions and implicitly time advance electric surface current densities by iteratively solving sparse systems of equations at all time steps. Contrary
Donoghue, John R.
2015-01-01
At the heart of van der Linden's approach to automated test assembly (ATA) is a linear programming/integer programming (LP/IP) problem. A variety of IP solvers are available, ranging in cost from free to hundreds of thousands of dollars. In this paper, I compare several approaches to solving the underlying IP problem. These approaches range from…
AQUASOL: An efficient solver for the dipolar Poisson-Boltzmann-Langevin equation.
Koehl, Patrice; Delarue, Marc
2010-02-14
The Poisson-Boltzmann (PB) formalism is among the most popular approaches to modeling the solvation of molecules. It assumes a continuum model for water, leading to a dielectric permittivity that only depends on position in space. In contrast, the dipolar Poisson-Boltzmann-Langevin (DPBL) formalism represents the solvent as a collection of orientable dipoles with nonuniform concentration; this leads to a nonlinear permittivity function that depends both on the position and on the local electric field at that position. The differences in the assumptions underlying these two models lead to significant differences in the equations they generate. The PB equation is a second order, elliptic, nonlinear partial differential equation (PDE). Its response coefficients correspond to the dielectric permittivity and are therefore constant within each subdomain of the system considered (i.e., inside and outside of the molecules considered). While the DPBL equation is also a second order, elliptic, nonlinear PDE, its response coefficients are nonlinear functions of the electrostatic potential. Many solvers have been developed for the PB equation; to our knowledge, none of these can be directly applied to the DPBL equation. The methods they use may adapt to the difference; their implementations however are PBE specific. We adapted the PBE solver originally developed by Holst and Saied [J. Comput. Chem. 16, 337 (1995)] to the problem of solving the DPBL equation. This solver uses a truncated Newton method with a multigrid preconditioner. Numerical evidences suggest that it converges for the DPBL equation and that the convergence is superlinear. It is found however to be slow and greedy in memory requirement for problems commonly encountered in computational biology and computational chemistry. To circumvent these problems, we propose two variants, a quasi-Newton solver based on a simplified, inexact Jacobian and an iterative self-consistent solver that is based directly on the PBE
Essential imposition of Neumann condition in Galerkin-Legendre elliptic solvers
Auteri, F; Quartapelle, L
2003-01-01
A new Galerkin-Legendre direct spectral solver for the Neumann problem associated with Laplace and Helmholtz operators in rectangular domains is presented. The algorithm differs from other Neumann spectral solvers by the high sparsity of the matrices, exploited in conjunction with the direct product structure of the problem. The homogeneous boundary condition is satisfied exactly by expanding the unknown variable into a polynomial basis of functions which are built upon the Legendre polynomials and have a zero slope at the interval extremes. A double diagonalization process is employed pivoting around the eigenstructure of the pentadiagonal mass matrices in both directions, instead of the full stiffness matrices encountered in the classical variational formulation of the problem with a weak natural imposition of the derivative boundary condition. Nonhomogeneous Neumann data are accounted for by means of a lifting. Numerical results are given to illustrate the performance of the proposed spectral elliptic solv...
The Openpipeflow Navier–Stokes solver
Directory of Open Access Journals (Sweden)
Ashley P. Willis
2017-01-01
Full Text Available Pipelines are used in a huge range of industrial processes involving fluids, and the ability to accurately predict properties of the flow through a pipe is of fundamental engineering importance. Armed with parallel MPI, Arnoldi and Newton–Krylov solvers, the Openpipeflow code can be used in a range of settings, from large-scale simulation of highly turbulent flow, to the detailed analysis of nonlinear invariant solutions (equilibria and periodic orbits and their influence on the dynamics of the flow.
New multigrid solver advances in TOPS
International Nuclear Information System (INIS)
Falgout, R D; Brannick, J; Brezina, M; Manteuffel, T; McCormick, S
2005-01-01
In this paper, we highlight new multigrid solver advances in the Terascale Optimal PDE Simulations (TOPS) project in the Scientific Discovery Through Advanced Computing (SciDAC) program. We discuss two new algebraic multigrid (AMG) developments in TOPS: the adaptive smoothed aggregation method (αSA) and a coarse-grid selection algorithm based on compatible relaxation (CR). The αSA method is showing promising results in initial studies for Quantum Chromodynamics (QCD) applications. The CR method has the potential to greatly improve the applicability of AMG
A finite different field solver for dipole modes
International Nuclear Information System (INIS)
Nelson, E.M.
1992-08-01
A finite element field solver for dipole modes in axisymmetric structures has been written. The second-order elements used in this formulation yield accurate mode frequencies with no spurious modes. Quasi-periodic boundaries are included to allow travelling waves in periodic structures. The solver is useful in applications requiring precise frequency calculations such as detuned accelerator structures for linear colliders. Comparisons are made with measurements and with the popular but less accurate field solver URMEL
A finite element field solver for dipole modes
International Nuclear Information System (INIS)
Nelson, E.M.
1992-01-01
A finite element field solver for dipole modes in axisymmetric structures has been written. The second-order elements used in this formulation yield accurate mode frequencies with no spurious modes. Quasi-periodic boundaries are included to allow travelling waves in periodic structures. The solver is useful in applications requiring precise frequency calculations such as detuned accelerator structures for linear colliders. Comparisons are made with measurements and with the popular but less accurate field solver URMEL. (author). 7 refs., 4 figs
Dolenc, Peter
2013-01-01
This thesis contains a description of a construction of subwoofer case that has an extra functionality of being able to produce special visual effects and display visualizations that match the currently playing sound. For this reason, multiple lighting elements made out of LED (Light Emitting Diode) diodes were installed onto the subwoofer case. The lighting elements are controlled by dedicated software that was also developed. The software runs on STM32F4-Discovery evaluation board inside a ...
Three-Dimensional Inverse Transport Solver Based on Compressive Sensing Technique
Cheng, Yuxiong; Wu, Hongchun; Cao, Liangzhi; Zheng, Youqi
2013-09-01
According to the direct exposure measurements from flash radiographic image, a compressive sensing-based method for three-dimensional inverse transport problem is presented. The linear absorption coefficients and interface locations of objects are reconstructed directly at the same time. It is always very expensive to obtain enough measurements. With limited measurements, compressive sensing sparse reconstruction technique orthogonal matching pursuit is applied to obtain the sparse coefficients by solving an optimization problem. A three-dimensional inverse transport solver is developed based on a compressive sensing-based technique. There are three features in this solver: (1) AutoCAD is employed as a geometry preprocessor due to its powerful capacity in graphic. (2) The forward projection matrix rather than Gauss matrix is constructed by the visualization tool generator. (3) Fourier transform and Daubechies wavelet transform are adopted to convert an underdetermined system to a well-posed system in the algorithm. Simulations are performed and numerical results in pseudo-sine absorption problem, two-cube problem and two-cylinder problem when using compressive sensing-based solver agree well with the reference value.
Directory of Open Access Journals (Sweden)
Sánchez Álvarez , I.
1998-01-01
Full Text Available La relevancia de los problemas de optimización en el mundo empresarial ha generado la introducción de herramientas de optimización cada vez más sofisticadas en las últimas versiones de las hojas de cálculo de utilización generalizada. Estas utilidades, conocidas habitualmente como «solvers», constituyen una alternativa a los programas especializados de optimización cuando no se trata de problemas de gran escala, presentado la ventaja de su facilidad de uso y de comunicación con el usuario final. Frontline Systems Inc es la empresa que desarrolla el «solver» de Excel, si bien existen asimismo versiones para Lotus y Quattro Pro con ligeras diferencias de uso. En su dirección de internet (www.frontsys.com se puede obtener información técnica sobre las diferentes versiones de dicha utilidad y diversos aspectos operativos del programa, algunos de los cuales se comentan en este trabajo.
A sparse-grid isogeometric solver
Beck, Joakim
2018-02-28
Isogeometric Analysis (IGA) typically adopts tensor-product splines and NURBS as a basis for the approximation of the solution of PDEs. In this work, we investigate to which extent IGA solvers can benefit from the so-called sparse-grids construction in its combination technique form, which was first introduced in the early 90’s in the context of the approximation of high-dimensional PDEs.The tests that we report show that, in accordance to the literature, a sparse-grid construction can indeed be useful if the solution of the PDE at hand is sufficiently smooth. Sparse grids can also be useful in the case of non-smooth solutions when some a-priori knowledge on the location of the singularities of the solution can be exploited to devise suitable non-equispaced meshes. Finally, we remark that sparse grids can be seen as a simple way to parallelize pre-existing serial IGA solvers in a straightforward fashion, which can be beneficial in many practical situations.
A sparse version of IGA solvers
Beck, Joakim
2017-07-30
Isogeometric Analysis (IGA) typically adopts tensor-product splines and NURBS as a basis for the approximation of the solution of PDEs. In this work, we investigate to which extent IGA solvers can benefit from the so-called sparse-grids construction in its combination technique form, which was first introduced in the early 90s in the context of the approximation of high-dimensional PDEs. The tests that we report show that, in accordance to the literature, a sparse grids construction can indeed be useful if the solution of the PDE at hand is sufficiently smooth. Sparse grids can also be useful in the case of non-smooth solutions when some a-priori knowledge on the location of the singularities of the solution can be exploited to devise suitable non-equispaced meshes. Finally, we remark that sparse grids can be seen as a simple way to parallelize pre-existing serial IGA solvers in a straightforward fashion, which can be beneficial in many practical situations.
A sparse-grid isogeometric solver
Beck, Joakim; Sangalli, Giancarlo; Tamellini, Lorenzo
2018-01-01
Isogeometric Analysis (IGA) typically adopts tensor-product splines and NURBS as a basis for the approximation of the solution of PDEs. In this work, we investigate to which extent IGA solvers can benefit from the so-called sparse-grids construction in its combination technique form, which was first introduced in the early 90’s in the context of the approximation of high-dimensional PDEs.The tests that we report show that, in accordance to the literature, a sparse-grid construction can indeed be useful if the solution of the PDE at hand is sufficiently smooth. Sparse grids can also be useful in the case of non-smooth solutions when some a-priori knowledge on the location of the singularities of the solution can be exploited to devise suitable non-equispaced meshes. Finally, we remark that sparse grids can be seen as a simple way to parallelize pre-existing serial IGA solvers in a straightforward fashion, which can be beneficial in many practical situations.
A sparse version of IGA solvers
Beck, Joakim; Sangalli, Giancarlo; Tamellini, Lorenzo
2017-01-01
Isogeometric Analysis (IGA) typically adopts tensor-product splines and NURBS as a basis for the approximation of the solution of PDEs. In this work, we investigate to which extent IGA solvers can benefit from the so-called sparse-grids construction in its combination technique form, which was first introduced in the early 90s in the context of the approximation of high-dimensional PDEs. The tests that we report show that, in accordance to the literature, a sparse grids construction can indeed be useful if the solution of the PDE at hand is sufficiently smooth. Sparse grids can also be useful in the case of non-smooth solutions when some a-priori knowledge on the location of the singularities of the solution can be exploited to devise suitable non-equispaced meshes. Finally, we remark that sparse grids can be seen as a simple way to parallelize pre-existing serial IGA solvers in a straightforward fashion, which can be beneficial in many practical situations.
A fast mass spring model solver for high-resolution elastic objects
Zheng, Mianlun; Yuan, Zhiyong; Zhu, Weixu; Zhang, Guian
2017-03-01
Real-time simulation of elastic objects is of great importance for computer graphics and virtual reality applications. The fast mass spring model solver can achieve visually realistic simulation in an efficient way. Unfortunately, this method suffers from resolution limitations and lack of mechanical realism for a surface geometry model, which greatly restricts its application. To tackle these problems, in this paper we propose a fast mass spring model solver for high-resolution elastic objects. First, we project the complex surface geometry model into a set of uniform grid cells as cages through *cages mean value coordinate method to reflect its internal structure and mechanics properties. Then, we replace the original Cholesky decomposition method in the fast mass spring model solver with a conjugate gradient method, which can make the fast mass spring model solver more efficient for detailed surface geometry models. Finally, we propose a graphics processing unit accelerated parallel algorithm for the conjugate gradient method. Experimental results show that our method can realize efficient deformation simulation of 3D elastic objects with visual reality and physical fidelity, which has a great potential for applications in computer animation.
A Comparison of Monte Carlo and Deterministic Solvers for keff and Sensitivity Calculations
Energy Technology Data Exchange (ETDEWEB)
Haeck, Wim [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Parsons, Donald Kent [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); White, Morgan Curtis [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Saller, Thomas [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Favorite, Jeffrey A. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-12-12
Verification and validation of our solutions for calculating the neutron reactivity for nuclear materials is a key issue to address for many applications, including criticality safety, research reactors, power reactors, and nuclear security. Neutronics codes solve variations of the Boltzmann transport equation. The two main variants are Monte Carlo versus deterministic solutions, e.g. the MCNP [1] versus PARTISN [2] codes, respectively. There have been many studies over the decades that examined the accuracy of such solvers and the general conclusion is that when the problems are well-posed, either solver can produce accurate results. However, the devil is always in the details. The current study examines the issue of self-shielding and the stress it puts on deterministic solvers. Most Monte Carlo neutronics codes use continuous-energy descriptions of the neutron interaction data that are not subject to this effect. The issue of self-shielding occurs because of the discretisation of data used by the deterministic solutions. Multigroup data used in these solvers are the average cross section and scattering parameters over an energy range. Resonances in cross sections can occur that change the likelihood of interaction by one to three orders of magnitude over a small energy range. Self-shielding is the numerical effect that the average cross section in groups with strong resonances can be strongly affected as neutrons within that material are preferentially absorbed or scattered out of the resonance energies. This affects both the average cross section and the scattering matrix.
Effects of high-frequency damping on iterative convergence of implicit viscous solver
Nishikawa, Hiroaki; Nakashima, Yoshitaka; Watanabe, Norihiko
2017-11-01
This paper discusses effects of high-frequency damping on iterative convergence of an implicit defect-correction solver for viscous problems. The study targets a finite-volume discretization with a one parameter family of damped viscous schemes. The parameter α controls high-frequency damping: zero damping with α = 0, and larger damping for larger α (> 0). Convergence rates are predicted for a model diffusion equation by a Fourier analysis over a practical range of α. It is shown that the convergence rate attains its minimum at α = 1 on regular quadrilateral grids, and deteriorates for larger values of α. A similar behavior is observed for regular triangular grids. In both quadrilateral and triangular grids, the solver is predicted to diverge for α smaller than approximately 0.5. Numerical results are shown for the diffusion equation and the Navier-Stokes equations on regular and irregular grids. The study suggests that α = 1 and 4/3 are suitable values for robust and efficient computations, and α = 4 / 3 is recommended for the diffusion equation, which achieves higher-order accuracy on regular quadrilateral grids. Finally, a Jacobian-Free Newton-Krylov solver with the implicit solver (a low-order Jacobian approximately inverted by a multi-color Gauss-Seidel relaxation scheme) used as a variable preconditioner is recommended for practical computations, which provides robust and efficient convergence for a wide range of α.
Scalable domain decomposition solvers for stochastic PDEs in high performance computing
International Nuclear Information System (INIS)
Desai, Ajit; Pettit, Chris; Poirel, Dominique; Sarkar, Abhijit
2017-01-01
Stochastic spectral finite element models of practical engineering systems may involve solutions of linear systems or linearized systems for non-linear problems with billions of unknowns. For stochastic modeling, it is therefore essential to design robust, parallel and scalable algorithms that can efficiently utilize high-performance computing to tackle such large-scale systems. Domain decomposition based iterative solvers can handle such systems. And though these algorithms exhibit excellent scalabilities, significant algorithmic and implementational challenges exist to extend them to solve extreme-scale stochastic systems using emerging computing platforms. Intrusive polynomial chaos expansion based domain decomposition algorithms are extended here to concurrently handle high resolution in both spatial and stochastic domains using an in-house implementation. Sparse iterative solvers with efficient preconditioners are employed to solve the resulting global and subdomain level local systems through multi-level iterative solvers. We also use parallel sparse matrix–vector operations to reduce the floating-point operations and memory requirements. Numerical and parallel scalabilities of these algorithms are presented for the diffusion equation having spatially varying diffusion coefficient modeled by a non-Gaussian stochastic process. Scalability of the solvers with respect to the number of random variables is also investigated.
Graph Grammar-Based Multi-Frontal Parallel Direct Solver for Two-Dimensional Isogeometric Analysis
Kuźnik, Krzysztof
2012-06-02
This paper introduces the graph grammar based model for developing multi-thread multi-frontal parallel direct solver for two dimensional isogeometric finite element method. Execution of the solver algorithm has been expressed as the sequence of graph grammar productions. At the beginning productions construct the elimination tree with leaves corresponding to finite elements. Following sequence of graph grammar productions generates element frontal matri-ces at leaf nodes, merges matrices at parent nodes and eliminates rows corresponding to fully assembled degrees of freedom. Finally, there are graph grammar productions responsible for root problem solution and recursive backward substitutions. Expressing the solver algorithm by graph grammar productions allows us to explore the concurrency of the algorithm. The graph grammar productions are grouped into sets of independent tasks that can be executed concurrently. The resulting concurrent multi-frontal solver algorithm is implemented and tested on NVIDIA GPU, providing O(NlogN) execution time complexity where N is the number of degrees of freedom. We have confirmed this complexity by solving up to 1 million of degrees of freedom with 448 cores GPU.
Bernede, Adrien; Poëtte, Gaël
2018-02-01
In this paper, we are interested in the resolution of the time-dependent problem of particle transport in a medium whose composition evolves with time due to interactions. As a constraint, we want to use of Monte-Carlo (MC) scheme for the transport phase. A common resolution strategy consists in a splitting between the MC/transport phase and the time discretization scheme/medium evolution phase. After going over and illustrating the main drawbacks of split solvers in a simplified configuration (monokinetic, scalar Bateman problem), we build a new Unsplit MC (UMC) solver improving the accuracy of the solutions, avoiding numerical instabilities, and less sensitive to time discretization. The new solver is essentially based on a Monte Carlo scheme with time dependent cross sections implying the on-the-fly resolution of a reduced model for each MC particle describing the time evolution of the matter along their flight path.
GPU TECHNOLOGIES EMBODIED IN PARALLEL SOLVERS OF LINEAR ALGEBRAIC EQUATION SYSTEMS
Directory of Open Access Journals (Sweden)
Sidorov Alexander Vladimirovich
2012-10-01
Full Text Available The author reviews existing shareware solvers that are operated by graphical computer devices. The purpose of this review is to explore the opportunities and limitations of the above parallel solvers applicable for resolution of linear algebraic problems that arise at Research and Educational Centre of Computer Modeling at MSUCE, and Research and Engineering Centre STADYO. The author has explored new applications of the GPU in the PETSc suite and compared them with the results generated absent of the GPU. The research is performed within the CUSP library developed to resolve the problems of linear algebra through the application of GPU. The author has also reviewed the new MAGMA project which is analogous to LAPACK for the GPU.
Domain decomposition methods for core calculations using the MINOS solver
International Nuclear Information System (INIS)
Guerin, P.; Baudron, A. M.; Lautard, J. J.
2007-01-01
Cell by cell homogenized transport calculations of an entire nuclear reactor core are currently too expensive for industrial applications, even if a simplified transport (SPn) approximation is used. In order to take advantage of parallel computers, we propose here two domain decomposition methods using the mixed dual finite element solver MINOS. The first one is a modal synthesis method on overlapping sub-domains: several Eigenmodes solutions of a local problem on each sub-domain are taken as basis functions used for the resolution of the global problem on the whole domain. The second one is an iterative method based on non-overlapping domain decomposition with Robin interface conditions. At each iteration, we solve the problem on each sub-domain with the interface conditions given by the solutions on the close sub-domains estimated at the previous iteration. For these two methods, we give numerical results which demonstrate their accuracy and their efficiency for the diffusion model on realistic 2D and 3D cores. (authors)
The Quantum Mechanics Solver How to Apply Quantum Theory to Modern Physics
Basdevant, Jean-Louis
2006-01-01
The Quantum Mechanics Solver grew from topics which are part of the final examination in quantum theory at the Ecole Polytechnique at Palaiseau near Paris, France. The aim of the text is to guide the student towards applying quantum mechanics to research problems in fields such as atomic and molecular physics, condensed matter physics, and laser physics. Advanced undergraduates and graduate students will find a rich and challenging source for improving their skills in this field.
Mang, Andreas; Ruthotto, Lars
2017-01-01
We present an efficient solver for diffeomorphic image registration problems in the framework of Large Deformations Diffeomorphic Metric Mappings (LDDMM). We use an optimal control formulation, in which the velocity field of a hyperbolic PDE needs to be found such that the distance between the final state of the system (the transformed/transported template image) and the observation (the reference image) is minimized. Our solver supports both stationary and non-stationary (i.e., transient or time-dependent) velocity fields. As transformation models, we consider both the transport equation (assuming intensities are preserved during the deformation) and the continuity equation (assuming mass-preservation). We consider the reduced form of the optimal control problem and solve the resulting unconstrained optimization problem using a discretize-then-optimize approach. A key contribution is the elimination of the PDE constraint using a Lagrangian hyperbolic PDE solver. Lagrangian methods rely on the concept of characteristic curves. We approximate these curves using a fourth-order Runge-Kutta method. We also present an efficient algorithm for computing the derivatives of the final state of the system with respect to the velocity field. This allows us to use fast Gauss-Newton based methods. We present quickly converging iterative linear solvers using spectral preconditioners that render the overall optimization efficient and scalable. Our method is embedded into the image registration framework FAIR and, thus, supports the most commonly used similarity measures and regularization functionals. We demonstrate the potential of our new approach using several synthetic and real world test problems with up to 14.7 million degrees of freedom.
International Nuclear Information System (INIS)
Na, Y. W.; Park, C. E.; Lee, S. Y.
2009-01-01
As a part of the Ministry of Knowledge Economy (MKE) project, 'Development of safety analysis codes for nuclear power plants', KOPEC has been developing the hydraulic solver code package applicable to the safety analyses of nuclear power plants (NPP's). The matrices of the hydraulic solver are usually sparse and may be asymmetric. In the earlier stage of this project, typical direct matrix solver packages MA48 and MA28 had been tested as matrix solver for the hydraulic solver code, SPACE. The selection was based on the reasonably reliable performance experience from their former version MA18 in RELAP computer code. In the later stage of this project, the iterative methodologies have been being tested in the SPACE code. Among a few candidate iterative solution methodologies tested so far, the biconjugate gradient stabilization methodology (BICGSTAB) has shown the best performance in the applicability test and in the application to the SPACE code. Regardless of all the merits of using the direct solver packages, there are some other aspects of tackling the iterative solution methodologies. The algorithm is much simpler and easier to handle. The potential problems related to the robustness of the iterative solution methodologies have been resolved by applying pre-conditioning methods adjusted and modified as appropriate to the application in the SPACE code. The application strategy of conjugate gradient method was introduced in detail by Schewchuk, Golub and Saad in the middle of 1990's. The application of his methodology to nuclear engineering in Korea started about the same time and is still going on and there are quite a few examples of application to neutronics. Besides, Yang introduced a conjugate gradient method programmed in C++ language. The purpose of this study is to assess the performance and behavior of the iterative solution methodology compared to those of the direct solution methodology still being preferred due to its robustness and reliability. The
A RADIATION TRANSFER SOLVER FOR ATHENA USING SHORT CHARACTERISTICS
International Nuclear Information System (INIS)
Davis, Shane W.; Stone, James M.; Jiang Yanfei
2012-01-01
We describe the implementation of a module for the Athena magnetohydrodynamics (MHD) code that solves the time-independent, multi-frequency radiative transfer (RT) equation on multidimensional Cartesian simulation domains, including scattering and non-local thermodynamic equilibrium (LTE) effects. The module is based on well known and well tested algorithms developed for modeling stellar atmospheres, including the method of short characteristics to solve the RT equation, accelerated Lambda iteration to handle scattering and non-LTE effects, and parallelization via domain decomposition. The module serves several purposes: it can be used to generate spectra and images, to compute a variable Eddington tensor (VET) for full radiation MHD simulations, and to calculate the heating and cooling source terms in the MHD equations in flows where radiation pressure is small compared with gas pressure. For the latter case, the module is combined with the standard MHD integrators using operator splitting: we describe this approach in detail, including a new constraint on the time step for stability due to radiation diffusion modes. Implementation of the VET method for radiation pressure dominated flows is described in a companion paper. We present results from a suite of test problems for both the RT solver itself and for dynamical problems that include radiative heating and cooling. These tests demonstrate that the radiative transfer solution is accurate and confirm that the operator split method is stable, convergent, and efficient for problems of interest. We demonstrate there is no need to adopt ad hoc assumptions of questionable accuracy to solve RT problems in concert with MHD: the computational cost for our general-purpose module for simple (e.g., LTE gray) problems can be comparable to or less than a single time step of Athena's MHD integrators, and only few times more expensive than that for more general (non-LTE) problems.
An accurate, fast, and scalable solver for high-frequency wave propagation
Zepeda-Núñez, L.; Taus, M.; Hewett, R.; Demanet, L.
2017-12-01
In many science and engineering applications, solving time-harmonic high-frequency wave propagation problems quickly and accurately is of paramount importance. For example, in geophysics, particularly in oil exploration, such problems can be the forward problem in an iterative process for solving the inverse problem of subsurface inversion. It is important to solve these wave propagation problems accurately in order to efficiently obtain meaningful solutions of the inverse problems: low order forward modeling can hinder convergence. Additionally, due to the volume of data and the iterative nature of most optimization algorithms, the forward problem must be solved many times. Therefore, a fast solver is necessary to make solving the inverse problem feasible. For time-harmonic high-frequency wave propagation, obtaining both speed and accuracy is historically challenging. Recently, there have been many advances in the development of fast solvers for such problems, including methods which have linear complexity with respect to the number of degrees of freedom. While most methods scale optimally only in the context of low-order discretizations and smooth wave speed distributions, the method of polarized traces has been shown to retain optimal scaling for high-order discretizations, such as hybridizable discontinuous Galerkin methods and for highly heterogeneous (and even discontinuous) wave speeds. The resulting fast and accurate solver is consequently highly attractive for geophysical applications. To date, this method relies on a layered domain decomposition together with a preconditioner applied in a sweeping fashion, which has limited straight-forward parallelization. In this work, we introduce a new version of the method of polarized traces which reveals more parallel structure than previous versions while preserving all of its other advantages. We achieve this by further decomposing each layer and applying the preconditioner to these new components separately and
A comparison of SuperLU solvers on the intel MIC architecture
Tuncel, Mehmet; Duran, Ahmet; Celebi, M. Serdar; Akaydin, Bora; Topkaya, Figen O.
2016-10-01
In many science and engineering applications, problems may result in solving a sparse linear system AX=B. For example, SuperLU_MCDT, a linear solver, was used for the large penta-diagonal matrices for 2D problems and hepta-diagonal matrices for 3D problems, coming from the incompressible blood flow simulation (see [1]). It is important to test the status and potential improvements of state-of-the-art solvers on new technologies. In this work, sequential, multithreaded and distributed versions of SuperLU solvers (see [2]) are examined on the Intel Xeon Phi coprocessors using offload programming model at the EURORA cluster of CINECA in Italy. We consider a portfolio of test matrices containing patterned matrices from UFMM ([3]) and randomly located matrices. This architecture can benefit from high parallelism and large vectors. We find that the sequential SuperLU benefited up to 45 % performance improvement from the offload programming depending on the sparse matrix type and the size of transferred and processed data.
ELSI: A unified software interface for Kohn-Sham electronic structure solvers
Yu, Victor Wen-zhe; Corsetti, Fabiano; García, Alberto; Huhn, William P.; Jacquelin, Mathias; Jia, Weile; Lange, Björn; Lin, Lin; Lu, Jianfeng; Mi, Wenhui; Seifitokaldani, Ali; Vázquez-Mayagoitia, Álvaro; Yang, Chao; Yang, Haizhao; Blum, Volker
2018-01-01
Solving the electronic structure from a generalized or standard eigenproblem is often the bottleneck in large scale calculations based on Kohn-Sham density-functional theory. This problem must be addressed by essentially all current electronic structure codes, based on similar matrix expressions, and by high-performance computation. We here present a unified software interface, ELSI, to access different strategies that address the Kohn-Sham eigenvalue problem. Currently supported algorithms include the dense generalized eigensolver library ELPA, the orbital minimization method implemented in libOMM, and the pole expansion and selected inversion (PEXSI) approach with lower computational complexity for semilocal density functionals. The ELSI interface aims to simplify the implementation and optimal use of the different strategies, by offering (a) a unified software framework designed for the electronic structure solvers in Kohn-Sham density-functional theory; (b) reasonable default parameters for a chosen solver; (c) automatic conversion between input and internal working matrix formats, and in the future (d) recommendation of the optimal solver depending on the specific problem. Comparative benchmarks are shown for system sizes up to 11,520 atoms (172,800 basis functions) on distributed memory supercomputing architectures.
Robust large-scale parallel nonlinear solvers for simulations.
Energy Technology Data Exchange (ETDEWEB)
Bader, Brett William; Pawlowski, Roger Patrick; Kolda, Tamara Gibson (Sandia National Laboratories, Livermore, CA)
2005-11-01
This report documents research to develop robust and efficient solution techniques for solving large-scale systems of nonlinear equations. The most widely used method for solving systems of nonlinear equations is Newton's method. While much research has been devoted to augmenting Newton-based solvers (usually with globalization techniques), little has been devoted to exploring the application of different models. Our research has been directed at evaluating techniques using different models than Newton's method: a lower order model, Broyden's method, and a higher order model, the tensor method. We have developed large-scale versions of each of these models and have demonstrated their use in important applications at Sandia. Broyden's method replaces the Jacobian with an approximation, allowing codes that cannot evaluate a Jacobian or have an inaccurate Jacobian to converge to a solution. Limited-memory methods, which have been successful in optimization, allow us to extend this approach to large-scale problems. We compare the robustness and efficiency of Newton's method, modified Newton's method, Jacobian-free Newton-Krylov method, and our limited-memory Broyden method. Comparisons are carried out for large-scale applications of fluid flow simulations and electronic circuit simulations. Results show that, in cases where the Jacobian was inaccurate or could not be computed, Broyden's method converged in some cases where Newton's method failed to converge. We identify conditions where Broyden's method can be more efficient than Newton's method. We also present modifications to a large-scale tensor method, originally proposed by Bouaricha, for greater efficiency, better robustness, and wider applicability. Tensor methods are an alternative to Newton-based methods and are based on computing a step based on a local quadratic model rather than a linear model. The advantage of Bouaricha's method is that it can use any
DEFF Research Database (Denmark)
Kauffmann, Lene Teglhus
as knowledge based on reflexive practices. I chose ‘health promotion’ as the field for my research as it utilises knowledge produced in several research disciplines, among these both quantitative and qualitative. I mapped out the institutions, actors, events, and documents that constituted the field of health...... of the research is to investigate what is considered to ‘work as evidence’ in health promotion and how the ‘evidence discourse’ influences social practices in policymaking and in research. From investigating knowledge practices in the field of health promotion, I develop the concept of sound knowledge...... result of a rigorous and standardized research method. However, this anthropological analysis shows that evidence and evidence-based is a hegemonic ‘way of knowing’ that sometimes transposes everyday reasoning into an epistemological form. However, the empirical material shows a variety of understandings...
Performance of the block-Krylov energy group solvers in Jaguar
Energy Technology Data Exchange (ETDEWEB)
Watson, A. M.; Kennedy, R. A. [Knolls Atomic Power Laboratory, Bechtel Marine Propulsion Corporation, P.O. Box 1072, Schenectady, NY 12301-1072 (United States)
2012-07-01
A new method of coupling the inner and outer iterations for deterministic transport problems is proposed. This method is termed the Multigroup Energy Blocking Method (MEBM) and has been implemented in the deterministic transport solver Jaguar, which is currently under development at KAPL. The method is derived for both fixed-source and eigenvalue problems. The method is then applied to a PWR pin cell model, both in fixed-source mode and eigenvalue mode. The results show that the MEBM improves the convergence of both types of problems when applied to the thermal (up-scattering) groups. (authors)
Parallelization of Unsteady Adaptive Mesh Refinement for Unstructured Navier-Stokes Solvers
Schwing, Alan M.; Nompelis, Ioannis; Candler, Graham V.
2014-01-01
This paper explores the implementation of the MPI parallelization in a Navier-Stokes solver using adaptive mesh re nement. Viscous and inviscid test problems are considered for the purpose of benchmarking, as are implicit and explicit time advancement methods. The main test problem for comparison includes e ects from boundary layers and other viscous features and requires a large number of grid points for accurate computation. Ex- perimental validation against double cone experiments in hypersonic ow are shown. The adaptive mesh re nement shows promise for a staple test problem in the hypersonic com- munity. Extension to more advanced techniques for more complicated ows is described.
Cor, Ken; Alves, Cecilia; Gierl, Mark J.
2008-01-01
This review describes and evaluates a software add-in created by Frontline Systems, Inc., that can be used with Microsoft Excel 2007 to solve large, complex test assembly problems. The combination of Microsoft Excel 2007 with the Frontline Systems Premium Solver Platform is significant because Microsoft Excel is the most commonly used spreadsheet…
DEFF Research Database (Denmark)
2006-01-01
Sound search is provided by the major search engines, however, indexing is text based, not sound based. We will establish a dedicated sound search services with based on sound feature indexing. The current demo shows the concept of the sound search engine. The first engine will be realased June...
Kuźnik, Krzysztof
2013-06-01
This paper introduces a grammar-based model for developing a multi-thread multi-frontal parallel direct solver for one- dimensional isogeometric finite element method. The model includes the integration of B-splines for construction of the element local matrices and the multi-frontal solver algorithm. The integration and the solver algorithm are partitioned into basic indivisible tasks, namely the grammar productions, that can be executed squentially. The partial order of execution of the basic tasks is analyzed to provide the scheduling for the execution of the concurrent integration and multi-frontal solver algo- rithm. This graph grammar analysis allows for optimal concurrent execution of all tasks. The model has been implemented and tested on NVIDIA CUDA GPU, delivering logarithmic execution time for linear, quadratic, cubic and higher order B-splines. Thus, the CUDA implementation delivers the optimal performance predicted by our graph grammar analysis. We utilize the solver for multiple right hand sides related to the solution of non-stationary or inverse problems.
Cardall, Christian Y.; Budiardja, Reuben D.
2018-01-01
The large-scale computer simulation of a system of physical fields governed by partial differential equations requires some means of approximating the mathematical limit of continuity. For example, conservation laws are often treated with a 'finite-volume' approach in which space is partitioned into a large number of small 'cells,' with fluxes through cell faces providing an intuitive discretization modeled on the mathematical definition of the divergence operator. Here we describe and make available Fortran 2003 classes furnishing extensible object-oriented implementations of simple meshes and the evolution of generic conserved currents thereon, along with individual 'unit test' programs and larger example problems demonstrating their use. These classes inaugurate the Mathematics division of our developing astrophysics simulation code GENASIS (Gen eral A strophysical Si mulation S ystem), which will be expanded over time to include additional meshing options, mathematical operations, solver types, and solver variations appropriate for many multiphysics applications.
A Massively Parallel Solver for the Mechanical Harmonic Analysis of Accelerator Cavities
International Nuclear Information System (INIS)
2015-01-01
ACE3P is a 3D massively parallel simulation suite that developed at SLAC National Accelerator Laboratory that can perform coupled electromagnetic, thermal and mechanical study. Effectively utilizing supercomputer resources, ACE3P has become a key simulation tool for particle accelerator R and D. A new frequency domain solver to perform mechanical harmonic response analysis of accelerator components is developed within the existing parallel framework. This solver is designed to determine the frequency response of the mechanical system to external harmonic excitations for time-efficient accurate analysis of the large-scale problems. Coupled with the ACE3P electromagnetic modules, this capability complements a set of multi-physics tools for a comprehensive study of microphonics in superconducting accelerating cavities in order to understand the RF response and feedback requirements for the operational reliability of a particle accelerator. (auth)
Constraint Solver Techniques for Implementing Precise and Scalable Static Program Analysis
DEFF Research Database (Denmark)
Zhang, Ye
solver using unification we could make a program analysis easier to design and implement, much more scalable, and still as precise as expected. We present an inclusion constraint language with the explicit equality constructs for specifying program analysis problems, and a parameterized framework...... developers to build reliable software systems more quickly and with fewer bugs or security defects. While designing and implementing a program analysis remains a hard work, making it both scalable and precise is even more challenging. In this dissertation, we show that with a general inclusion constraint...... data flow analyses for C language, we demonstrate a large amount of equivalences could be detected by off-line analyses, and they could then be used by a constraint solver to significantly improve the scalability of an analysis without sacrificing any precision....
Solving non-linear Horn clauses using a linear Horn clause solver
DEFF Research Database (Denmark)
Kafle, Bishoksan; Gallagher, John Patrick; Ganty, Pierre
2016-01-01
In this paper we show that checking satisfiability of a set of non-linear Horn clauses (also called a non-linear Horn clause program) can be achieved using a solver for linear Horn clauses. We achieve this by interleaving a program transformation with a satisfiability checker for linear Horn...... clauses (also called a solver for linear Horn clauses). The program transformation is based on the notion of tree dimension, which we apply to a set of non-linear clauses, yielding a set whose derivation trees have bounded dimension. Such a set of clauses can be linearised. The main algorithm...... dimension. We constructed a prototype implementation of this approach and performed some experiments on a set of verification problems, which shows some promise....
Learning Domain-Specific Heuristics for Answer Set Solvers
Balduccini, Marcello
2010-01-01
In spite of the recent improvements in the performance of Answer Set Programming (ASP) solvers, when the search space is sufficiently large, it is still possible for the search algorithm to mistakenly focus on areas of the search space that contain no solutions or very few. When that happens, performance degrades substantially, even to the point that the solver may need to be terminated before returning an answer. This prospect is a concern when one is considering using such a solver in an in...
A non-conforming 3D spherical harmonic transport solver
Energy Technology Data Exchange (ETDEWEB)
Van Criekingen, S. [Commissariat a l' Energie Atomique CEA-Saclay, DEN/DM2S/SERMA/LENR Bat 470, 91191 Gif-sur-Yvette, Cedex (France)
2006-07-01
A new 3D transport solver for the time-independent Boltzmann transport equation has been developed. This solver is based on the second-order even-parity form of the transport equation. The angular discretization is performed through the expansion of the angular neutron flux in spherical harmonics (PN method). The novelty of this solver is the use of non-conforming finite elements for the spatial discretization. Such elements lead to a discontinuous flux approximation. This interface continuity requirement relaxation property is shared with mixed-dual formulations such as the ones based on Raviart-Thomas finite elements. Encouraging numerical results are presented. (authors)
A non-conforming 3D spherical harmonic transport solver
International Nuclear Information System (INIS)
Van Criekingen, S.
2006-01-01
A new 3D transport solver for the time-independent Boltzmann transport equation has been developed. This solver is based on the second-order even-parity form of the transport equation. The angular discretization is performed through the expansion of the angular neutron flux in spherical harmonics (PN method). The novelty of this solver is the use of non-conforming finite elements for the spatial discretization. Such elements lead to a discontinuous flux approximation. This interface continuity requirement relaxation property is shared with mixed-dual formulations such as the ones based on Raviart-Thomas finite elements. Encouraging numerical results are presented. (authors)
National Aeronautics and Space Administration — NASA has released a series of space sounds via sound cloud. We have abstracted away some of the hassle in accessing these sounds, so that developers can play with...
libmpdata++ 1.0: a library of parallel MPDATA solvers for systems of generalised transport equations
Jaruga, A.; Arabas, S.; Jarecka, D.; Pawlowska, H.; Smolarkiewicz, P. K.; Waruszewski, M.
2015-04-01
This paper accompanies the first release of libmpdata++, a C++ library implementing the multi-dimensional positive-definite advection transport algorithm (MPDATA) on regular structured grid. The library offers basic numerical solvers for systems of generalised transport equations. The solvers are forward-in-time, conservative and non-linearly stable. The libmpdata++ library covers the basic second-order-accurate formulation of MPDATA, its third-order variant, the infinite-gauge option for variable-sign fields and a flux-corrected transport extension to guarantee non-oscillatory solutions. The library is equipped with a non-symmetric variational elliptic solver for implicit evaluation of pressure gradient terms. All solvers offer parallelisation through domain decomposition using shared-memory parallelisation. The paper describes the library programming interface, and serves as a user guide. Supported options are illustrated with benchmarks discussed in the MPDATA literature. Benchmark descriptions include code snippets as well as quantitative representations of simulation results. Examples of applications include homogeneous transport in one, two and three dimensions in Cartesian and spherical domains; a shallow-water system compared with analytical solution (originally derived for a 2-D case); and a buoyant convection problem in an incompressible Boussinesq fluid with interfacial instability. All the examples are implemented out of the library tree. Regardless of the differences in the problem dimensionality, right-hand-side terms, boundary conditions and parallelisation approach, all the examples use the same unmodified library, which is a key goal of libmpdata++ design. The design, based on the principle of separation of concerns, prioritises the user and developer productivity. The libmpdata++ library is implemented in C++, making use of the Blitz++ multi-dimensional array containers, and is released as free/libre and open-source software.
libmpdata++ 0.1: a library of parallel MPDATA solvers for systems of generalised transport equations
Jaruga, A.; Arabas, S.; Jarecka, D.; Pawlowska, H.; Smolarkiewicz, P. K.; Waruszewski, M.
2014-11-01
This paper accompanies first release of libmpdata++, a C++ library implementing the Multidimensional Positive-Definite Advection Transport Algorithm (MPDATA). The library offers basic numerical solvers for systems of generalised transport equations. The solvers are forward-in-time, conservative and non-linearly stable. The libmpdata++ library covers the basic second-order-accurate formulation of MPDATA, its third-order variant, the infinite-gauge option for variable-sign fields and a flux-corrected transport extension to guarantee non-oscillatory solutions. The library is equipped with a non-symmetric variational elliptic solver for implicit evaluation of pressure gradient terms. All solvers offer parallelisation through domain decomposition using shared-memory parallelisation. The paper describes the library programming interface, and serves as a user guide. Supported options are illustrated with benchmarks discussed in the MPDATA literature. Benchmark descriptions include code snippets as well as quantitative representations of simulation results. Examples of applications include: homogeneous transport in one, two and three dimensions in Cartesian and spherical domains; shallow-water system compared with analytical solution (originally derived for a 2-D case); and a buoyant convection problem in an incompressible Boussinesq fluid with interfacial instability. All the examples are implemented out of the library tree. Regardless of the differences in the problem dimensionality, right-hand-side terms, boundary conditions and parallelisation approach, all the examples use the same unmodified library, which is a key goal of libmpdata++ design. The design, based on the principle of separation of concerns, prioritises the user and developer productivity. The libmpdata++ library is implemented in C++, making use of the Blitz++ multi-dimensional array containers, and is released as free/libre and open-source software.
Problem solving stages in the five square problem
Directory of Open Access Journals (Sweden)
Anna eFedor
2015-08-01
Full Text Available According to the restructuring hypothesis, insight problem solving typically progresses through consecutive stages of search, impasse, insight and search again for someone, who solves the task. The order of these stages was determined through self-reports of problem solvers and has never been verified behaviourally. We asked whether individual analysis of problem solving attempts of participants revealed the same order of problem solving stages as defined by the theory and whether their subjective feelings corresponded to the problem solving stages they were in. 101 participants tried to solve the Five-Square problem in an online task, while we recorded the time and trajectory of their stick movements. After the task they were asked about their feelings related to insight and 67 of them also had the possibility of reporting impasse while working on the task. We have found that 49% (19 out of 39 of the solvers and 13% (8 out of 62 of the non-solvers followed the classic four-stage model of insight. The rest of the participants had more complex sequences of problem solving stages, with search and impasse recurring several times. This means that the classic four-stage model must be extended to explain variability on the individual level. We provide a model that can generate all sequences found. Solvers reported insight more often than non-solvers and non-solvers reported impasse more often than solvers, as expected; but participants did not report impasse more often during behaviourally defined impasse stages than during other stages. This shows that impasse reports might be unreliable indicators of impasse. Our study highlights the importance of individual analysis of problem solving behaviour to verify insight theory.
Refined isogeometric analysis for a preconditioned conjugate gradient solver
Garcia, Daniel; Pardo, D.; Dalcin, Lisandro; Calo, Victor M.
2018-01-01
Starting from a highly continuous Isogeometric Analysis (IGA) discretization, refined Isogeometric Analysis (rIGA) introduces C0 hyperplanes that act as separators for the direct LU factorization solver. As a result, the total computational cost
Resolving Neighbourhood Relations in a Parallel Fluid Dynamic Solver
Frisch, Jerome; Mundani, Ralf-Peter; Rank, Ernst
2012-01-01
solver with a special aspect on the hierarchical data structure, unique cell and grid identification, and the neighbourhood relations in-between grids on different processes. A special server concept keeps track of every grid over all processes while
Advanced Algebraic Multigrid Solvers for Subsurface Flow Simulation
Chen, Meng-Huo; Sun, Shuyu; Salama, Amgad
2015-01-01
and issues will be addressed and the corresponding remedies will be studied. As the multigrid methods are used as the linear solver, the simulator can be parallelized (although not trivial) and the high-resolution simulation become feasible, the ultimately
A Family of High-Performance Solvers for Linear Model Predictive Control
DEFF Research Database (Denmark)
Frison, Gianluca; Sokoler, Leo Emil; Jørgensen, John Bagterp
2014-01-01
In Model Predictive Control (MPC), an optimization problem has to be solved at each sampling time, and this has traditionally limited the use of MPC to systems with slow dynamic. In this paper, we propose an e_cient solution strategy for the unconstrained sub-problems that give the search......-direction in Interior-Point (IP) methods for MPC, and that usually are the computational bottle-neck. This strategy combines a Riccati-like solver with the use of high-performance computing techniques: in particular, in this paper we explore the performance boost given by the use of single precision computation...
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)
Development and acceleration of unstructured mesh-based cfd solver
Emelyanov, V.; Karpenko, A.; Volkov, K.
2017-06-01
The study was undertaken as part of a larger effort to establish a common computational fluid dynamics (CFD) code for simulation of internal and external flows and involves some basic validation studies. The governing equations are solved with ¦nite volume code on unstructured meshes. The computational procedure involves reconstruction of the solution in each control volume and extrapolation of the unknowns to find the flow variables on the faces of control volume, solution of Riemann problem for each face of the control volume, and evolution of the time step. The nonlinear CFD solver works in an explicit time-marching fashion, based on a three-step Runge-Kutta stepping procedure. Convergence to a steady state is accelerated by the use of geometric technique and by the application of Jacobi preconditioning for high-speed flows, with a separate low Mach number preconditioning method for use with low-speed flows. The CFD code is implemented on graphics processing units (GPUs). Speedup of solution on GPUs with respect to solution on central processing units (CPU) is compared with the use of different meshes and different methods of distribution of input data into blocks. The results obtained provide promising perspective for designing a GPU-based software framework for applications in CFD.
A generalized Poisson solver for first-principles device simulations
Energy Technology Data Exchange (ETDEWEB)
Bani-Hashemian, Mohammad Hossein; VandeVondele, Joost, E-mail: joost.vandevondele@mat.ethz.ch [Nanoscale Simulations, ETH Zürich, 8093 Zürich (Switzerland); Brück, Sascha; Luisier, Mathieu [Integrated Systems Laboratory, ETH Zürich, 8092 Zürich (Switzerland)
2016-01-28
Electronic structure calculations of atomistic systems based on density functional theory involve solving the Poisson equation. In this paper, we present a plane-wave based algorithm for solving the generalized Poisson equation subject to periodic or homogeneous Neumann conditions on the boundaries of the simulation cell and Dirichlet type conditions imposed at arbitrary subdomains. In this way, source, drain, and gate voltages can be imposed across atomistic models of electronic devices. Dirichlet conditions are enforced as constraints in a variational framework giving rise to a saddle point problem. The resulting system of equations is then solved using a stationary iterative method in which the generalized Poisson operator is preconditioned with the standard Laplace operator. The solver can make use of any sufficiently smooth function modelling the dielectric constant, including density dependent dielectric continuum models. For all the boundary conditions, consistent derivatives are available and molecular dynamics simulations can be performed. The convergence behaviour of the scheme is investigated and its capabilities are demonstrated.
Parallelizable approximate solvers for recursions arising in preconditioning
Energy Technology Data Exchange (ETDEWEB)
Shapira, Y. [Israel Inst. of Technology, Haifa (Israel)
1996-12-31
For the recursions used in the Modified Incomplete LU (MILU) preconditioner, namely, the incomplete decomposition, forward elimination and back substitution processes, a parallelizable approximate solver is presented. The present analysis shows that the solutions of the recursions depend only weakly on their initial conditions and may be interpreted to indicate that the inexact solution is close, in some sense, to the exact one. The method is based on a domain decomposition approach, suitable for parallel implementations with message passing architectures. It requires a fixed number of communication steps per preconditioned iteration, independently of the number of subdomains or the size of the problem. The overlapping subdomains are either cubes (suitable for mesh-connected arrays of processors) or constructed by the data-flow rule of the recursions (suitable for line-connected arrays with possibly SIMD or vector processors). Numerical examples show that, in both cases, the overhead in the number of iterations required for convergence of the preconditioned iteration is small relatively to the speed-up gained.
A Python interface to Diffpack-based classes and solvers
Munthe-Kaas, Heidi Vikki
2013-01-01
Python is a programming language that has gained a lot of popularity during the last 15 years, and as a very easy-to-learn and flexible scripting language it is very well suited for computa- tional science, both in mathematics and in physics. Diffpack is a PDE library written in C++, made for easier implementation of both smaller PDE solvers and for larger libraries of simu- lators. It contains large class hierarchies for different solvers, grids, arrays, parallel computing and almost everyth...
International Nuclear Information System (INIS)
Hofer, E.
1981-01-01
Simulations in thermo- and fluiddynamics often require the numerical solution of large initial value problems with stiffness caused by eigenvalues close to the imaginary axis. The regions of absolute stability of the most widely used ordinary differential equation (ODE) solvers, for stiff problems, do not properly account for this. The paper introduces a general purpose ODE-solver with considerably larger stability regions. Its reliability is illustrated by test problems, with complex eigenvalues, from a well known test package. Applications in large codes, for simulations in thermo- and fluiddynamics, demonstrate its practical usability. (orig.) [de
International Nuclear Information System (INIS)
Boucker, M.; Laviaville, J.; Martin, A.; Bechaud, C.; Bestion, D.; Coste, P.
2004-01-01
The objective of this communication is to present some preliminary applications to pressurized thermal shock (PTS) investigations of the CFD (Computational Fluid Dynamics) two-phase flow solver of the new NEPTUNE thermal-hydraulics platform. In the framework of plant life extension, the Reactor Pressure Vessel (RPV) integrity is a major concern, and an important part of RPV integrity assessment is related to PTS analysis. In the case where the cold legs are partially filled with steam, it becomes a two-phase problem and new important effects occur, such as condensation due to the Emergency Core Cooling (ECC) injections of sub-cooled water. Thus, an advanced prediction of RPV thermal loading during these transients requires sophisticated two-phase, local scale, 3-dimensional codes. In that purpose, a program has been set up to extend the capabilities of the NEPTUNE two-phase CFD solver. A simple set of turbulence and condensation model for free surface steam-water flow has been tested in simulation of an ECC high pressure injection representing facility, using a full 3-dimensional mesh and the new NEPTUNE solver. Encouraging results have been obtained but it should be noticed that several sources of error can compensate for one another. Nevertheless, the computation presented here allows to be reasonable confident in the use of two-phase CFD in order to carry out refined analysis of two-phase PTS scenarios within the next years
Sound Probabilistic #SAT with Projection
Directory of Open Access Journals (Sweden)
Vladimir Klebanov
2016-10-01
Full Text Available We present an improved method for a sound probabilistic estimation of the model count of a boolean formula under projection. The problem solved can be used to encode a variety of quantitative program analyses, such as concerning security of resource consumption. We implement the technique and discuss its application to quantifying information flow in programs.
Verifying generalized soundness for workflow nets
Hee, van K.M.; Oanea, O.I.; Sidorova, N.; Voorhoeve, M.; Virbitskaite, I.; Voronkov, A.
2007-01-01
We improve the decision procedure from [10] for the problem of generalized soundness of workflow nets. A workflow net is generalized sound iff every marking reachable from an initial marking with k tokens on the initial place terminates properly, i.e. it can reach a marking with k tokens on the
Merwade, Venkatesh; Eichinger, David; Harriger, Bradley; Doherty, Erin; Habben, Ryan
2014-01-01
While the science of sound can be taught by explaining the concept of sound waves and vibrations, the authors of this article focused their efforts on creating a more engaging way to teach the science of sound--through engineering design. In this article they share the experience of teaching sound to third graders through an engineering challenge…
Sounds Exaggerate Visual Shape
Sweeny, Timothy D.; Guzman-Martinez, Emmanuel; Ortega, Laura; Grabowecky, Marcia; Suzuki, Satoru
2012-01-01
While perceiving speech, people see mouth shapes that are systematically associated with sounds. In particular, a vertically stretched mouth produces a /woo/ sound, whereas a horizontally stretched mouth produces a /wee/ sound. We demonstrate that hearing these speech sounds alters how we see aspect ratio, a basic visual feature that contributes…
Deal, Walter F., III
2007-01-01
Sound provides and offers amazing insights into the world. Sound waves may be defined as mechanical energy that moves through air or other medium as a longitudinal wave and consists of pressure fluctuations. Humans and animals alike use sound as a means of communication and a tool for survival. Mammals, such as bats, use ultrasonic sound waves to…
Directory of Open Access Journals (Sweden)
Baker M. Bani-Khair
2017-10-01
Full Text Available The Spider and the Fly You little spider, To death you aspire... Or seeking a web wider, To death all walking, No escape you all fighters… Weak and fragile in shape and might, Whatever you see in the horizon, That is destiny whatever sight. And tomorrow the spring comes, And the flowers bloom, And the grasshopper leaps high, And the frogs happily cry, And the flies smile nearby, To that end, The spider has a plot, To catch the flies by his net, A mosquito has fallen down in his net, Begging him to set her free, Out of that prison, To her freedom she aspires, Begging...Imploring...crying, That is all what she requires, But the spider vows never let her free, His power he admires, Turning blind to light, And with his teeth he shall bite, Leaving her in desperate might, Unable to move from site to site, Tied up with strings in white, Wrapped up like a dead man, Waiting for his grave at night, The mosquito says, Oh little spider, A stronger you are than me in power, But listen to my words before death hour, Today is mine and tomorrow is yours, No escape from death... Whatever the color of your flower… Little sounds The Ant The ant is a little creature with a ferocious soul, Looking and looking for more and more, You can simply crush it like dead mold, Or you can simply leave it alone, I wonder how strong and strong they are! Working day and night in a small hole, Their motto is work or whatever you call… A big boon they have and joy in fall, Because they found what they store, A lesson to learn and memorize all in all, Work is something that you should not ignore! The butterfly: I’m the butterfly Beautiful like a blue clear sky, Or sometimes look like snow, Different in colors, shapes and might, But something to know that we always die, So fragile, weak and thin, Lighter than a glimpse and delicate as light, Something to know for sure… Whatever you have in life and all these fields, You are not happier than a butterfly
Structure-borne sound structural vibrations and sound radiation at audio frequencies
Cremer, L; Petersson, Björn AT
2005-01-01
Structure-Borne Sound"" is a thorough introduction to structural vibrations with emphasis on audio frequencies and the associated radiation of sound. The book presents in-depth discussions of fundamental principles and basic problems, in order to enable the reader to understand and solve his own problems. It includes chapters dealing with measurement and generation of vibrations and sound, various types of structural wave motion, structural damping and its effects, impedances and vibration responses of the important types of structures, as well as with attenuation of vibrations, and sound radi
Continuous-time quantum Monte Carlo impurity solvers
Gull, Emanuel; Werner, Philipp; Fuchs, Sebastian; Surer, Brigitte; Pruschke, Thomas; Troyer, Matthias
2011-04-01
Continuous-time quantum Monte Carlo impurity solvers are algorithms that sample the partition function of an impurity model using diagrammatic Monte Carlo techniques. The present paper describes codes that implement the interaction expansion algorithm originally developed by Rubtsov, Savkin, and Lichtenstein, as well as the hybridization expansion method developed by Werner, Millis, Troyer, et al. These impurity solvers are part of the ALPS-DMFT application package and are accompanied by an implementation of dynamical mean-field self-consistency equations for (single orbital single site) dynamical mean-field problems with arbitrary densities of states. Program summaryProgram title: dmft Catalogue identifier: AEIL_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIL_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: ALPS LIBRARY LICENSE version 1.1 No. of lines in distributed program, including test data, etc.: 899 806 No. of bytes in distributed program, including test data, etc.: 32 153 916 Distribution format: tar.gz Programming language: C++ Operating system: The ALPS libraries have been tested on the following platforms and compilers: Linux with GNU Compiler Collection (g++ version 3.1 and higher), and Intel C++ Compiler (icc version 7.0 and higher) MacOS X with GNU Compiler (g++ Apple-version 3.1, 3.3 and 4.0) IBM AIX with Visual Age C++ (xlC version 6.0) and GNU (g++ version 3.1 and higher) compilers Compaq Tru64 UNIX with Compq C++ Compiler (cxx) SGI IRIX with MIPSpro C++ Compiler (CC) HP-UX with HP C++ Compiler (aCC) Windows with Cygwin or coLinux platforms and GNU Compiler Collection (g++ version 3.1 and higher) RAM: 10 MB-1 GB Classification: 7.3 External routines: ALPS [1], BLAS/LAPACK, HDF5 Nature of problem: (See [2].) Quantum impurity models describe an atom or molecule embedded in a host material with which it can exchange electrons. They are basic to nanoscience as
A high performance dual revised simplex solver
Hall, Julian; Huangfu, Qi
2012-01-01
When solving families of related linear programming (LP) problems and many classes of single LP problems, the simplex method is the preferred computational technique. Hitherto there has been no efficient parallel implementation of the simplex method that gives good speed-up on general, large sparse LP problems. This paper presents a variant of the dual simplex method and a prototype parallelisation scheme. The resulting implementation, ParISS, is efficient when run in serial and offers modest...
BCYCLIC: A parallel block tridiagonal matrix cyclic solver
Hirshman, S. P.; Perumalla, K. S.; Lynch, V. E.; Sanchez, R.
2010-09-01
A block tridiagonal matrix is factored with minimal fill-in using a cyclic reduction algorithm that is easily parallelized. Storage of the factored blocks allows the application of the inverse to multiple right-hand sides which may not be known at factorization time. Scalability with the number of block rows is achieved with cyclic reduction, while scalability with the block size is achieved using multithreaded routines (OpenMP, GotoBLAS) for block matrix manipulation. This dual scalability is a noteworthy feature of this new solver, as well as its ability to efficiently handle arbitrary (non-powers-of-2) block row and processor numbers. Comparison with a state-of-the art parallel sparse solver is presented. It is expected that this new solver will allow many physical applications to optimally use the parallel resources on current supercomputers. Example usage of the solver in magneto-hydrodynamic (MHD), three-dimensional equilibrium solvers for high-temperature fusion plasmas is cited.
MINOS: A simplified Pn solver for core calculation
International Nuclear Information System (INIS)
Baudron, A.M.; Lautard, J.J.
2007-01-01
This paper describes a new generation of the neutronic core solver MINOS resulting from developments done in the DESCARTES project. For performance reasons, the numerical method of the existing MINOS solver in the SAPHYR system has been reused in the new system. It is based on the mixed-dual finite element approximation of the simplified transport equation. We have extended the previous method to the treatment of unstructured geometries composed by quadrilaterals, allowing us to treat geometries where fuel pins are exactly represented. For Cartesian geometries, the solver takes into account assembly discontinuity coefficients in the simplified P n context. The solver has been rewritten in C + + programming language using an object-oriented design. Its general architecture was reconsidered in order to improve its capability of evolution and its maintainability. Moreover, the performance of the previous version has been improved mainly regarding the matrix construction time; this result improves significantly the performance of the solver in the context of industrial application requiring thermal-hydraulic feedback and depletion calculations. (authors)
International Nuclear Information System (INIS)
Lozano, Juan-Andres; Garcia-Herranz, Nuria; Ahnert, Carol; Aragones, Jose-Maria
2008-01-01
In this work we address the development and implementation of the analytic coarse-mesh finite-difference (ACMFD) method in a nodal neutron diffusion solver called ANDES. The first version of the solver is implemented in any number of neutron energy groups, and in 3D Cartesian geometries; thus it mainly addresses PWR and BWR core simulations. The details about the generalization to multigroups and 3D, as well as the implementation of the method are given. The transverse integration procedure is the scheme chosen to extend the ACMFD formulation to multidimensional problems. The role of the transverse leakage treatment in the accuracy of the nodal solutions is analyzed in detail: the involved assumptions, the limitations of the method in terms of nodal width, the alternative approaches to implement the transverse leakage terms in nodal methods - implicit or explicit -, and the error assessment due to transverse integration. A new approach for solving the control rod 'cusping' problem, based on the direct application of the ACMFD method, is also developed and implemented in ANDES. The solver architecture turns ANDES into an user-friendly, modular and easily linkable tool, as required to be integrated into common software platforms for multi-scale and multi-physics simulations. ANDES can be used either as a stand-alone nodal code or as a solver to accelerate the convergence of whole core pin-by-pin code systems. The verification and performance of the solver are demonstrated using both proof-of-principle test cases and well-referenced international benchmarks
International Nuclear Information System (INIS)
Vadlamani, Srinath; Kruger, Scott; Austin, Travis
2008-01-01
Extended magnetohydrodynamic (MHD) codes are used to model the large, slow-growing instabilities that are projected to limit the performance of International Thermonuclear Experimental Reactor (ITER). The multiscale nature of the extended MHD equations requires an implicit approach. The current linear solvers needed for the implicit algorithm scale poorly because the resultant matrices are so ill-conditioned. A new solver is needed, especially one that scales to the petascale. The most successful scalable parallel processor solvers to date are multigrid solvers. Applying multigrid techniques to a set of equations whose fundamental modes are dispersive waves is a promising solution to CEMM problems. For the Phase 1, we implemented multigrid preconditioners from the HYPRE project of the Center for Applied Scientific Computing at LLNL via PETSc of the DOE SciDAC TOPS for the real matrix systems of the extended MHD code NIMROD which is a one of the primary modeling codes of the OFES-funded Center for Extended Magnetohydrodynamic Modeling (CEMM) SciDAC. We implemented the multigrid solvers on the fusion test problem that allows for real matrix systems with success, and in the process learned about the details of NIMROD data structures and the difficulties of inverting NIMROD operators. The further success of this project will allow for efficient usage of future petascale computers at the National Leadership Facilities: Oak Ridge National Laboratory, Argonne National Laboratory, and National Energy Research Scientific Computing Center. The project will be a collaborative effort between computational plasma physicists and applied mathematicians at Tech-X Corporation, applied mathematicians Front Range Scientific Computations, Inc. (who are collaborators on the HYPRE project), and other computational plasma physicists involved with the CEMM project.
AbouEisha, Hassan M.
2016-06-02
In this paper we present a multi-criteria optimization of element partition trees and resulting orderings for multi-frontal solver algorithms executed for two dimensional h adaptive finite element method. In particular, the problem of optimal ordering of elimination of rows in the sparse matrices resulting from adaptive finite element method computations is reduced to the problem of finding of optimal element partition trees. Given a two dimensional h refined mesh, we find all optimal element partition trees by using the dynamic programming approach. An element partition tree defines a prescribed order of elimination of degrees of freedom over the mesh. We utilize three different metrics to estimate the quality of the element partition tree. As the first criterion we consider the number of floating point operations(FLOPs) performed by the multi-frontal solver. As the second criterion we consider the number of memory transfers (MEMOPS) performed by the multi-frontal solver algorithm. As the third criterion we consider memory usage (NONZEROS) of the multi-frontal direct solver. We show the optimization results for FLOPs vs MEMOPS as well as for the execution time estimated as FLOPs+100MEMOPS vs NONZEROS. We obtain Pareto fronts with multiple optimal trees, for each mesh, and for each refinement level. We generate a library of optimal elimination trees for small grids with local singularities. We also propose an algorithm that for a given large mesh with identified local sub-grids, each one with local singularity. We compute Schur complements over the sub-grids using the optimal trees from the library, and we submit the sequence of Schur complements into the iterative solver ILUPCG.
An h-adaptive finite element solver for the calculations of the electronic structures
International Nuclear Information System (INIS)
Bao Gang; Hu Guanghui; Liu Di
2012-01-01
In this paper, a framework of using h-adaptive finite element method for the Kohn–Sham equation on the tetrahedron mesh is presented. The Kohn–Sham equation is discretized by the finite element method, and the h-adaptive technique is adopted to optimize the accuracy and the efficiency of the algorithm. The locally optimal block preconditioned conjugate gradient method is employed for solving the generalized eigenvalue problem, and an algebraic multigrid preconditioner is used to accelerate the solver. A variety of numerical experiments demonstrate the effectiveness of our algorithm for both the all-electron and the pseudo-potential calculations.
Multilevel solvers of first-order system least-squares for Stokes equations
Energy Technology Data Exchange (ETDEWEB)
Lai, Chen-Yao G. [National Chung Cheng Univ., Chia-Yi (Taiwan, Province of China)
1996-12-31
Recently, The use of first-order system least squares principle for the approximate solution of Stokes problems has been extensively studied by Cai, Manteuffel, and McCormick. In this paper, we study multilevel solvers of first-order system least-squares method for the generalized Stokes equations based on the velocity-vorticity-pressure formulation in three dimensions. The least-squares functionals is defined to be the sum of the L{sup 2}-norms of the residuals, which is weighted appropriately by the Reynolds number. We develop convergence analysis for additive and multiplicative multilevel methods applied to the resulting discrete equations.
Description and use of LSODE, the Livermore Solver for Ordinary Differential Equations
Radhakrishnan, Krishnan; Hindmarsh, Alan C.
1993-01-01
LSODE, the Livermore Solver for Ordinary Differential Equations, is a package of FORTRAN subroutines designed for the numerical solution of the initial value problem for a system of ordinary differential equations. It is particularly well suited for 'stiff' differential systems, for which the backward differentiation formula method of orders 1 to 5 is provided. The code includes the Adams-Moulton method of orders 1 to 12, so it can be used for nonstiff problems as well. In addition, the user can easily switch methods to increase computational efficiency for problems that change character. For both methods a variety of corrector iteration techniques is included in the code. Also, to minimize computational work, both the step size and method order are varied dynamically. This report presents complete descriptions of the code and integration methods, including their implementation. It also provides a detailed guide to the use of the code, as well as an illustrative example problem.
Control of error and convergence in ODE solvers
International Nuclear Information System (INIS)
Gustafsson, K.
1992-03-01
Feedback is a general principle that can be used in many different contexts. In this thesis it is applied to numerical integration of ordinary differential equations. An advanced integration method includes parameters and variables that should be adjusted during the execution. In addition, the integration method should be able to automatically handle situations such as: initialization, restart after failures, etc. In this thesis we regard the algorithms for parameter adjustment and supervision as a controller. The controlled measures different variable that tell the current status of the integration, and based on this information it decides how to continue. The design of the controller is vital in order to accurately and efficiently solve a large class of ordinary differential equations. The application of feedback control may appear farfetched, but numerical integration methods are in fact dynamical systems. This is often overlooked in traditional numerical analysis. We derive dynamic models that describe the behavior of the integration method as well as the standard control algorithms in use today. Using these models it is possible to analyze properties of current algorithms, and also explain some generally observed misbehaviors. Further, we use the acquired insight to derive new and improved control algorithms, both for explicit and implicit Runge-Kutta methods. In the explicit case, the new controller gives good overall performance. In particular it overcomes the problem with oscillating stepsize sequence that is often experienced when the stepsize is restricted by numerical stability. The controller for implicit methods is designed so that it tracks changes in the differential equation better than current algorithms. In addition, it includes a new strategy for the equation solver, which allows the stepsize to vary more freely. This leads to smoother error control without excessive operations on the iteration matrix. (87 refs.) (au)
Efficient techniques for wave-based sound propagation in interactive applications
Mehra, Ravish
Sound propagation techniques model the effect of the environment on sound waves and predict their behavior from point of emission at the source to the final point of arrival at the listener. Sound is a pressure wave produced by mechanical vibration of a surface that propagates through a medium such as air or water, and the problem of sound propagation can be formulated mathematically as a second-order partial differential equation called the wave equation. Accurate techniques based on solving the wave equation, also called the wave-based techniques, are too expensive computationally and memory-wise. Therefore, these techniques face many challenges in terms of their applicability in interactive applications including sound propagation in large environments, time-varying source and listener directivity, and high simulation cost for mid-frequencies. In this dissertation, we propose a set of efficient wave-based sound propagation techniques that solve these three challenges and enable the use of wave-based sound propagation in interactive applications. Firstly, we propose a novel equivalent source technique for interactive wave-based sound propagation in large scenes spanning hundreds of meters. It is based on the equivalent source theory used for solving radiation and scattering problems in acoustics and electromagnetics. Instead of using a volumetric or surface-based approach, this technique takes an object-centric approach to sound propagation. The proposed equivalent source technique generates realistic acoustic effects and takes orders of magnitude less runtime memory compared to prior wave-based techniques. Secondly, we present an efficient framework for handling time-varying source and listener directivity for interactive wave-based sound propagation. The source directivity is represented as a linear combination of elementary spherical harmonic sources. This spherical harmonic-based representation of source directivity can support analytical, data
Energy consumption optimization of the total-FETI solver by changing the CPU frequency
Horak, David; Riha, Lubomir; Sojka, Radim; Kruzik, Jakub; Beseda, Martin; Cermak, Martin; Schuchart, Joseph
2017-07-01
The energy consumption of supercomputers is one of the critical problems for the upcoming Exascale supercomputing era. The awareness of power and energy consumption is required on both software and hardware side. This paper deals with the energy consumption evaluation of the Finite Element Tearing and Interconnect (FETI) based solvers of linear systems, which is an established method for solving real-world engineering problems. We have evaluated the effect of the CPU frequency on the energy consumption of the FETI solver using a linear elasticity 3D cube synthetic benchmark. In this problem, we have evaluated the effect of frequency tuning on the energy consumption of the essential processing kernels of the FETI method. The paper provides results for two types of frequency tuning: (1) static tuning and (2) dynamic tuning. For static tuning experiments, the frequency is set before execution and kept constant during the runtime. For dynamic tuning, the frequency is changed during the program execution to adapt the system to the actual needs of the application. The paper shows that static tuning brings up 12% energy savings when compared to default CPU settings (the highest clock rate). The dynamic tuning improves this further by up to 3%.
Sound wave transmission (image)
When sounds waves reach the ear, they are translated into nerve impulses. These impulses then travel to the brain where they are interpreted by the brain as sound. The hearing mechanisms within the inner ear, can ...
DEFF Research Database (Denmark)
Langkjær, Birger
2010-01-01
This article examines the role that sound plays in making fictions perceptually real to film audiences, whether these fictions are realist or non-realist in content and narrative form. I will argue that some aspects of film sound practices and the kind of experiences they trigger are related...... to basic rules of human perception, whereas others are more properly explained in relation to how aesthetic devices, including sound, are used to characterise the fiction and thereby make it perceptually real to its audience. Finally, I will argue that not all genres can be defined by a simple taxonomy...... of sounds. Apart from an account of the kinds of sounds that typically appear in a specific genre, a genre analysis of sound may also benefit from a functionalist approach that focuses on how sounds can make both realist and non-realist aspects of genres sound real to audiences....
MINARET: Towards a time-dependent neutron transport parallel solver
International Nuclear Information System (INIS)
Baudron, A.M.; Lautard, J.J.; Maday, Y.; Mula, O.
2013-01-01
We present the newly developed time-dependent 3D multigroup discrete ordinates neutron transport solver that has recently been implemented in the MINARET code. The solver is the support for a study about computing acceleration techniques that involve parallel architectures. In this work, we will focus on the parallelization of two of the variables involved in our equation: the angular directions and the time. This last variable has been parallelized by a (time) domain decomposition method called the para-real in time algorithm. (authors)
DEFF Research Database (Denmark)
Groth, Sanne Krogh
2015-01-01
PROFESSOR PORTRAIT: Sanne Krogh Groth met Holger Schulze, newly appointed professor in Musicology at the Department for Arts and Cultural Studies, University of Copenhagen, to a talk about anthropology of sound, sound studies, musical canons and ideology.......PROFESSOR PORTRAIT: Sanne Krogh Groth met Holger Schulze, newly appointed professor in Musicology at the Department for Arts and Cultural Studies, University of Copenhagen, to a talk about anthropology of sound, sound studies, musical canons and ideology....
Talbot-Smith, Michael
1990-01-01
Broadcast Sound Technology provides an explanation of the underlying principles of modern audio technology. Organized into 21 chapters, the book first describes the basic sound; behavior of sound waves; aspects of hearing, harming, and charming the ear; room acoustics; reverberation; microphones; phantom power; loudspeakers; basic stereo; and monitoring of audio signal. Subsequent chapters explore the processing of audio signal, sockets, sound desks, and digital audio. Analogue and digital tape recording and reproduction, as well as noise reduction, are also explained.
DEFF Research Database (Denmark)
Wahlberg, Magnus; Larsen, Ole Næsbye
2017-01-01
properties can be modified by sound absorption, refraction, and interference from multi paths caused by reflections.The path from the source to the receiver may be bent due to refraction. Besides geometrical attenuation, the ground effect and turbulence are the most important mechanisms to influence...... communication sounds for airborne acoustics and bottom and surface effects for underwater sounds. Refraction becomes very important close to shadow zones. For echolocation signals, geometric attenuation and sound absorption have the largest effects on the signals....
Computational cost of isogeometric multi-frontal solvers on parallel distributed memory machines
Woźniak, Maciej
2015-02-01
This paper derives theoretical estimates of the computational cost for isogeometric multi-frontal direct solver executed on parallel distributed memory machines. We show theoretically that for the Cp-1 global continuity of the isogeometric solution, both the computational cost and the communication cost of a direct solver are of order O(log(N)p2) for the one dimensional (1D) case, O(Np2) for the two dimensional (2D) case, and O(N4/3p2) for the three dimensional (3D) case, where N is the number of degrees of freedom and p is the polynomial order of the B-spline basis functions. The theoretical estimates are verified by numerical experiments performed with three parallel multi-frontal direct solvers: MUMPS, PaStiX and SuperLU, available through PETIGA toolkit built on top of PETSc. Numerical results confirm these theoretical estimates both in terms of p and N. For a given problem size, the strong efficiency rapidly decreases as the number of processors increases, becoming about 20% for 256 processors for a 3D example with 1283 unknowns and linear B-splines with C0 global continuity, and 15% for a 3D example with 643 unknowns and quartic B-splines with C3 global continuity. At the same time, one cannot arbitrarily increase the problem size, since the memory required by higher order continuity spaces is large, quickly consuming all the available memory resources even in the parallel distributed memory version. Numerical results also suggest that the use of distributed parallel machines is highly beneficial when solving higher order continuity spaces, although the number of processors that one can efficiently employ is somehow limited.
Acceleration of the OpenFOAM-based MHD solver using graphics processing units
International Nuclear Information System (INIS)
He, Qingyun; Chen, Hongli; Feng, Jingchao
2015-01-01
Highlights: • A 3D PISO-MHD was implemented on Kepler-class graphics processing units (GPUs) using CUDA technology. • A consistent and conservative scheme is used in the code which was validated by three basic benchmarks in a rectangular and round ducts. • Parallelized of CPU and GPU acceleration were compared relating to single core CPU in MHD problems and non-MHD problems. • Different preconditions for solving MHD solver were compared and the results showed that AMG method is better for calculations. - Abstract: The pressure-implicit with splitting of operators (PISO) magnetohydrodynamics MHD solver of the couple of Navier–Stokes equations and Maxwell equations was implemented on Kepler-class graphics processing units (GPUs) using the CUDA technology. The solver is developed on open source code OpenFOAM based on consistent and conservative scheme which is suitable for simulating MHD flow under strong magnetic field in fusion liquid metal blanket with structured or unstructured mesh. We verified the validity of the implementation on several standard cases including the benchmark I of Shercliff and Hunt's cases, benchmark II of fully developed circular pipe MHD flow cases and benchmark III of KIT experimental case. Computational performance of the GPU implementation was examined by comparing its double precision run times with those of essentially the same algorithms and meshes. The resulted showed that a GPU (GTX 770) can outperform a server-class 4-core, 8-thread CPU (Intel Core i7-4770k) by a factor of 2 at least.
Acceleration of the OpenFOAM-based MHD solver using graphics processing units
Energy Technology Data Exchange (ETDEWEB)
He, Qingyun; Chen, Hongli, E-mail: hlchen1@ustc.edu.cn; Feng, Jingchao
2015-12-15
Highlights: • A 3D PISO-MHD was implemented on Kepler-class graphics processing units (GPUs) using CUDA technology. • A consistent and conservative scheme is used in the code which was validated by three basic benchmarks in a rectangular and round ducts. • Parallelized of CPU and GPU acceleration were compared relating to single core CPU in MHD problems and non-MHD problems. • Different preconditions for solving MHD solver were compared and the results showed that AMG method is better for calculations. - Abstract: The pressure-implicit with splitting of operators (PISO) magnetohydrodynamics MHD solver of the couple of Navier–Stokes equations and Maxwell equations was implemented on Kepler-class graphics processing units (GPUs) using the CUDA technology. The solver is developed on open source code OpenFOAM based on consistent and conservative scheme which is suitable for simulating MHD flow under strong magnetic field in fusion liquid metal blanket with structured or unstructured mesh. We verified the validity of the implementation on several standard cases including the benchmark I of Shercliff and Hunt's cases, benchmark II of fully developed circular pipe MHD flow cases and benchmark III of KIT experimental case. Computational performance of the GPU implementation was examined by comparing its double precision run times with those of essentially the same algorithms and meshes. The resulted showed that a GPU (GTX 770) can outperform a server-class 4-core, 8-thread CPU (Intel Core i7-4770k) by a factor of 2 at least.
Scalable multi-grid preconditioning techniques for the even-parity S_N solver in UNIC
International Nuclear Information System (INIS)
Mahadevan, Vijay S.; Smith, Michael A.
2011-01-01
The Even-parity neutron transport equation with FE-S_N discretization is solved traditionally using SOR preconditioned CG method at the lowest level of iterations in order to compute the criticality in reactor analysis problems. The use of high order isoparametric finite elements prohibits the formation of the discrete operator explicitly due to memory constraints in peta scale architectures. Hence, a h-p multi-grid preconditioner based on linear tessellation of the higher order mesh is introduced here for the space-angle system and compared against SOR and Algebraic MG black-box solvers. The performance and scalability of the multi-grid scheme was determined for two test problems and found to be competitive in terms of both computational time and memory requirements. The implementation of this preconditioner in an even-parity solver like UNIC from ANL can further enable high fidelity calculations in a scalable manner on peta flop machines. (author)
Abnormal sound detection device
International Nuclear Information System (INIS)
Yamada, Izumi; Matsui, Yuji.
1995-01-01
Only components synchronized with rotation of pumps are sampled from detected acoustic sounds, to judge the presence or absence of abnormality based on the magnitude of the synchronized components. A synchronized component sampling means can remove resonance sounds and other acoustic sounds generated at a synchronously with the rotation based on the knowledge that generated acoustic components in a normal state are a sort of resonance sounds and are not precisely synchronized with the number of rotation. On the other hand, abnormal sounds of a rotating body are often caused by compulsory force accompanying the rotation as a generation source, and the abnormal sounds can be detected by extracting only the rotation-synchronized components. Since components of normal acoustic sounds generated at present are discriminated from the detected sounds, reduction of the abnormal sounds due to a signal processing can be avoided and, as a result, abnormal sound detection sensitivity can be improved. Further, since it is adapted to discriminate the occurrence of the abnormal sound from the actually detected sounds, the other frequency components which are forecast but not generated actually are not removed, so that it is further effective for the improvement of detection sensitivity. (N.H.)
Modelling Hyperboloid Sound Scattering
DEFF Research Database (Denmark)
Burry, Jane; Davis, Daniel; Peters, Brady
2011-01-01
The Responsive Acoustic Surfaces workshop project described here sought new understandings about the interaction between geometry and sound in the arena of sound scattering. This paper reports on the challenges associated with modelling, simulating, fabricating and measuring this phenomenon using...... both physical and digital models at three distinct scales. The results suggest hyperboloid geometry, while difficult to fabricate, facilitates sound scattering....
A parallel solver for huge dense linear systems
Badia, J. M.; Movilla, J. L.; Climente, J. I.; Castillo, M.; Marqués, M.; Mayo, R.; Quintana-Ortí, E. S.; Planelles, J.
2011-11-01
HDSS (Huge Dense Linear System Solver) is a Fortran Application Programming Interface (API) to facilitate the parallel solution of very large dense systems to scientists and engineers. The API makes use of parallelism to yield an efficient solution of the systems on a wide range of parallel platforms, from clusters of processors to massively parallel multiprocessors. It exploits out-of-core strategies to leverage the secondary memory in order to solve huge linear systems O(100.000). The API is based on the parallel linear algebra library PLAPACK, and on its Out-Of-Core (OOC) extension POOCLAPACK. Both PLAPACK and POOCLAPACK use the Message Passing Interface (MPI) as the communication layer and BLAS to perform the local matrix operations. The API provides a friendly interface to the users, hiding almost all the technical aspects related to the parallel execution of the code and the use of the secondary memory to solve the systems. In particular, the API can automatically select the best way to store and solve the systems, depending of the dimension of the system, the number of processes and the main memory of the platform. Experimental results on several parallel platforms report high performance, reaching more than 1 TFLOP with 64 cores to solve a system with more than 200 000 equations and more than 10 000 right-hand side vectors. New version program summaryProgram title: Huge Dense System Solver (HDSS) Catalogue identifier: AEHU_v1_1 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHU_v1_1.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 87 062 No. of bytes in distributed program, including test data, etc.: 1 069 110 Distribution format: tar.gz Programming language: Fortran90, C Computer: Parallel architectures: multiprocessors, computer clusters Operating system
Clark, S.G.; Rutherford, M.B.; Auer, M.R.; Cherney, D.N.; Wallace, R.L.; Mattson, D.J.; Clark, D.A.; Foote, L.; Krogman, N.; Wilshusen, P.; Steelman, T.
2011-01-01
The environmental sciences/studies movement, with more than 1000 programs at colleges and universities in the United States and Canada, is unified by a common interest-ameliorating environmental problems through empirical enquiry and analytic judgment. Unfortunately, environmental programs have struggled in their efforts to integrate knowledge across disciplines and educate students to become sound problem solvers and leaders. We examine the environmental program movement as a policy problem, looking at overall goals, mapping trends in relation to those goals, identifying the underlying factors contributing to trends, and projecting the future. We argue that despite its shared common interest, the environmental program movement is disparate and fragmented by goal ambiguity, positivistic disciplinary approaches, and poorly rationalized curricula, pedagogies, and educational philosophies. We discuss these challenges and the nature of the changes that are needed in order to overcome them. In a subsequent article (Part 2) we propose specific strategies for improvement. ?? 2011 Springer Science+Business Media, LLC.
Diffuse sound field: challenges and misconceptions
DEFF Research Database (Denmark)
Jeong, Cheol-Ho
2016-01-01
Diffuse sound field is a popular, yet widely misused concept. Although its definition is relatively well established, acousticians use this term for different meanings. The diffuse sound field is defined by a uniform sound pressure distribution (spatial diffusion or homogeneity) and uniform...... tremendously in different chambers because the chambers are non-diffuse in variously different ways. Therefore, good objective measures that can quantify the degree of diffusion and potentially indicate how to fix such problems in reverberation chambers are needed. Acousticians often blend the concept...... of mixing and diffuse sound field. Acousticians often refer diffuse reflections from surfaces to diffuseness in rooms, and vice versa. Subjective aspects of diffuseness have not been much investigated. Finally, ways to realize a diffuse sound field in a finite space are discussed....
Numerical solver for compressible two-fluid flow
J. Naber (Jorick)
2005-01-01
textabstractThis report treats the development of a numerical solver for the simulation of flows of two non-mixing fluids described by the two-dimensional Euler equations. A level-set equation in conservative form describes the interface. After each time step the deformed level-set function is
Using a satisfiability solver to identify deterministic finite state automata
Heule, M.J.H.; Verwer, S.
2009-01-01
We present an exact algorithm for identification of deterministic finite automata (DFA) which is based on satisfiability (SAT) solvers. Despite the size of the low level SAT representation, our approach seems to be competitive with alternative techniques. Our contributions are threefold: First, we
A High Performance QDWH-SVD Solver using Hardware Accelerators
Sukkari, Dalal E.; Ltaief, Hatem; Keyes, David E.
2015-01-01
few digits of accuracy, compared to the full double precision floating point arithmetic. We further leverage the single GPU QDWH-SVD implementation by introducing the first multi-GPU SVD solver to study the scalability of the QDWH-SVD framework.
Hypersonic simulations using open-source CFD and DSMC solvers
Casseau, V.; Scanlon, T. J.; John, B.; Emerson, D. R.; Brown, R. E.
2016-11-01
Hypersonic hybrid hydrodynamic-molecular gas flow solvers are required to satisfy the two essential requirements of any high-speed reacting code, these being physical accuracy and computational efficiency. The James Weir Fluids Laboratory at the University of Strathclyde is currently developing an open-source hybrid code which will eventually reconcile the direct simulation Monte-Carlo method, making use of the OpenFOAM application called dsmcFoam, and the newly coded open-source two-temperature computational fluid dynamics solver named hy2Foam. In conjunction with employing the CVDV chemistry-vibration model in hy2Foam, novel use is made of the QK rates in a CFD solver. In this paper, further testing is performed, in particular with the CFD solver, to ensure its efficacy before considering more advanced test cases. The hy2Foam and dsmcFoam codes have shown to compare reasonably well, thus providing a useful basis for other codes to compare against.
Implementing parallel elliptic solver on a Beowulf cluster
Directory of Open Access Journals (Sweden)
Marcin Paprzycki
1999-12-01
Full Text Available In a recent paper cite{zara} a parallel direct solver for the linear systems arising from elliptic partial differential equations has been proposed. The aim of this note is to present the initial evaluation of the performance characteristics of this algorithm on Beowulf-type cluster. In this context the performance of PVM and MPI based implementations is compared.
Implementation of Generalized Adjoint Equation Solver for DeCART
International Nuclear Information System (INIS)
Han, Tae Young; Cho, Jin Young; Lee, Hyun Chul; Noh, Jae Man
2013-01-01
In this paper, the generalized adjoint solver based on the generalized perturbation theory is implemented on DeCART and the verification calculations were carried out. As the results, the adjoint flux for the general response coincides with the reference solution and it is expected that the solver could produce the parameters for the sensitivity and uncertainty analysis. Recently, MUSAD (Modules of Uncertainty and Sensitivity Analysis for DeCART) was developed for the uncertainty analysis of PMR200 core and the fundamental adjoint solver was implemented into DeCART. However, the application of the code was limited to the uncertainty to the multiplication factor, k eff , because it was based on the classical perturbation theory. For the uncertainty analysis to the general response as like the power density, it is necessary to develop the analysis module based on the generalized perturbation theory and it needs the generalized adjoint solutions from DeCART. In this paper, the generalized adjoint solver is implemented on DeCART and the calculation results are compared with the results by TSUNAMI of SCALE 6.1
A Parallel Algebraic Multigrid Solver on Graphics Processing Units
Haase, Gundolf; Liebmann, Manfred; Douglas, Craig C.; Plank, Gernot
2010-01-01
-vector multiplication scheme underlying the PCG-AMG algorithm is presented for the many-core GPU architecture. A performance comparison of the parallel solver shows that a singe Nvidia Tesla C1060 GPU board delivers the performance of a sixteen node Infiniband cluster
Analysis of transient plasmonic interactions using an MOT-PMCHWT integral equation solver
Uysal, Ismail Enes; Ulku, Huseyin Arda; Bagci, Hakan
2014-01-01
that discretize only on the interfaces. Additionally, IE solvers implicitly enforce the radiation condition and consequently do not need (approximate) absorbing boundary conditions. Despite these advantages, IE solvers, especially in time domain, have not been
Operator performance and annunciation sounds
International Nuclear Information System (INIS)
Patterson, B.K.; Bradley, M.T.; Artiss, W.G.
1997-01-01
This paper discusses the audible component of annunciation found in typical operating power stations. The purpose of the audible alarm is stated and the psychological elements involved in the human processing of alarm sounds is explored. Psychological problems with audible annunciation are noted. Simple and more complex improvements to existing systems are described. A modern alarm system is suggested for retrofits or new plant designs. (author)
Operator performance and annunciation sounds
Energy Technology Data Exchange (ETDEWEB)
Patterson, B K; Bradley, M T; Artiss, W G [Human Factors Practical, Dipper Harbour, NB (Canada)
1998-12-31
This paper discusses the audible component of annunciation found in typical operating power stations. The purpose of the audible alarm is stated and the psychological elements involved in the human processing of alarm sounds is explored. Psychological problems with audible annunciation are noted. Simple and more complex improvements to existing systems are described. A modern alarm system is suggested for retrofits or new plant designs. (author) 3 refs.
2013-03-01
...-123-LNG; 12-128-NG; 12-148-NG; 12- 158-NG] Puget Sound Energy, Inc.; Puget Sound Energy, Inc.; Puget Sound Energy, Inc.; Puget Sound Energy, Inc.; Puget Sound Energy, Inc.; CE FLNG, LLC; Consolidated...-NG Puget Sound Energy, Inc Order granting long- term authority to import/export natural gas from/to...
A High Performance QDWH-SVD Solver using Hardware Accelerators
Sukkari, Dalal E.
2015-04-08
This paper describes a new high performance implementation of the QR-based Dynamically Weighted Halley Singular Value Decomposition (QDWH-SVD) solver on multicore architecture enhanced with multiple GPUs. The standard QDWH-SVD algorithm was introduced by Nakatsukasa and Higham (SIAM SISC, 2013) and combines three successive computational stages: (1) the polar decomposition calculation of the original matrix using the QDWH algorithm, (2) the symmetric eigendecomposition of the resulting polar factor to obtain the singular values and the right singular vectors and (3) the matrix-matrix multiplication to get the associated left singular vectors. A comprehensive test suite highlights the numerical robustness of the QDWH-SVD solver. Although it performs up to two times more flops when computing all singular vectors compared to the standard SVD solver algorithm, our new high performance implementation on single GPU results in up to 3.8x improvements for asymptotic matrix sizes, compared to the equivalent routines from existing state-of-the-art open-source and commercial libraries. However, when only singular values are needed, QDWH-SVD is penalized by performing up to 14 times more flops. The singular value only implementation of QDWH-SVD on single GPU can still run up to 18% faster than the best existing equivalent routines. Integrating mixed precision techniques in the solver can additionally provide up to 40% improvement at the price of losing few digits of accuracy, compared to the full double precision floating point arithmetic. We further leverage the single GPU QDWH-SVD implementation by introducing the first multi-GPU SVD solver to study the scalability of the QDWH-SVD framework.
Memory transfer optimization for a lattice Boltzmann solver on Kepler architecture nVidia GPUs
Mawson, Mark J.; Revell, Alistair J.
2014-10-01
The Lattice Boltzmann method (LBM) for solving fluid flow is naturally well suited to an efficient implementation for massively parallel computing, due to the prevalence of local operations in the algorithm. This paper presents and analyses the performance of a 3D lattice Boltzmann solver, optimized for third generation nVidia GPU hardware, also known as 'Kepler'. We provide a review of previous optimization strategies and analyse data read/write times for different memory types. In LBM, the time propagation step (known as streaming), involves shifting data to adjacent locations and is central to parallel performance; here we examine three approaches which make use of different hardware options. Two of which make use of 'performance enhancing' features of the GPU; shared memory and the new shuffle instruction found in Kepler based GPUs. These are compared to a standard transfer of data which relies instead on optimized storage to increase coalesced access. It is shown that the more simple approach is most efficient; since the need for large numbers of registers per thread in LBM limits the block size and thus the efficiency of these special features is reduced. Detailed results are obtained for a D3Q19 LBM solver, which is benchmarked on nVidia K5000M and K20C GPUs. In the latter case the use of a read-only data cache is explored, and peak performance of over 1036 Million Lattice Updates Per Second (MLUPS) is achieved. The appearance of a periodic bottleneck in the solver performance is also reported, believed to be hardware related; spikes in iteration-time occur with a frequency of around 11 Hz for both GPUs, independent of the size of the problem.
Riemann solvers for multi-component gas mixtures with temperature dependent heat capacities
International Nuclear Information System (INIS)
Beccantini, A.
2001-01-01
This thesis represents a contribution to the development of upwind splitting schemes for the Euler equations for ideal gaseous mixtures and their investigation in computing multidimensional flows in irregular geometries. In the preliminary part we develop and investigate the parameterization of the shock and rarefaction curves in the phase space. Then, we apply them to perform some field-by-field decompositions of the Riemann problem: the entropy-respecting one, the one which supposes that genuinely-non-linear (GNL) waves are both shocks (shock-shock one) and the one which supposes that GNL waves are both rarefactions (rarefaction-rarefaction one). We emphasize that their analysis is fundamental in Riemann solvers developing: the simpler the field-by-field decomposition, the simpler the Riemann solver based on it. As the specific heat capacities of the gases depend on the temperature, the shock-shock field-by-field decomposition is the easiest to perform. Then, in the second part of the thesis, we develop an upwind splitting scheme based on such decomposition. Afterwards, we investigate its robustness, precision and CPU-time consumption, with respect to some of the most popular upwind splitting schemes for polytropic/non-polytropic ideal gases. 1-D test-cases show that this scheme is both precise (exact capturing of stationary shock and stationary contact) and robust in dealing with strong shock and rarefaction waves. Multidimensional test-cases show that it suffers from some of the typical deficiencies which affect the upwind splitting schemes capable of exact capturing stationary contact discontinuities i.e the developing of non-physical instabilities in computing strong shock waves. In the final part, we use the high-order multidimensional solver here developed to compute fully-developed detonation flows. (author)
Toward robust scalable algebraic multigrid solvers
International Nuclear Information System (INIS)
Waisman, Haim; Schroder, Jacob; Olson, Luke; Hiriyur, Badri; Gaidamour, Jeremie; Siefert, Christopher; Hu, Jonathan Joseph; Tuminaro, Raymond Stephen
2010-01-01
This talk highlights some multigrid challenges that arise from several application areas including structural dynamics, fluid flow, and electromagnetics. A general framework is presented to help introduce and understand algebraic multigrid methods based on energy minimization concepts. Connections between algebraic multigrid prolongators and finite element basis functions are made to explored. It is shown how the general algebraic multigrid framework allows one to adapt multigrid ideas to a number of different situations. Examples are given corresponding to linear elasticity and specifically in the solution of linear systems associated with extended finite elements for fracture problems.
Efficient Parallel Kernel Solvers for Computational Fluid Dynamics Applications
Sun, Xian-He
1997-01-01
Distributed-memory parallel computers dominate today's parallel computing arena. These machines, such as Intel Paragon, IBM SP2, and Cray Origin2OO, have successfully delivered high performance computing power for solving some of the so-called "grand-challenge" problems. Despite initial success, parallel machines have not been widely accepted in production engineering environments due to the complexity of parallel programming. On a parallel computing system, a task has to be partitioned and distributed appropriately among processors to reduce communication cost and to attain load balance. More importantly, even with careful partitioning and mapping, the performance of an algorithm may still be unsatisfactory, since conventional sequential algorithms may be serial in nature and may not be implemented efficiently on parallel machines. In many cases, new algorithms have to be introduced to increase parallel performance. In order to achieve optimal performance, in addition to partitioning and mapping, a careful performance study should be conducted for a given application to find a good algorithm-machine combination. This process, however, is usually painful and elusive. The goal of this project is to design and develop efficient parallel algorithms for highly accurate Computational Fluid Dynamics (CFD) simulations and other engineering applications. The work plan is 1) developing highly accurate parallel numerical algorithms, 2) conduct preliminary testing to verify the effectiveness and potential of these algorithms, 3) incorporate newly developed algorithms into actual simulation packages. The work plan has well achieved. Two highly accurate, efficient Poisson solvers have been developed and tested based on two different approaches: (1) Adopting a mathematical geometry which has a better capacity to describe the fluid, (2) Using compact scheme to gain high order accuracy in numerical discretization. The previously developed Parallel Diagonal Dominant (PDD) algorithm
A Sound Abstraction of the Parsing Problem
DEFF Research Database (Denmark)
Mödersheim, Sebastian Alexander; Katsoris, Georgios
2014-01-01
In formal verification, cryptographic messages are often represented by algebraic terms. This abstracts not only from the intricate details of the real cryptography, but also from the details of the non-cryptographic aspects: the actual formatting and structuring of messages. We introduce a new a...
Sound Insulation between Dwellings
DEFF Research Database (Denmark)
Rasmussen, Birgit
2011-01-01
Regulatory sound insulation requirements for dwellings exist in more than 30 countries in Europe. In some countries, requirements have existed since the 1950s. Findings from comparative studies show that sound insulation descriptors and requirements represent a high degree of diversity...... and initiate – where needed – improvement of sound insulation of new and existing dwellings in Europe to the benefit of the inhabitants and the society. A European COST Action TU0901 "Integrating and Harmonizing Sound Insulation Aspects in Sustainable Urban Housing Constructions", has been established and runs...... 2009-2013. The main objectives of TU0901 are to prepare proposals for harmonized sound insulation descriptors and for a European sound classification scheme with a number of quality classes for dwellings. Findings from the studies provide input for the discussions in COST TU0901. Data collected from 24...
Fast Solvers for Cahn--Hilliard Inpainting
Bosch, Jessica; Kay, David; Stoll, Martin; Wathen, Andrew J.
2014-01-01
The solution of Cahn-Hilliard variational inequalities is of interest in many applications. We discuss the use of them as a tool for binary image inpainting. This has been done before using double-well potentials but not for nonsmooth potentials as considered here. The existing bound constraints are incorporated via the Moreau-Yosida regularization technique. We develop effective preconditioners for the efficient solution of the Newton steps associated with the fast solution of the Moreau-Yosida regularized problem. Numerical results illustrate the efficiency of our approach. Moreover, precise eigenvalue intervals are given for the preconditioned system using a double-well potential. A comparison between the smooth and nonsmooth Cahn-Hilliard inpainting models shows that the latter achieves better results. © 2014 Society for Industrial and Applied Mathematics.
Fast Solvers for Cahn--Hilliard Inpainting
Bosch, Jessica
2014-01-02
The solution of Cahn-Hilliard variational inequalities is of interest in many applications. We discuss the use of them as a tool for binary image inpainting. This has been done before using double-well potentials but not for nonsmooth potentials as considered here. The existing bound constraints are incorporated via the Moreau-Yosida regularization technique. We develop effective preconditioners for the efficient solution of the Newton steps associated with the fast solution of the Moreau-Yosida regularized problem. Numerical results illustrate the efficiency of our approach. Moreover, precise eigenvalue intervals are given for the preconditioned system using a double-well potential. A comparison between the smooth and nonsmooth Cahn-Hilliard inpainting models shows that the latter achieves better results. © 2014 Society for Industrial and Applied Mathematics.
Periodic Poisson Solver for Particle Tracking
International Nuclear Information System (INIS)
Dohlus, M.; Henning, C.
2015-05-01
A method is described to solve the Poisson problem for a three dimensional source distribution that is periodic into one direction. Perpendicular to the direction of periodicity a free space (or open) boundary is realized. In beam physics, this approach allows to calculate the space charge field of a continualized charged particle distribution with periodic pattern. The method is based on a particle mesh approach with equidistant grid and fast convolution with a Green's function. The periodic approach uses only one period of the source distribution, but a periodic extension of the Green's function. The approach is numerically efficient and allows the investigation of periodic- and pseudo-periodic structures with period lengths that are small compared to the source dimensions, for instance of laser modulated beams or of the evolution of micro bunch structures. Applications for laser modulated beams are given.
Woźniak, M.
2016-06-02
We study the features of a new mixed integration scheme dedicated to solving the non-stationary variational problems. The scheme is composed of the FEM approximation with respect to the space variable coupled with a 3-leveled time integration scheme with a linearized right-hand side operator. It was applied in solving the Cahn-Hilliard parabolic equation with a nonlinear, fourth-order elliptic part. The second order of the approximation along the time variable was proven. Moreover, the good scalability of the software based on this scheme was confirmed during simulations. We verify the proposed time integration scheme by monitoring the Ginzburg-Landau free energy. The numerical simulations are performed by using a parallel multi-frontal direct solver executed over STAMPEDE Linux cluster. Its scalability was compared to the results of the three direct solvers, including MUMPS, SuperLU and PaSTiX.
Florio, Adrien; Pieloni, Tatiana; CERN. Geneva. ATS Department
2015-01-01
We present two different approaches to solve the 2-dimensional electrostatic problem with open boundary conditions to be used in fast tracking codes for beam-beam and space charge simulations in high energy accelerators. We compare a fast multipoles method with a hybrid Poisson solver based on the fast Fourier transform and finite differences in polar coordinates. We show that the latter outperforms the first in terms of execution time and precision, allowing for a reduction of the noise in the tracking simulation. Furthermore the new algorithm is shown to scale linearly on parallel architectures with shared memory. We conclude by effectively replacing the HFMM by the new Poisson solver in the COMBI code.
Paszyński, Maciej R.
2013-04-01
This paper describes a direct solver algorithm for a sequence of finite element meshes that are h-refined towards one or several point singularities. For such a sequence of grids, the solver delivers linear computational cost O(N) in terms of CPU time and memory with respect to the number of unknowns N. The linear computational cost is achieved by utilizing the recursive structure provided by the sequence of h-adaptive grids with a special construction of the elimination tree that allows for reutilization of previously computed partial LU (or Cholesky) factorizations over the entire unrefined part of the computational mesh. The reutilization technique reduces the computational cost of the entire sequence of h-refined grids from O(N2) down to O(N). Theoretical estimates are illustrated with numerical results on two- and three-dimensional model problems exhibiting one or several point singularities. © 2013 Elsevier Ltd. All rights reserved.
DEFF Research Database (Denmark)
Amini Afshar, Mostafa; Bingham, Harry B.; Read, Robert
During recent years a computational strategy has been developed at the Technical University of Denmark for numerical simulation of water wave problems based on the high-order nite-dierence method, [2],[4]. These methods exhibit a linear scaling of the computational eort as the number of grid points...... increases. This understanding is being applied to develop a tool for predicting the added resistance (drift force) of ships in ocean waves. We expect that the optimal scaling properties of this solver will allow us to make a convincing demonstration of convergence of the added resistance calculations based...... on both near-eld and far-eld methods. The solver has been written inside a C++ library known as Overture [3], which can be used to solve partial dierential equations on overlapping grids based on the high-order nite-dierence method. The resulting code is able to solve, in the time domain, the linearised...
Paszyński, Maciej R.; Calo, Victor M.; Pardo, David
2013-01-01
This paper describes a direct solver algorithm for a sequence of finite element meshes that are h-refined towards one or several point singularities. For such a sequence of grids, the solver delivers linear computational cost O(N) in terms of CPU time and memory with respect to the number of unknowns N. The linear computational cost is achieved by utilizing the recursive structure provided by the sequence of h-adaptive grids with a special construction of the elimination tree that allows for reutilization of previously computed partial LU (or Cholesky) factorizations over the entire unrefined part of the computational mesh. The reutilization technique reduces the computational cost of the entire sequence of h-refined grids from O(N2) down to O(N). Theoretical estimates are illustrated with numerical results on two- and three-dimensional model problems exhibiting one or several point singularities. © 2013 Elsevier Ltd. All rights reserved.
International Nuclear Information System (INIS)
Beyer, R.T.
1985-01-01
The paper reviews the work carried out on the velocity of sound in liquid alkali metals. The experimental methods to determine the velocity measurements are described. Tables are presented of reported data on the velocity of sound in lithium, sodium, potassium, rubidium and caesium. A formula is given for alkali metals, in which the sound velocity is a function of shear viscosity, atomic mass and atomic volume. (U.K.)
A fast nonlinear conjugate gradient based method for 3D concentrated frictional contact problems
J. Zhao (Jing); E.A.H. Vollebregt (Edwin); C.W. Oosterlee (Cornelis)
2015-01-01
htmlabstractThis paper presents a fast numerical solver for a nonlinear constrained optimization problem, arising from 3D concentrated frictional shift and rolling contact problems with dry Coulomb friction. The solver combines an active set strategy with a nonlinear conjugate gradient method. One
Problem solving stages in the five square problem.
Fedor, Anna; Szathmáry, Eörs; Öllinger, Michael
2015-01-01
According to the restructuring hypothesis, insight problem solving typically progresses through consecutive stages of search, impasse, insight, and search again for someone, who solves the task. The order of these stages was determined through self-reports of problem solvers and has never been verified behaviorally. We asked whether individual analysis of problem solving attempts of participants revealed the same order of problem solving stages as defined by the theory and whether their subjective feelings corresponded to the problem solving stages they were in. Our participants tried to solve the Five-Square problem in an online task, while we recorded the time and trajectory of their stick movements. After the task they were asked about their feelings related to insight and some of them also had the possibility of reporting impasse while working on the task. We found that the majority of participants did not follow the classic four-stage model of insight, but had more complex sequences of problem solving stages, with search and impasse recurring several times. This means that the classic four-stage model is not sufficient to describe variability on the individual level. We revised the classic model and we provide a new model that can generate all sequences found. Solvers reported insight more often than non-solvers and non-solvers reported impasse more often than solvers, as expected; but participants did not report impasse more often during behaviorally defined impasse stages than during other stages. This shows that impasse reports might be unreliable indicators of impasse. Our study highlights the importance of individual analysis of problem solving behavior to verify insight theory.
Directory of Open Access Journals (Sweden)
Liyang Wang
2017-01-01
Full Text Available The application of biped robots is always trapped by their high energy consumption. This paper makes a contribution by optimizing the joint torques to decrease the energy consumption without changing the biped gaits. In this work, a constrained quadratic programming (QP problem for energy optimization is formulated. A neurodynamics-based solver is presented to solve the QP problem. Differing from the existing literatures, the proposed neurodynamics-based energy optimization (NEO strategy minimizes the energy consumption and guarantees the following three important constraints simultaneously: (i the force-moment equilibrium equation of biped robots, (ii frictions applied by each leg on the ground to hold the biped robot without slippage and tipping over, and (iii physical limits of the motors. Simulations demonstrate that the proposed strategy is effective for energy-efficient biped walking.
Michael Jackson's Sound Stages
Morten Michelsen
2012-01-01
In order to discuss analytically spatial aspects of recorded sound William Moylan’s concept of ‘sound stage’ is developed within a musicological framework as part of a sound paradigm which includes timbre, texture and sound stage. Two Michael Jackson songs (‘The Lady in My Life’ from 1982 and ‘Scream’ from 1995) are used to: a) demonstrate the value of such a conceptualisation, and b) demonstrate that the model has its limits, as record producers in the 1990s began ignoring the conventions of...
Nelson, Peter
2014-01-01
What is sound? This question is posed in contradiction to the every-day understanding that sound is a phenomenon apart from us, to be heard, made, shaped and organised. Thinking through the history of computer music, and considering the current configuration of digital communi-cations, sound is reconfigured as a type of network. This network is envisaged as non-hierarchical, in keeping with currents of thought that refuse to prioritise the human in the world. The relationship of sound to musi...
Karam, P Andrew
2010-01-01
Our world is largely defined by what we see and hear-but our uses for light and sound go far beyond simply seeing a photo or hearing a song. A concentrated beam of light, lasers are powerful tools used in industry, research, and medicine, as well as in everyday electronics like DVD and CD players. Ultrasound, sound emitted at a high frequency, helps create images of a developing baby, cleans teeth, and much more. Light and Sound teaches how light and sound work, how they are used in our day-to-day lives, and how they can be used to learn about the universe at large.
Tables of the velocity of sound in sea water
Bark, L S; Meister, N A
1964-01-01
Tables of the Velocity of Sound in Sea Water contains tables of the velocity of sound in sea water computed on a ""Strela-3"" high-speed electronic computer and a T-5 tabulator at the Computational Center of the Academy of Sciences. Knowledge of the precise velocity of sound in sea water is of great importance when investigating sound propagations in the ocean and when solving practical problems involving the use of hydro-acoustic devices. This book demonstrates the computations made for the velocity of sound in sea water, which can be found in two ways: by direct measurement with the aid of s
Early Sound Symbolism for Vowel Sounds
Directory of Open Access Journals (Sweden)
Ferrinne Spector
2013-06-01
Full Text Available Children and adults consistently match some words (e.g., kiki to jagged shapes and other words (e.g., bouba to rounded shapes, providing evidence for non-arbitrary sound–shape mapping. In this study, we investigated the influence of vowels on sound–shape matching in toddlers, using four contrasting pairs of nonsense words differing in vowel sound (/i/ as in feet vs. /o/ as in boat and four rounded–jagged shape pairs. Crucially, we used reduplicated syllables (e.g., kiki vs. koko rather than confounding vowel sound with consonant context and syllable variability (e.g., kiki vs. bouba. Toddlers consistently matched words with /o/ to rounded shapes and words with /i/ to jagged shapes (p < 0.01. The results suggest that there may be naturally biased correspondences between vowel sound and shape.
Application of GPU to Multi-interfaces Advection and Reconstruction Solver (MARS)
International Nuclear Information System (INIS)
Nagatake, Taku; Takase, Kazuyuki; Kunugi, Tomoaki
2010-01-01
In the nuclear engineering fields, a high performance computer system is necessary to perform the large scale computations. Recently, a Graphics Processing Unit (GPU) has been developed as a rendering computational system in order to reduce a Central Processing Unit (CPU) load. In the graphics processing, the high performance computing is needed to render the high-quality 3D objects in some video games. Thus the GPU consists of many processing units and a wide memory bandwidth. In this study, the Multi-interfaces Advection and Reconstruction Solver (MARS) which is one of the interface volume tracking methods for multi-phase flows has been performed. The multi-phase flow computation is very important for the nuclear reactors and other engineering fields. The MARS consists of two computing parts: the interface tracking part and the fluid motion computing part. As for the interface tracking part, the performance of GPU (GTX280) was 6 times faster than that of the CPU (Dual-Xeon 5040), and in the fluid motion computing part the Poisson Solver by the GPU (GTX285) was 22 times faster than that by the CPU(Core i7). As for the Dam Breaking Problem, the result of GPU-MARS showed slightly different from the experimental result. Because the GPU-MARS was developed using the single-precision GPU, it can be considered that the round-off error might be accumulated. (author)
Parallelization of pressure equation solver for incompressible N-S equations
International Nuclear Information System (INIS)
Ichihara, Kiyoshi; Yokokawa, Mitsuo; Kaburaki, Hideo.
1996-03-01
A pressure equation solver in a code for 3-dimensional incompressible flow analysis has been parallelized by using red-black SOR method and PCG method on Fujitsu VPP500, a vector parallel computer with distributed memory. For the comparison of scalability, the solver using the red-black SOR method has been also parallelized on the Intel Paragon, a scalar parallel computer with a distributed memory. The scalability of the red-black SOR method on both VPP500 and Paragon was lost, when number of processor elements was increased. The reason of non-scalability on both systems is increasing communication time between processor elements. In addition, the parallelization by DO-loop division makes the vectorizing efficiency lower on VPP500. For an effective implementation on VPP500, a large scale problem which holds very long vectorized DO-loops in the parallel program should be solved. PCG method with red-black SOR method applied to incomplete LU factorization (red-black PCG) has more iteration steps than normal PCG method with forward and backward substitution, in spite of same number of the floating point operations in a DO-loop of incomplete LU factorization. The parallelized red-black PCG method has less merits than the parallelized red-black SOR method when the computational region has fewer grids, because the low vectorization efficiency is obtained in red-black PCG method. (author)
International Nuclear Information System (INIS)
Hindmarsh, A.D.; Brown, P.N.
1996-01-01
1 - Description of program or function: LSODKR is a new initial value ODE solver for stiff and non-stiff systems. It is a variant of the LSODPK and LSODE solvers, intended mainly for large stiff systems. The main differences between LSODKR and LSODE are the following: a) for stiff systems, LSODKR uses a corrector iteration composed of Newton iteration and one of four preconditioned Krylov subspace iteration methods. The user must supply routines for the preconditioning operations, b) within the corrector iteration, LSODKR does automatic switching between functional (fix point) iteration and modified Newton iteration, c) LSODKR includes the ability to find roots of given functions of the solution during the integration. 2 - Method of solution: Integration is by Adams or BDF (Backward Differentiation Formula) methods, at user option. Corrector iteration is by Newton or fix point iteration, determined dynamically. Linear system solution is by a preconditioned Krylov iteration, selected by user from Incomplete Orthogonalization Method, Generalized Minimum Residual Method, and two variants of Preconditioned Conjugate Gradient Method. Preconditioning is to be supplied by the user. 3 - Restrictions on the complexity of the problem: None
Effective high-order solver with thermally perfect gas model for hypersonic heating prediction
International Nuclear Information System (INIS)
Jiang, Zhenhua; Yan, Chao; Yu, Jian; Qu, Feng; Ma, Libin
2016-01-01
Highlights: • Design proper numerical flux for thermally perfect gas. • Line-implicit LUSGS enhances efficiency without extra memory consumption. • Develop unified framework for both second-order MUSCL and fifth-order WENO. • The designed gas model can be applied to much wider temperature range. - Abstract: Effective high-order solver based on the model of thermally perfect gas has been developed for hypersonic heat transfer computation. The technique of polynomial curve fit coupling to thermodynamics equation is suggested to establish the current model and particular attention has been paid to the design of proper numerical flux for thermally perfect gas. We present procedures that unify five-order WENO (Weighted Essentially Non-Oscillatory) scheme in the existing second-order finite volume framework and a line-implicit method that improves the computational efficiency without increasing memory consumption. A variety of hypersonic viscous flows are performed to examine the capability of the resulted high order thermally perfect gas solver. Numerical results demonstrate its superior performance compared to low-order calorically perfect gas method and indicate its potential application to hypersonic heating predictions for real-life problem.
Energy Technology Data Exchange (ETDEWEB)
Jouvet, Guillaume, E-mail: jouvet@vaw.baug.ethz.ch [Institut für Mathematik, Freie Universität Berlin (Germany); Laboratory of Hydraulics, Hydrology and Glaciology, ETH Zurich (Switzerland)
2015-04-15
In this paper, a multilayer generalisation of the Shallow Shelf Approximation (SSA) is considered. In this recent hybrid ice flow model, the ice thickness is divided into thin layers, which can spread out, contract and slide over each other in such a way that the velocity profile is layer-wise constant. Like the SSA (1-layer model), the multilayer model can be reformulated as a minimisation problem. However, unlike the SSA, the functional to be minimised involves a new penalisation term for the interlayer jumps of the velocity, which represents the vertical shear stresses induced by interlayer sliding. Taking advantage of this reformulation, numerical solvers developed for the SSA can be naturally extended layer-wise or column-wise. Numerical results show that the column-wise extension of a Newton multigrid solver proves to be robust in the sense that its convergence is barely influenced by the number of layers and the type of ice flow. In addition, the multilayer formulation appears to be naturally better conditioned than the one of the first-order approximation to face the anisotropic conditions of the sliding-dominant ice flow of ISMIP-HOM experiments.
Design of a Modular Monolithic Implicit Solver for Multi-Physics Applications
Carton De Wiart, Corentin; Diosady, Laslo T.; Garai, Anirban; Burgess, Nicholas; Blonigan, Patrick; Ekelschot, Dirk; Murman, Scott M.
2018-01-01
The design of a modular multi-physics high-order space-time finite-element framework is presented together with its extension to allow monolithic coupling of different physics. One of the main objectives of the framework is to perform efficient high- fidelity simulations of capsule/parachute systems. This problem requires simulating multiple physics including, but not limited to, the compressible Navier-Stokes equations, the dynamics of a moving body with mesh deformations and adaptation, the linear shell equations, non-re effective boundary conditions and wall modeling. The solver is based on high-order space-time - finite element methods. Continuous, discontinuous and C1-discontinuous Galerkin methods are implemented, allowing one to discretize various physical models. Tangent and adjoint sensitivity analysis are also targeted in order to conduct gradient-based optimization, error estimation, mesh adaptation, and flow control, adding another layer of complexity to the framework. The decisions made to tackle these challenges are presented. The discussion focuses first on the "single-physics" solver and later on its extension to the monolithic coupling of different physics. The implementation of different physics modules, relevant to the capsule/parachute system, are also presented. Finally, examples of coupled computations are presented, paving the way to the simulation of the full capsule/parachute system.
International Nuclear Information System (INIS)
Navarro, V.; Alonso, J.; Asensio, L.; Yustres, A.; Pintado, X.
2012-01-01
Document available in extended abstract form only. The use of numerical methods, especially the Finite Element Method (FEM), for solving boundary problems in Unsaturated Soil Mechanics has experienced significant progress. Several codes, both built mainly for research purposes and commercial software, are now available. In the last years, Multi-physic Partial Differentiation Equation Solvers (MPDES) have turned out to be an interesting proposal. In this family of solvers, the user defines the governing equations and the behaviour models, generally using a computer algebra environment. The code automatically assembles and solves the equation systems, saving the user having to redefine the structures of memory storage or to implement solver algorithms. The user can focus on the definition of the physics of the problem, while it is possible to couple virtually any physical or chemical process that can be described by a PDE. This can be done, for instance, in COMSOL Multiphysics (CM). Nonetheless, the versatility of CM is compromised by the impossibility to implement models with variables defined by implicit functions. Elasto-plastic models involve an implicit coupling among stress increments, plastic strains and plastic variables increments. For this reason, they cannot be implemented in CM in a straightforward way. This means a very relevant limitation for the use of this tool in the analysis of geomechanical boundary value problems. In this work, a strategy to overcome this problem using the multi-physics concept is presented. A mixed method is proposed, considering the constitutive stresses, the pre-consolidation pressure and the plastic variables as main unknowns of the model. Mixed methods usually present stability problems. However, the algorithmics present in CM include several numerical strategies to minimise this kind of problems. Besides, CM is based on the application of the FEM with Lagrange multipliers, an approach that significantly contributes stability
Benchmarking ICRF Full-wave Solvers for ITER
International Nuclear Information System (INIS)
Budny, R.V.; Berry, L.; Bilato, R.; Bonoli, P.; Brambilla, M.; Dumont, R.J.; Fukuyama, A.; Harvey, R.; Jaeger, E.F.; Indireshkumar, K.; Lerche, E.; McCune, D.; Phillips, C.K.; Vdovin, V.; Wright, J.
2011-01-01
Benchmarking of full-wave solvers for ICRF simulations is performed using plasma profiles and equilibria obtained from integrated self-consistent modeling predictions of four ITER plasmas. One is for a high performance baseline (5.3 T, 15 MA) DT H-mode. The others are for half-field, half-current plasmas of interest for the pre-activation phase with bulk plasma ion species being either hydrogen or He4. The predicted profiles are used by six full-wave solver groups to simulate the ICRF electromagnetic fields and heating, and by three of these groups to simulate the current-drive. Approximate agreement is achieved for the predicted heating power for the DT and He4 cases. Factor of two disagreements are found for the cases with second harmonic He3 heating in bulk H cases. Approximate agreement is achieved simulating the ICRF current drive.
Minaret, a deterministic neutron transport solver for nuclear core calculations
International Nuclear Information System (INIS)
Moller, J-Y.; Lautard, J-J.
2011-01-01
We present here MINARET a deterministic transport solver for nuclear core calculations to solve the steady state Boltzmann equation. The code follows the multi-group formalism to discretize the energy variable. It uses discrete ordinate method to deal with the angular variable and a DGFEM to solve spatially the Boltzmann equation. The mesh is unstructured in 2D and semi-unstructured in 3D (cylindrical). Curved triangles can be used to fit the exact geometry. For the curved elements, two different sets of basis functions can be used. Transport solver is accelerated with a DSA method. Diffusion and SPN calculations are made possible by skipping the transport sweep in the source iteration. The transport calculations are parallelized with respect to the angular directions. Numerical results are presented for simple geometries and for the C5G7 Benchmark, JHR reactor and the ESFR (in 2D and 3D). Straight and curved finite element results are compared. (author)
Comparison of Einstein-Boltzmann solvers for testing general relativity
Bellini, E.; Barreira, A.; Frusciante, N.; Hu, B.; Peirone, S.; Raveri, M.; Zumalacárregui, M.; Avilez-Lopez, A.; Ballardini, M.; Battye, R. A.; Bolliet, B.; Calabrese, E.; Dirian, Y.; Ferreira, P. G.; Finelli, F.; Huang, Z.; Ivanov, M. M.; Lesgourgues, J.; Li, B.; Lima, N. A.; Pace, F.; Paoletti, D.; Sawicki, I.; Silvestri, A.; Skordis, C.; Umiltà, C.; Vernizzi, F.
2018-01-01
We compare Einstein-Boltzmann solvers that include modifications to general relativity and find that, for a wide range of models and parameters, they agree to a high level of precision. We look at three general purpose codes that primarily model general scalar-tensor theories, three codes that model Jordan-Brans-Dicke (JBD) gravity, a code that models f (R ) gravity, a code that models covariant Galileons, a code that models Hořava-Lifschitz gravity, and two codes that model nonlocal models of gravity. Comparing predictions of the angular power spectrum of the cosmic microwave background and the power spectrum of dark matter for a suite of different models, we find agreement at the subpercent level. This means that this suite of Einstein-Boltzmann solvers is now sufficiently accurate for precision constraints on cosmological and gravitational parameters.
Minaret, a deterministic neutron transport solver for nuclear core calculations
Energy Technology Data Exchange (ETDEWEB)
Moller, J-Y.; Lautard, J-J., E-mail: jean-yves.moller@cea.fr, E-mail: jean-jacques.lautard@cea.fr [CEA - Centre de Saclay , Gif sur Yvette (France)
2011-07-01
We present here MINARET a deterministic transport solver for nuclear core calculations to solve the steady state Boltzmann equation. The code follows the multi-group formalism to discretize the energy variable. It uses discrete ordinate method to deal with the angular variable and a DGFEM to solve spatially the Boltzmann equation. The mesh is unstructured in 2D and semi-unstructured in 3D (cylindrical). Curved triangles can be used to fit the exact geometry. For the curved elements, two different sets of basis functions can be used. Transport solver is accelerated with a DSA method. Diffusion and SPN calculations are made possible by skipping the transport sweep in the source iteration. The transport calculations are parallelized with respect to the angular directions. Numerical results are presented for simple geometries and for the C5G7 Benchmark, JHR reactor and the ESFR (in 2D and 3D). Straight and curved finite element results are compared. (author)
An alternative solver for the nodal expansion method equations - 106
International Nuclear Information System (INIS)
Carvalho da Silva, F.; Carlos Marques Alvim, A.; Senra Martinez, A.
2010-01-01
An automated procedure for nuclear reactor core design is accomplished by using a quick and accurate 3D nodal code, aiming at solving the diffusion equation, which describes the spatial neutron distribution in the reactor. This paper deals with an alternative solver for nodal expansion method (NEM), with only two inner iterations (mesh sweeps) per outer iteration, thus having the potential to reduce the time required to calculate the power distribution in nuclear reactors, but with accuracy similar to the ones found in conventional NEM. The proposed solver was implemented into a computational system which, besides solving the diffusion equation, also solves the burnup equations governing the gradual changes in material compositions of the core due to fuel depletion. Results confirm the effectiveness of the method for practical purposes. (authors)
A Nonlinear Modal Aeroelastic Solver for FUN3D
Goldman, Benjamin D.; Bartels, Robert E.; Biedron, Robert T.; Scott, Robert C.
2016-01-01
A nonlinear structural solver has been implemented internally within the NASA FUN3D computational fluid dynamics code, allowing for some new aeroelastic capabilities. Using a modal representation of the structure, a set of differential or differential-algebraic equations are derived for general thin structures with geometric nonlinearities. ODEPACK and LAPACK routines are linked with FUN3D, and the nonlinear equations are solved at each CFD time step. The existing predictor-corrector method is retained, whereby the structural solution is updated after mesh deformation. The nonlinear solver is validated using a test case for a flexible aeroshell at transonic, supersonic, and hypersonic flow conditions. Agreement with linear theory is seen for the static aeroelastic solutions at relatively low dynamic pressures, but structural nonlinearities limit deformation amplitudes at high dynamic pressures. No flutter was found at any of the tested trajectory points, though LCO may be possible in the transonic regime.
CASTRO: A NEW COMPRESSIBLE ASTROPHYSICAL SOLVER. II. GRAY RADIATION HYDRODYNAMICS
International Nuclear Information System (INIS)
Zhang, W.; Almgren, A.; Bell, J.; Howell, L.; Burrows, A.
2011-01-01
We describe the development of a flux-limited gray radiation solver for the compressible astrophysics code, CASTRO. CASTRO uses an Eulerian grid with block-structured adaptive mesh refinement based on a nested hierarchy of logically rectangular variable-sized grids with simultaneous refinement in both space and time. The gray radiation solver is based on a mixed-frame formulation of radiation hydrodynamics. In our approach, the system is split into two parts, one part that couples the radiation and fluid in a hyperbolic subsystem, and another parabolic part that evolves radiation diffusion and source-sink terms. The hyperbolic subsystem is solved explicitly with a high-order Godunov scheme, whereas the parabolic part is solved implicitly with a first-order backward Euler method.
Boltzmann Solver with Adaptive Mesh in Velocity Space
International Nuclear Information System (INIS)
Kolobov, Vladimir I.; Arslanbekov, Robert R.; Frolova, Anna A.
2011-01-01
We describe the implementation of direct Boltzmann solver with Adaptive Mesh in Velocity Space (AMVS) using quad/octree data structure. The benefits of the AMVS technique are demonstrated for the charged particle transport in weakly ionized plasmas where the collision integral is linear. We also describe the implementation of AMVS for the nonlinear Boltzmann collision integral. Test computations demonstrate both advantages and deficiencies of the current method for calculations of narrow-kernel distributions.
Resolving Neighbourhood Relations in a Parallel Fluid Dynamic Solver
Frisch, Jerome
2012-06-01
Computational Fluid Dynamics simulations require an enormous computational effort if a physically reasonable accuracy should be reached. Therefore, a parallel implementation is inevitable. This paper describes the basics of our implemented fluid solver with a special aspect on the hierarchical data structure, unique cell and grid identification, and the neighbourhood relations in-between grids on different processes. A special server concept keeps track of every grid over all processes while minimising data transfer between the nodes. © 2012 IEEE.
A contribution to the great Riemann solver debate
Quirk, James J.
1992-01-01
The aims of this paper are threefold: to increase the level of awareness within the shock capturing community to the fact that many Godunov-type methods contain subtle flaws that can cause spurious solutions to be computed; to identify one mechanism that might thwart attempts to produce very high resolution simulations; and to proffer a simple strategy for overcoming the specific failings of individual Riemann solvers.
Applications of 3-D Maxwell solvers to accelerator design
International Nuclear Information System (INIS)
Chou, W.
1990-01-01
This paper gives a brief discussion on various applications of 3-D Maxwell solvers to accelerator design. The work is based on our experience gained during the design of the storage ring of the 7-GeV Advanced Photon Source (APS). It shows that 3-D codes are not replaceable in many cases, and that a lot of work remains to be done in order to establish a solid base for 3-D simulations
An immersed interface vortex particle-mesh solver
Marichal, Yves; Chatelain, Philippe; Winckelmans, Gregoire
2014-11-01
An immersed interface-enabled vortex particle-mesh (VPM) solver is presented for the simulation of 2-D incompressible viscous flows, in the framework of external aerodynamics. Considering the simulation of free vortical flows, such as wakes and jets, vortex particle-mesh methods already provide a valuable alternative to standard CFD methods, thanks to the interesting numerical properties arising from its Lagrangian nature. Yet, accounting for solid bodies remains challenging, despite the extensive research efforts that have been made for several decades. The present immersed interface approach aims at improving the consistency and the accuracy of one very common technique (based on Lighthill's model) for the enforcement of the no-slip condition at the wall in vortex methods. Targeting a sharp treatment of the wall calls for substantial modifications at all computational levels of the VPM solver. More specifically, the solution of the underlying Poisson equation, the computation of the diffusion term and the particle-mesh interpolation are adapted accordingly and the spatial accuracy is assessed. The immersed interface VPM solver is subsequently validated on the simulation of some challenging impulsively started flows, such as the flow past a cylinder and that past an airfoil. Research Fellow (PhD student) of the F.R.S.-FNRS of Belgium.
Direct solvers performance on h-adapted grids
Paszynski, Maciej; Pardo, David; Calo, Victor M.
2015-01-01
We analyse the performance of direct solvers when applied to a system of linear equations arising from an hh-adapted, C0C0 finite element space. Theoretical estimates are derived for typical hh-refinement patterns arising as a result of a point, edge, or face singularity as well as boundary layers. They are based on the elimination trees constructed specifically for the considered grids. Theoretical estimates are compared with experiments performed with MUMPS using the nested-dissection algorithm for construction of the elimination tree from METIS library. The numerical experiments provide the same performance for the cases where our trees are identical with those constructed by the nested-dissection algorithm, and worse performance for some cases where our trees are different. We also present numerical experiments for the cases with mixed singularities, where how to construct optimal elimination trees is unknown. In all analysed cases, the use of hh-adaptive grids significantly reduces the cost of the direct solver algorithm per unknown as compared to uniform grids. The theoretical estimates predict and the experimental data confirm that the computational complexity is linear for various refinement patterns. In most cases, the cost of the direct solver per unknown is lower when employing anisotropic refinements as opposed to isotropic ones.
A Survey of Solver-Related Geometry and Meshing Issues
Masters, James; Daniel, Derick; Gudenkauf, Jared; Hine, David; Sideroff, Chris
2016-01-01
There is a concern in the computational fluid dynamics community that mesh generation is a significant bottleneck in the CFD workflow. This is one of several papers that will help set the stage for a moderated panel discussion addressing this issue. Although certain general "rules of thumb" and a priori mesh metrics can be used to ensure that some base level of mesh quality is achieved, inadequate consideration is often given to the type of solver or particular flow regime on which the mesh will be utilized. This paper explores how an analyst may want to think differently about a mesh based on considerations such as if a flow is compressible vs. incompressible or hypersonic vs. subsonic or if the solver is node-centered vs. cell-centered. This paper is a high-level investigation intended to provide general insight into how considering the nature of the solver or flow when performing mesh generation has the potential to increase the accuracy and/or robustness of the solution and drive the mesh generation process to a state where it is no longer a hindrance to the analysis process.
Direct solvers performance on h-adapted grids
Paszynski, Maciej
2015-05-27
We analyse the performance of direct solvers when applied to a system of linear equations arising from an hh-adapted, C0C0 finite element space. Theoretical estimates are derived for typical hh-refinement patterns arising as a result of a point, edge, or face singularity as well as boundary layers. They are based on the elimination trees constructed specifically for the considered grids. Theoretical estimates are compared with experiments performed with MUMPS using the nested-dissection algorithm for construction of the elimination tree from METIS library. The numerical experiments provide the same performance for the cases where our trees are identical with those constructed by the nested-dissection algorithm, and worse performance for some cases where our trees are different. We also present numerical experiments for the cases with mixed singularities, where how to construct optimal elimination trees is unknown. In all analysed cases, the use of hh-adaptive grids significantly reduces the cost of the direct solver algorithm per unknown as compared to uniform grids. The theoretical estimates predict and the experimental data confirm that the computational complexity is linear for various refinement patterns. In most cases, the cost of the direct solver per unknown is lower when employing anisotropic refinements as opposed to isotropic ones.
DEFF Research Database (Denmark)
Sonnenwald, Diane H.; Gopinath, B.; Haberman, Gary O.
1990-01-01
The authors explore ways to enhance users' comprehension of complex applications using music and sound effects to present application-program events that are difficult to detect visually. A prototype system, Infosound, allows developers to create and store musical sequences and sound effects with...
Brown, Tom; Boehringer, Kim
2007-01-01
Students in a fourth-grade class participated in a series of dynamic sound learning centers followed by a dramatic capstone event--an exploration of the amazing Trashcan Whoosh Waves. It's a notoriously difficult subject to teach, but this hands-on, exploratory approach ignited student interest in sound, promoted language acquisition, and built…
Salomons, E.; Polinder, H.; Lohman, W.; Zhou, H.; Borst, H.
2009-01-01
A new engineering model for sound propagation in cities is presented. The model is based on numerical and experimental studies of sound propagation between street canyons. Multiple reflections in the source canyon and the receiver canyon are taken into account in an efficient way, while weak
DEFF Research Database (Denmark)
1996-01-01
A sound source comprising a loudspeaker (6) and a hollow coupler (4) with an open inlet which communicates with and is closed by the loudspeaker (6) and an open outlet, said coupler (4) comprising rigid walls which cannot respond to the sound pressures produced by the loudspeaker (6). According...
Fina, Allan de
1992-01-01
Explains how elementary teachers can help students understand onomatopoeia, suggesting that they define onomatopoeia, share examples of it, read poems and have students discuss onomatopoeic words, act out common household sounds, write about sound effects, and create choral readings of onomatopoeic poems. Two appropriate poems are included. (SM)
Exploring Noise: Sound Pollution.
Rillo, Thomas J.
1979-01-01
Part one of a three-part series about noise pollution and its effects on humans. This section presents the background information for teachers who are preparing a unit on sound. The next issues will offer learning activities for measuring the effects of sound and some references. (SA)
Deterministic Approach to Detect Heart Sound Irregularities
Directory of Open Access Journals (Sweden)
Richard Mengko
2017-07-01
Full Text Available A new method to detect heart sound that does not require machine learning is proposed. The heart sound is a time series event which is generated by the heart mechanical system. From the analysis of heart sound S-transform and the understanding of how heart works, it can be deducted that each heart sound component has unique properties in terms of timing, frequency, and amplitude. Based on these facts, a deterministic method can be designed to identify each heart sound components. The recorded heart sound then can be printed with each component correctly labeled. This greatly help the physician to diagnose the heart problem. The result shows that most known heart sounds were successfully detected. There are some murmur cases where the detection failed. This can be improved by adding more heuristics including setting some initial parameters such as noise threshold accurately, taking into account the recording equipment and also the environmental condition. It is expected that this method can be integrated into an electronic stethoscope biomedical system.
Tohyama, Mikio
2015-01-01
What is this sound? What does that sound indicate? These are two questions frequently heard in daily conversation. Sound results from the vibrations of elastic media and in daily life provides informative signals of events happening in the surrounding environment. In interpreting auditory sensations, the human ear seems particularly good at extracting the signal signatures from sound waves. Although exploring auditory processing schemes may be beyond our capabilities, source signature analysis is a very attractive area in which signal-processing schemes can be developed using mathematical expressions. This book is inspired by such processing schemes and is oriented to signature analysis of waveforms. Most of the examples in the book are taken from data of sound and vibrations; however, the methods and theories are mostly formulated using mathematical expressions rather than by acoustical interpretation. This book might therefore be attractive and informative for scientists, engineers, researchers, and graduat...
Sound classification of dwellings
DEFF Research Database (Denmark)
Rasmussen, Birgit
2012-01-01
National schemes for sound classification of dwellings exist in more than ten countries in Europe, typically published as national standards. The schemes define quality classes reflecting different levels of acoustical comfort. Main criteria concern airborne and impact sound insulation between...... dwellings, facade sound insulation and installation noise. The schemes have been developed, implemented and revised gradually since the early 1990s. However, due to lack of coordination between countries, there are significant discrepancies, and new standards and revisions continue to increase the diversity...... is needed, and a European COST Action TU0901 "Integrating and Harmonizing Sound Insulation Aspects in Sustainable Urban Housing Constructions", has been established and runs 2009-2013, one of the main objectives being to prepare a proposal for a European sound classification scheme with a number of quality...
Adaptive multi-resolution 3D Hartree-Fock-Bogoliubov solver for nuclear structure
Pei, J. C.; Fann, G. I.; Harrison, R. J.; Nazarewicz, W.; Shi, Yue; Thornton, S.
2014-08-01
Background: Complex many-body systems, such as triaxial and reflection-asymmetric nuclei, weakly bound halo states, cluster configurations, nuclear fragments produced in heavy-ion fusion reactions, cold Fermi gases, and pasta phases in neutron star crust, are all characterized by large sizes and complex topologies in which many geometrical symmetries characteristic of ground-state configurations are broken. A tool of choice to study such complex forms of matter is an adaptive multi-resolution wavelet analysis. This method has generated much excitement since it provides a common framework linking many diversified methodologies across different fields, including signal processing, data compression, harmonic analysis and operator theory, fractals, and quantum field theory. Purpose: To describe complex superfluid many-fermion systems, we introduce an adaptive pseudospectral method for solving self-consistent equations of nuclear density functional theory in three dimensions, without symmetry restrictions. Methods: The numerical method is based on the multi-resolution and computational harmonic analysis techniques with a multi-wavelet basis. The application of state-of-the-art parallel programming techniques include sophisticated object-oriented templates which parse the high-level code into distributed parallel tasks with a multi-thread task queue scheduler for each multi-core node. The internode communications are asynchronous. The algorithm is variational and is capable of solving coupled complex-geometric systems of equations adaptively, with functional and boundary constraints, in a finite spatial domain of very large size, limited by existing parallel computer memory. For smooth functions, user-defined finite precision is guaranteed. Results: The new adaptive multi-resolution Hartree-Fock-Bogoliubov (HFB) solver madness-hfb is benchmarked against a two-dimensional coordinate-space solver hfb-ax that is based on the B-spline technique and a three-dimensional solver
Inverse problem of solar oscillations
International Nuclear Information System (INIS)
Sekii, T.; Shibahashi, H.
1987-01-01
The authors present some preliminary results of numerical simulation to infer the sound velocity distribution in the solar interior from the oscillation data of the Sun as the inverse problem. They analyze the acoustic potential itself by taking account of some factors other than the sound velocity, and infer the sound velocity distribution in the deep interior of the Sun
Java Based Symbolic Circuit Solver For Electrical Engineering Curriculum
Directory of Open Access Journals (Sweden)
Ruba Akram Amarin
2012-11-01
Full Text Available The interactive technical electronic book, TechEBook, currently under development at the University of Central Florida (UCF, introduces a paradigm shift by replacing the traditional electrical engineering course with topic-driven modules that provide a useful tool for engineers and scientists. The TechEBook comprises the two worlds of classical circuit books and interactive operating platforms such as iPads, laptops and desktops. The TechEBook provides an interactive applets screen that holds many modules, each of which has a specific application in the self learning process. This paper describes one of the interactive techniques in the TechEBook known as Symbolic Circuit Solver (SymCirc. The SymCirc develops a versatile symbolic based linear circuit with a switches solver. The solver works by accepting a Netlist and the element that the user wants to find the voltage across or current on, as input parameters. Then it either produces the plot or the time domain expression of the output. Frequency domain plots or Symbolic Transfer Functions are also produced. The solver gets its input from a Web-based GUI circuit drawer developed at UCF. Typical simulation tools that electrical engineers encounter are numerical in nature, that is, when presented with an input circuit they iteratively solve the circuit across a set of small time steps. The result is represented as a data set of output versus time, which can be plotted for further inspection. Such results do not help users understand the ultimate nature of circuits as Linear Time Invariant systems with a finite dimensional basis in the solution space. SymCirc provides all simulation results as time domain expressions composed of the basic functions that exclusively include exponentials, sines, cosines and/or t raised to any power. This paper explains the motivation behind SymCirc, the Graphical User Interface front end and how the solver actually works. The paper also presents some examples and
Sound For Animation And Virtual Reality
Hahn, James K.; Docter, Pete; Foster, Scott H.; Mangini, Mark; Myers, Tom; Wenzel, Elizabeth M.; Null, Cynthia (Technical Monitor)
1995-01-01
Sound is an integral part of the experience in computer animation and virtual reality. In this course, we will present some of the important technical issues in sound modeling, rendering, and synchronization as well as the "art" and business of sound that are being applied in animations, feature films, and virtual reality. The central theme is to bring leading researchers and practitioners from various disciplines to share their experiences in this interdisciplinary field. The course will give the participants an understanding of the problems and techniques involved in producing and synchronizing sounds, sound effects, dialogue, and music. The problem spans a number of domains including computer animation and virtual reality. Since sound has been an integral part of animations and films much longer than for computer-related domains, we have much to learn from traditional animation and film production. By bringing leading researchers and practitioners from a wide variety of disciplines, the course seeks to give the audience a rich mixture of experiences. It is expected that the audience will be able to apply what they have learned from this course in their research or production.
Energy Technology Data Exchange (ETDEWEB)
Fisher, A. C. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Bailey, D. S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Kaiser, T. B. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Eder, D. C. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Gunney, B. T. N. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Masters, N. D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Koniges, A. E. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Anderson, R. W. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2015-02-01
Here, we present a novel method for the solution of the diffusion equation on a composite AMR mesh. This approach is suitable for including diffusion based physics modules to hydrocodes that support ALE and AMR capabilities. To illustrate, we proffer our implementations of diffusion based radiation transport and heat conduction in a hydrocode called ALE-AMR. Numerical experiments conducted with the diffusion solver and associated physics packages yield 2nd order convergence in the L_{2} norm.
International Nuclear Information System (INIS)
Suzuki, Yoshio; Kushida, Noriyuki; Tatekawa, Takayuki; Teshima, Naoya; Caniou, Yves; Guivarch, Ronan; Dayde, Michel; Ramet, Pierre
2010-01-01
The 'Research and Development of International Matrix-Solver Prediction System (REDIMPS)' project aimed at improving the TLSE sparse linear algebra expert website by establishing an international grid computing environment between Japan and France. To help users in identifying the best solver or sparse linear algebra tool for their problems, we have developed an interoperable environment between French and Japanese grid infrastructures (respectively managed by DIET and AEGIS). Two main issues were considered. The first issue is how to submit a job from DIET to AEGIS. The second issue is how to bridge the difference of security between DIET and AEGIS. To overcome these issues, we developed APIs to communicate between different grid infrastructures by improving the client API of AEGIS. By developing a server deamon program (SeD) of DIET which behaves like an AEGIS user, DIET can call functions in AEGIS: authentication, file transfer, job submission, and so on. To intensify the security, we also developed functionalities to authenticate DIET sites and DIET users in order to access AEGIS computing resources. By this study, the set of software and computers available within TLSE to find an appropriate solver is enlarged over France (DIET) and Japan (AEGIS). (author)
O'Donnell, Michael J.; Bisnovatyi, Ilia
2000-11-01
Computing practice today depends on visual output to drive almost all user interaction. Other senses, such as audition, may be totally neglected, or used tangentially, or used in highly restricted specialized ways. We have excellent audio rendering through D-A conversion, but we lack rich general facilities for modeling and manipulating sound comparable in quality and flexibility to graphics. We need coordinated research in several disciplines to improve the use of sound as an interactive information channel. Incremental and separate improvements in synthesis, analysis, speech processing, audiology, acoustics, music, etc. will not alone produce the radical progress that we seek in sonic practice. We also need to create a new central topic of study in digital audio research. The new topic will assimilate the contributions of different disciplines on a common foundation. The key central concept that we lack is sound as a general-purpose information channel. We must investigate the structure of this information channel, which is driven by the cooperative development of auditory perception and physical sound production. Particular audible encodings, such as speech and music, illuminate sonic information by example, but they are no more sufficient for a characterization than typography is sufficient for characterization of visual information. To develop this new conceptual topic of sonic information structure, we need to integrate insights from a number of different disciplines that deal with sound. In particular, we need to coordinate central and foundational studies of the representational models of sound with specific applications that illuminate the good and bad qualities of these models. Each natural or artificial process that generates informative sound, and each perceptual mechanism that derives information from sound, will teach us something about the right structure to attribute to the sound itself. The new Sound topic will combine the work of computer
Salomons, Erik M; Lohman, Walter J A; Zhou, Han
2016-01-01
Propagation of sound waves in air can be considered as a special case of fluid dynamics. Consequently, the lattice Boltzmann method (LBM) for fluid flow can be used for simulating sound propagation. In this article application of the LBM to sound propagation is illustrated for various cases: free-field propagation, propagation over porous and non-porous ground, propagation over a noise barrier, and propagation in an atmosphere with wind. LBM results are compared with solutions of the equations of acoustics. It is found that the LBM works well for sound waves, but dissipation of sound waves with the LBM is generally much larger than real dissipation of sound waves in air. To circumvent this problem it is proposed here to use the LBM for assessing the excess sound level, i.e. the difference between the sound level and the free-field sound level. The effect of dissipation on the excess sound level is much smaller than the effect on the sound level, so the LBM can be used to estimate the excess sound level for a non-dissipative atmosphere, which is a useful quantity in atmospheric acoustics. To reduce dissipation in an LBM simulation two approaches are considered: i) reduction of the kinematic viscosity and ii) reduction of the lattice spacing.
Numerical simulations of coupled problems in engineering
2014-01-01
This book presents and discusses mathematical models, numerical methods and computational techniques used for solving coupled problems in science and engineering. It takes a step forward in the formulation and solution of real-life problems with a multidisciplinary vision, accounting for all of the complex couplings involved in the physical description. Simulation of multifaceted physics problems is a common task in applied research and industry. Often a suitable solver is built by connecting together several single-aspect solvers into a network. In this book, research in various fields was selected for consideration: adaptive methodology for multi-physics solvers, multi-physics phenomena and coupled-field solutions, leading to computationally intensive structural analysis. The strategies which are used to keep these problems computationally affordable are of special interest, and make this an essential book.
DEFF Research Database (Denmark)
Cone, Louise
2017-01-01
Danish and international artists. His methodology left us with a large collection of unique and inspirational time-based media sound artworks that have, until very recently, been inaccessible. Existing on an array of different media formats, such as open reel tapes, 8-track and 4 track cassettes, VHS......In 1990 an artist by the name of William Louis Sørensen was hired by the National Gallery of Denmark to collect important works of art – made from sound. His job was to acquire sound art, but also recordings that captured rare artistic occurrences, music, performances and happenings from both...
New sparse matrix solver in the KIKO3D 3-dimensional reactor dynamics code
International Nuclear Information System (INIS)
Panka, I.; Kereszturi, A.; Hegedus, C.
2005-01-01
The goal of this paper is to present a more effective method Bi-CGSTAB for accelerating the large sparse matrix equation solution in the KIKO3D code. This equation system is obtained by using the factorization of the improved quasi static (IQS) method for the time dependent nodal kinetic equations. In the old methodology standard large sparse matrix techniques were considered, where Gauss-Seidel preconditioning and a GMRES-type solver were applied. The validation of KIKO3D using Bi-CGSTAB has been performed by solving of a VVER-1000 kinetic benchmark problem. Additionally, the convergence characteristics were investigated in given macro time steps of Control Rod Ejection transients. The results have been obtained by the old GMRES and new Bi-CGSTAB methods are compared. (author)
PetClaw: A scalable parallel nonlinear wave propagation solver for Python
Alghamdi, Amal; Ahmadia, Aron; Ketcheson, David I.; Knepley, Matthew; Mandli, Kyle; Dalcin, Lisandro
2011-01-01
We present PetClaw, a scalable distributed-memory solver for time-dependent nonlinear wave propagation. PetClaw unifies two well-known scientific computing packages, Clawpack and PETSc, using Python interfaces into both. We rely on Clawpack to provide the infrastructure and kernels for time-dependent nonlinear wave propagation. Similarly, we rely on PETSc to manage distributed data arrays and the communication between them.We describe both the implementation and performance of PetClaw as well as our challenges and accomplishments in scaling a Python-based code to tens of thousands of cores on the BlueGene/P architecture. The capabilities of PetClaw are demonstrated through application to a novel problem involving elastic waves in a heterogeneous medium. Very finely resolved simulations are used to demonstrate the suppression of shock formation in this system.
PyOperators: Operators and solvers for high-performance computing
Chanial, P.; Barbey, N.
2012-12-01
PyOperators is a publicly available library that provides basic operators and solvers for small-to-very large inverse problems ({http://pchanial.github.com/pyoperators}). It forms the backbone of the package PySimulators, which implements specific operators to construct an instrument model and means to conveniently represent a map, a timeline or a time-dependent observation ({http://pchanial.github.com/pysimulators}). Both are part of the Tamasis (Tools for Advanced Map-making, Analysis and SImulations of Submillimeter surveys) toolbox, aiming at providing versatile, reliable, easy-to-use, and optimal map-making tools for Herschel and future generation of sub-mm instruments. The project is a collaboration between 4 institutes (ESO Garching, IAS Orsay, CEA Saclay, Univ. Leiden).
Directory of Open Access Journals (Sweden)
Yan Chen
2017-03-01
Full Text Available Based on the vectorised and cache optimised kernel, a parallel lower upper decomposition with a novel communication avoiding pivoting scheme is developed to solve dense complex matrix equations generated by the method of moments. The fine-grain data rearrangement and assembler instructions are adopted to reduce memory accessing times and improve CPU cache utilisation, which also facilitate vectorisation of the code. Through grouping processes in a binary tree, a parallel pivoting scheme is designed to optimise the communication pattern and thus reduces the solving time of the proposed solver. Two large electromagnetic radiation problems are solved on two supercomputers, respectively, and the numerical results demonstrate that the proposed method outperforms those in open source and commercial libraries.
Effect which environmental sound causes for memory retrieval
武良,徹文
1999-01-01
The research judges the relation and no relation between the stimulation at prime and the target stimulation with hearing of pleasantness and an unpleasant sound. It is a purpose what influence for you give to examine a reaction time and a miss-rate of responding as an index when the problem is accomplished. The subjects are 50 university students to the graduate school students from one year. The subject was distributed to 21 pleasant sound condition groups, 10 unpleasant sound condition gro...
Interactive physically-based sound simulation
Raghuvanshi, Nikunj
The realization of interactive, immersive virtual worlds requires the ability to present a realistic audio experience that convincingly compliments their visual rendering. Physical simulation is a natural way to achieve such realism, enabling deeply immersive virtual worlds. However, physically-based sound simulation is very computationally expensive owing to the high-frequency, transient oscillations underlying audible sounds. The increasing computational power of desktop computers has served to reduce the gap between required and available computation, and it has become possible to bridge this gap further by using a combination of algorithmic improvements that exploit the physical, as well as perceptual properties of audible sounds. My thesis is a step in this direction. My dissertation concentrates on developing real-time techniques for both sub-problems of sound simulation: synthesis and propagation. Sound synthesis is concerned with generating the sounds produced by objects due to elastic surface vibrations upon interaction with the environment, such as collisions. I present novel techniques that exploit human auditory perception to simulate scenes with hundreds of sounding objects undergoing impact and rolling in real time. Sound propagation is the complementary problem of modeling the high-order scattering and diffraction of sound in an environment as it travels from source to listener. I discuss my work on a novel numerical acoustic simulator (ARD) that is hundred times faster and consumes ten times less memory than a high-accuracy finite-difference technique, allowing acoustic simulations on previously-intractable spaces, such as a cathedral, on a desktop computer. Lastly, I present my work on interactive sound propagation that leverages my ARD simulator to render the acoustics of arbitrary static scenes for multiple moving sources and listener in real time, while accounting for scene-dependent effects such as low-pass filtering and smooth attenuation
IRMHD: an implicit radiative and magnetohydrodynamical solver for self-gravitating systems
Hujeirat, A.
1998-07-01
The 2D implicit hydrodynamical solver developed by Hujeirat & Rannacher is now modified to include the effects of radiation, magnetic fields and self-gravity in different geometries. The underlying numerical concept is based on the operator splitting approach, and the resulting 2D matrices are inverted using different efficient preconditionings such as ADI (alternating direction implicit), the approximate factorization method and Line-Gauss-Seidel or similar iteration procedures. Second-order finite volume with third-order upwinding and second-order time discretization is used. To speed up convergence and enhance efficiency we have incorporated an adaptive time-step control and monotonic multilevel grid distributions as well as vectorizing the code. Test calculations had shown that it requires only 38 per cent more computational effort than its explicit counterpart, whereas its range of application to astrophysical problems is much larger. For example, strongly time-dependent, quasi-stationary and steady-state solutions for the set of Euler and Navier-Stokes equations can now be sought on a non-linearly distributed and strongly stretched mesh. As most of the numerical techniques used to build up this algorithm have been described by Hujeirat & Rannacher in an earlier paper, we focus in this paper on the inclusion of self-gravity, radiation and magnetic fields. Strategies for satisfying the condition ∇.B=0 in the implicit evolution of MHD flows are given. A new discretization strategy for the vector potential which allows alternating use of the direct method is prescribed. We investigate the efficiencies of several 2D solvers for a Poisson-like equation and compare their convergence rates. We provide a splitting approach for the radiative flux within the FLD (flux-limited diffusion) approximation to enhance consistency and accuracy between regions of different optical depths. The results of some test problems are presented to demonstrate the accuracy and
Simplified Eigen-structure decomposition solver for the simulation of two-phase flow systems
International Nuclear Information System (INIS)
Kumbaro, Anela
2012-01-01
This paper discusses the development of a new solver for a system of first-order non-linear differential equations that model the dynamics of compressible two-phase flow. The solver presents a lower-complexity alternative to Roe-type solvers because it only makes use of a partial Eigen-structure information while maintaining its accuracy: the outcome is hence a good complexity-tractability trade-off to consider as relevant in a large number of situations in the scope of two-phase flow numerical simulation. A number of numerical and physical benchmarks are presented to assess the solver. Comparison between the computational results from the simplified Eigen-structure decomposition solver and the conventional Roe-type solver gives insight upon the issues of accuracy, robustness and efficiency. (authors)
DEFF Research Database (Denmark)
Jessen, Iben Bredahl; Graakjær, Nicolai Jørgensgaard
2010-01-01
Sound seems to be a neglected issue in the study of web ads. Web advertising is predominantly regarded as visual phenomena–commercial messages, as for instance banner ads that we watch, read, and eventually click on–but only rarely as something that we listen to. The present chapter presents...... an overview of the auditory dimensions in web advertising: Which kinds of sounds do we hear in web ads? What are the conditions and functions of sound in web ads? Moreover, the chapter proposes a theoretical framework in order to analyse the communicative functions of sound in web advertising. The main...... argument is that an understanding of the auditory dimensions in web advertising must include a reflection on the hypertextual settings of the web ad as well as a perspective on how users engage with web content....
DEFF Research Database (Denmark)
Krogh Groth, Sanne; Samson, Kristine
2017-01-01
and combine theories from several fields. Aspects of sound art studies, performance studies and contemporary art studies are presented in order to theoretically explore the very diverse dimensions of the two sound art pieces: Visual, auditory, performative, social, spatial and durational dimensions become......This article is an analysis of two sound art performances that took place June 2015 in outdoor public spaces in the social housing area Urbanplanen in Copenhagen, Denmark. The two performances were On the production of a poor acoustics by Brandon LaBelle and Green Interactive Biofeedback...... Environments (GIBE) by Jeremy Woodruff. In order to investigate the complex situation that arises when sound art is staged in such contexts, the authors of this article suggest exploring the events through approaching them as ‘situations’ (Doherty 2009). With this approach it becomes possible to engage...
DEFF Research Database (Denmark)
The wide-ranging texts in this book take as their premise the idea that sound is a subject through which popular culture can be analyzed in an innovative way. From an infant’s gurgles over a baby monitor to the roar of the crowd in a stadium to the sub-bass frequencies produced by sound systems...... in the disco era, sound—not necessarily aestheticized as music—is inextricably part of the many domains of popular culture. Expanding the view taken by many scholars of cultural studies, the contributors consider cultural practices concerning sound not merely as semiotic or signifying processes but as material......, physical, perceptual, and sensory processes that integrate a multitude of cultural traditions and forms of knowledge. The chapters discuss conceptual issues as well as terminologies and research methods; analyze historical and contemporary case studies of listening in various sound cultures; and consider...
CERN Bulletin
2010-01-01
Both the atmosphere and we ourselves are hit by hundreds of particles every second and yet nobody has ever heard a sound coming from these processes. Like cosmic rays, particles interacting inside the detectors at the LHC do not make any noise…unless you've decided to use the ‘sonification’ technique, in which case you might even hear the Higgs boson sound like music. Screenshot of the first page of the "LHC sound" site. A group of particle physicists, composers, software developers and artists recently got involved in the ‘LHC sound’ project to make the particles at the LHC produce music. Yes…music! The ‘sonification’ technique converts data into sound. “In this way, if you implement the right software you can get really nice music out of the particle tracks”, says Lily Asquith, a member of the ATLAS collaboration and one of the initiators of the project. The ‘LHC...
Sound Visualization and Holography
Kock, Winston E.
1975-01-01
Describes liquid surface holograms including their application to medicine. Discusses interference and diffraction phenomena using sound wave scanning techniques. Compares focussing by zone plate to holographic image development. (GH)
Using Solver Interfaced Virtual Reality in PEACER Design Process
International Nuclear Information System (INIS)
Lee, Hyong Won; Nam, Won Chang; Jeong, Seung Ho; Hwang, Il Soon; Shin, Jong Gye; Kim, Chang Hyo
2006-01-01
The recent research progress in the area of plant design and simulation highlighted the importance of integrating design and analysis models on a unified environment. For currently developed advanced reactors, either for power production or research, this effort has embraced impressive state-of-the-art information and automation technology. The PEACER (Proliferation-resistant, Environment friendly, Accident-tolerant, Continual and Economical Reactor) is one of the conceptual fast reactor system cooled by LBE (Lead Bismuth Eutectic) for nuclear waste transmutation. This reactor system is composed of innovative combination between design process and analysis. To establish an integrated design process by coupling design, analysis, and post-processing technology while minimizing the repetitive and costly manual interactions for design changes, a solver interfaced virtual reality simulation system (SIVR) has been developed for a nuclear transmutation energy system as PEACER. The SIVR was developed using Virtual Reality Modeling Language (VRML) in order to interface a commercial 3D CAD tool with various engineering solvers and to implement virtual reality presentation of results in a neutral format. In this paper, we have shown the SIVR approach viable and effective in the life-cycle management of complex nuclear energy systems, including design, construction and operation. For instance, The HELIOS is a down scaled model of the PEACER prototype to demonstrate the operability and safety as well as preliminary test of PEACER PLM (Product Life-cycle Management) with SIVR (Solver Interfaced Virtual Reality) concepts. Most components are designed by CATIA, which is 3D CAD tool. During the construction, 3D drawing by CATIA was effective to handle and arrange the loop configuration, especially when we changed the design. Most of all, This system shows the transparency of design and operational status of an energy complex to operators and inspectors can help ensure accident
Application of Nearly Linear Solvers to Electric Power System Computation
Grant, Lisa L.
To meet the future needs of the electric power system, improvements need to be made in the areas of power system algorithms, simulation, and modeling, specifically to achieve a time frame that is useful to industry. If power system time-domain simulations could run in real-time, then system operators would have situational awareness to implement online control and avoid cascading failures, significantly improving power system reliability. Several power system applications rely on the solution of a very large linear system. As the demands on power systems continue to grow, there is a greater computational complexity involved in solving these large linear systems within reasonable time. This project expands on the current work in fast linear solvers, developed for solving symmetric and diagonally dominant linear systems, in order to produce power system specific methods that can be solved in nearly-linear run times. The work explores a new theoretical method that is based on ideas in graph theory and combinatorics. The technique builds a chain of progressively smaller approximate systems with preconditioners based on the system's low stretch spanning tree. The method is compared to traditional linear solvers and shown to reduce the time and iterations required for an accurate solution, especially as the system size increases. A simulation validation is performed, comparing the solution capabilities of the chain method to LU factorization, which is the standard linear solver for power flow. The chain method was successfully demonstrated to produce accurate solutions for power flow simulation on a number of IEEE test cases, and a discussion on how to further improve the method's speed and accuracy is included.
Computational aeroelasticity using a pressure-based solver
Kamakoti, Ramji
A computational methodology for performing fluid-structure interaction computations for three-dimensional elastic wing geometries is presented. The flow solver used is based on an unsteady Reynolds-Averaged Navier-Stokes (RANS) model. A well validated k-ε turbulence model with wall function treatment for near wall region was used to perform turbulent flow calculations. Relative merits of alternative flow solvers were investigated. The predictor-corrector-based Pressure Implicit Splitting of Operators (PISO) algorithm was found to be computationally economic for unsteady flow computations. Wing structure was modeled using Bernoulli-Euler beam theory. A fully implicit time-marching scheme (using the Newmark integration method) was used to integrate the equations of motion for structure. Bilinear interpolation and linear extrapolation techniques were used to transfer necessary information between fluid and structure solvers. Geometry deformation was accounted for by using a moving boundary module. The moving grid capability was based on a master/slave concept and transfinite interpolation techniques. Since computations were performed on a moving mesh system, the geometric conservation law must be preserved. This is achieved by appropriately evaluating the Jacobian values associated with each cell. Accurate computation of contravariant velocities for unsteady flows using the momentum interpolation method on collocated, curvilinear grids was also addressed. Flutter computations were performed for the AGARD 445.6 wing at subsonic, transonic and supersonic Mach numbers. Unsteady computations were performed at various dynamic pressures to predict the flutter boundary. Results showed favorable agreement of experiment and previous numerical results. The computational methodology exhibited capabilities to predict both qualitative and quantitative features of aeroelasticity.
Karatas, Ilhan; Baki, Adnan
2013-01-01
Problem solving is recognized as an important life skill involving a range of processes including analyzing, interpreting, reasoning, predicting, evaluating and reflecting. For that reason educating students as efficient problem solvers is an important role of mathematics education. Problem solving skill is the centre of mathematics curriculum.…
Modeling Microbunching from Shot Noise Using Vlasov Solvers
International Nuclear Information System (INIS)
Venturini, Marco; Venturini, Marco; Zholents, Alexander
2008-01-01
Unlike macroparticle simulations, which are sensitive to unphysical statistical fluctuations when the number of macroparticles is smaller than the bunch population, direct methods for solving the Vlasov equation are free from sampling noise and are ideally suited for studying microbunching instabilities evolving from shot noise. We review a 2D (longitudinal dynamics) Vlasov solver we have recently developed to study the microbunching instability in the beam delivery systems for x-ray FELs and present an application to FERMI(at)Elettra. We discuss, in particular, the impact of the spreader design on microbunching
Parallel implementations of 2D explicit Euler solvers
International Nuclear Information System (INIS)
Giraud, L.; Manzini, G.
1996-01-01
In this work we present a subdomain partitioning strategy applied to an explicit high-resolution Euler solver. We describe the design of a portable parallel multi-domain code suitable for parallel environments. We present several implementations on a representative range of MlMD computers that include shared memory multiprocessors, distributed virtual shared memory computers, as well as networks of workstations. Computational results are given to illustrate the efficiency, the scalability, and the limitations of the different approaches. We discuss also the effect of the communication protocol on the optimal domain partitioning strategy for the distributed memory computers
Sound field control for a low-frequency test facility
DEFF Research Database (Denmark)
Pedersen, Christian Sejer; Møller, Henrik
2013-01-01
The two largest problems in controlling the reproduction of low-frequency sound for psychoacoustic experiments is the effect of the room due to standing waves and the relatively large sound pressure levels needed. Anechoic rooms are limited downward in frequency and distortion may be a problem even...... at moderate levels, while pressure-field playback can give higher sound pressures but is limited upwards in frequency. A new solution that addresses both problems has been implemented in the laboratory of Acoustics, Aalborg University. The solution uses one wall with 20 loudspeakers to generate a plane wave...... that is actively absorbed when it reaches the 20 loudspeakers on the opposing wall. This gives a homogeneous sound field in the majority of the room with a flat frequency response in the frequency range 2-300 Hz. The lowest frequencies are limited to sound pressure levels in the order of 95 dB. If larger levels...
On the implicit density based OpenFOAM solver for turbulent compressible flows
Fürst, Jiří
The contribution deals with the development of coupled implicit density based solver for compressible flows in the framework of open source package OpenFOAM. However the standard distribution of OpenFOAM contains several ready-made segregated solvers for compressible flows, the performance of those solvers is rather week in the case of transonic flows. Therefore we extend the work of Shen [15] and we develop an implicit semi-coupled solver. The main flow field variables are updated using lower-upper symmetric Gauss-Seidel method (LU-SGS) whereas the turbulence model variables are updated using implicit Euler method.
Integrating Multimedia and Physics Problems
Titus, Aaron P.
1997-11-01
Although expert problem solvers typically use pictorial representations when solving problems, novices tend to proceed from the given problem statement to a mathematical solution without first developing a visual representation of the problem. For this reason, multimedia may be an effective tool to enhance students' success at solving problems. However, merely presenting a video of motion described in a problem is not necessarily the most effective method as was found in a recent study of students' responses on Web-based homework questions. Rather, multimedia-focused problems, where data relevant to solving the problem is embedded in a video or animation, may be the best use of multimedia in problem solving. Examples of multimedia-enhanced problems and multimedia-focused problems will be demonstrated, and their differences from "traditional" problems will be highlighted. Recommendations on the use of multimedia with problem solving and preliminary data on students' success at solving these problems will be discussed.
Curating sound performance as laboratories of envisioning
DEFF Research Database (Denmark)
Holmboe, Rasmus
This paper is based on my dissertation research that investigates how sound performance can be presented and represented - in real time, as well as in and through the archive. This double perspective opens a field of curatorial problems related to the simultaneous movements of both envisioning...
The quantum mechanics solver. How to apply quantum theory to modern physics. 2. ed.
International Nuclear Information System (INIS)
Basdevant, J.L.; Dalibard, J.
2006-01-01
The Quantum Mechanics Solver uniquely illustrates the application of quantum mechanical concepts to various fields of modern physics. It aims at encouraging the reader to apply quantum mechanics to research problems in fields such as molecular physics, condensed matter physics or laser physics. Advanced undergraduates and graduate students will find a rich and challenging source of material for further exploration. This book consists of a series of problems concerning present-day experimental or theoretical questions on quantum mechanics. All of these problems are based on actual physical examples, even if sometimes the mathematical structure of the models under consideration is simplified intentionally in order to get hold of the physics more rapidly. The new edition features new themes, such as the progress in measuring neutrino oscillations, quantum boxes, the quantum thermometer etc. Secondly, it includes a brief summary on the basics of quantum mechanics and the formalism we use. Finally, the problems under three main themes: Elementary Particles, Nuclei and Atoms; Quantum Entanglement and Measurement; and Complex Systems. (orig.)
Mullenmeister, Paul
1988-01-01
The quasi-geostrophic omega-equation in flux form is developed as an example of a Poisson problem over a spherical shell. Solutions of this equation are obtained by applying a two-parameter Chebyshev solver in vector layout for CDC 200 series computers. The performance of this vectorized algorithm greatly exceeds the performance of its scalar analog. The algorithm generates solutions of the omega-equation which are compared with the omega fields calculated with the aid of the mass continuity equation.
Development of a Cartesian grid based CFD solver (CARBS)
International Nuclear Information System (INIS)
Vaidya, A.M.; Maheshwari, N.K.; Vijayan, P.K.
2013-12-01
Formulation for 3D transient incompressible CFD solver is developed. The solution of variable property, laminar/turbulent, steady/unsteady, single/multi specie, incompressible with heat transfer in complex geometry will be obtained. The formulation can handle a flow system in which any number of arbitrarily shaped solid and fluid regions are present. The solver is based on the use of Cartesian grids. A method is proposed to handle complex shaped objects and boundaries on Cartesian grids. Implementation of multi-material, different types of boundary conditions, thermo physical properties is also considered. The proposed method is validated by solving two test cases. 1 st test case is that of lid driven flow in inclined cavity. 2 nd test case is the flow over cylinder. The 1 st test case involved steady internal flow subjected to WALL boundaries. The 2 nd test case involved unsteady external flow subjected to INLET, OUTLET and FREE-SLIP boundary types. In both the test cases, non-orthogonal geometry was involved. It was found that, under such a wide conditions, the Cartesian grid based code was found to give results which were matching well with benchmark data. Convergence characteristics are excellent. In all cases, the mass residue was converged to 1E-8. Based on this, development of 3D general purpose code based on the proposed approach can be taken up. (author)
CASTRO: A NEW COMPRESSIBLE ASTROPHYSICAL SOLVER. III. MULTIGROUP RADIATION HYDRODYNAMICS
International Nuclear Information System (INIS)
Zhang, W.; Almgren, A.; Bell, J.; Howell, L.; Burrows, A.; Dolence, J.
2013-01-01
We present a formulation for multigroup radiation hydrodynamics that is correct to order O(v/c) using the comoving-frame approach and the flux-limited diffusion approximation. We describe a numerical algorithm for solving the system, implemented in the compressible astrophysics code, CASTRO. CASTRO uses a Eulerian grid with block-structured adaptive mesh refinement based on a nested hierarchy of logically rectangular variable-sized grids with simultaneous refinement in both space and time. In our multigroup radiation solver, the system is split into three parts: one part that couples the radiation and fluid in a hyperbolic subsystem, another part that advects the radiation in frequency space, and a parabolic part that evolves radiation diffusion and source-sink terms. The hyperbolic subsystem and the frequency space advection are solved explicitly with high-order Godunov schemes, whereas the parabolic part is solved implicitly with a first-order backward Euler method. Our multigroup radiation solver works for both neutrino and photon radiation.
Anisotropic resonator analysis using the Fourier-Bessel mode solver
Gauthier, Robert C.
2018-03-01
A numerical mode solver for optical structures that conform to cylindrical symmetry using Faraday's and Ampere's laws as starting expressions is developed when electric or magnetic anisotropy is present. The technique builds on the existing Fourier-Bessel mode solver which allows resonator states to be computed exploiting the symmetry properties of the resonator and states to reduce the matrix system. The introduction of anisotropy into the theoretical frame work facilitates the inclusion of PML borders permitting the computation of open ended structures and a better estimation of the resonator state quality factor. Matrix populating expressions are provided that can accommodate any material anisotropy with arbitrary orientation in the computation domain. Several example of electrical anisotropic computations are provided for rationally symmetric structures such as standard optical fibers, axial Bragg-ring fibers and bottle resonators. The anisotropy present in the materials introduces off diagonal matrix elements in the permittivity tensor when expressed in cylindrical coordinates. The effects of the anisotropy of computed states are presented and discussed.
Tree-based solvers for adaptive mesh refinement code FLASH - I: gravity and optical depths
Wünsch, R.; Walch, S.; Dinnbier, F.; Whitworth, A.
2018-04-01
We describe an OctTree algorithm for the MPI parallel, adaptive mesh refinement code FLASH, which can be used to calculate the gas self-gravity, and also the angle-averaged local optical depth, for treating ambient diffuse radiation. The algorithm communicates to the different processors only those parts of the tree that are needed to perform the tree-walk locally. The advantage of this approach is a relatively low memory requirement, important in particular for the optical depth calculation, which needs to process information from many different directions. This feature also enables a general tree-based radiation transport algorithm that will be described in a subsequent paper, and delivers excellent scaling up to at least 1500 cores. Boundary conditions for gravity can be either isolated or periodic, and they can be specified in each direction independently, using a newly developed generalization of the Ewald method. The gravity calculation can be accelerated with the adaptive block update technique by partially re-using the solution from the previous time-step. Comparison with the FLASH internal multigrid gravity solver shows that tree-based methods provide a competitive alternative, particularly for problems with isolated or mixed boundary conditions. We evaluate several multipole acceptance criteria (MACs) and identify a relatively simple approximate partial error MAC which provides high accuracy at low computational cost. The optical depth estimates are found to agree very well with those of the RADMC-3D radiation transport code, with the tree-solver being much faster. Our algorithm is available in the standard release of the FLASH code in version 4.0 and later.
International Nuclear Information System (INIS)
Hindmarsh, A.C.; Petzold, L.R.
2005-01-01
1 - Description of program or function: LSODKR is a new initial value ODE solver for stiff and non-stiff systems. It is a variant of the LSODPK and LSODE solvers, intended mainly for large stiff systems. The main differences between LSODKR and LSODE are the following: a) for stiff systems, LSODKR uses a corrector iteration composed of Newton iteration and one of four preconditioned Krylov subspace iteration methods. The user must supply routines for the preconditioning operations, b) within the corrector iteration, LSODKR does automatic switching between functional (fix point) iteration and modified Newton iteration, The nonlinear iteration method-switching differs from the method-switching in LSODA and LSODAR, but provides similar savings by using the cheaper method in the non-stiff regions of the problem. c) LSODKR includes the ability to find roots of given functions of the solution during the integration. d) LSODKR also improves on the Krylov methods in LSODPK by offering the option to save and reuse the approximate Jacobian data underlying the pre-conditioner. The LSODKR source is commented extensively to facilitate modification. Both a single-precision version and a double-precision version are available. 2 - Methods: It is assumed that the ODEs are given explicitly, so that the system can be written in the form dy/dt = f(t,y), where y is the vector of dependent variables, and t is the independent variable. Integration is by Adams or BDF (Backward Differentiation Formula) methods, at user option. Corrector iteration is by Newton or fix point iteration, determined dynamically. Linear system solution is by a preconditioned Krylov iteration, selected by user from Incomplete Orthogonalization Method, Generalized Minimum Residual Method, and two variants of Preconditioned Conjugate Gradient Method. Preconditioning is to be supplied by the user
Parallel CFD Algorithms for Aerodynamical Flow Solvers on Unstructured Meshes. Parts 1 and 2
Barth, Timothy J.; Kwak, Dochan (Technical Monitor)
1995-01-01
The Advisory Group for Aerospace Research and Development (AGARD) has requested my participation in the lecture series entitled Parallel Computing in Computational Fluid Dynamics to be held at the von Karman Institute in Brussels, Belgium on May 15-19, 1995. In addition, a request has been made from the US Coordinator for AGARD at the Pentagon for NASA Ames to hold a repetition of the lecture series on October 16-20, 1995. I have been asked to be a local coordinator for the Ames event. All AGARD lecture series events have attendance limited to NATO allied countries. A brief of the lecture series is provided in the attached enclosure. Specifically, I have been asked to give two lectures of approximately 75 minutes each on the subject of parallel solution techniques for the fluid flow equations on unstructured meshes. The title of my lectures is "Parallel CFD Algorithms for Aerodynamical Flow Solvers on Unstructured Meshes" (Parts I-II). The contents of these lectures will be largely review in nature and will draw upon previously published work in this area. Topics of my lectures will include: (1) Mesh partitioning algorithms. Recursive techniques based on coordinate bisection, Cuthill-McKee level structures, and spectral bisection. (2) Newton's method for large scale CFD problems. Size and complexity estimates for Newton's method, modifications for insuring global convergence. (3) Techniques for constructing the Jacobian matrix. Analytic and numerical techniques for Jacobian matrix-vector products, constructing the transposed matrix, extensions to optimization and homotopy theories. (4) Iterative solution algorithms. Practical experience with GIVIRES and BICG-STAB matrix solvers. (5) Parallel matrix preconditioning. Incomplete Lower-Upper (ILU) factorization, domain-decomposed ILU, approximate Schur complement strategies.
DEFF Research Database (Denmark)
Schulze, Holger
2014-01-01
How are those sounds you hear right now socially constructed and evaluated, how are they architecturally conceptualized and how dependant on urban planning, industrial developments and political decisions are they really? How is your ability to hear intertwined with social interactions and their ...... and their professional design? And how is listening and sounding a deeply social activity – constructing our way of living together in cities as well as in apartment houses? A radio feature with Nina Backmann, Jochen Bonz, Stefan Krebs, Esther Schelander & Holger Schulze......How are those sounds you hear right now socially constructed and evaluated, how are they architecturally conceptualized and how dependant on urban planning, industrial developments and political decisions are they really? How is your ability to hear intertwined with social interactions...
DEFF Research Database (Denmark)
Breinbjerg, Morten
2012-01-01
This paper draws on the theories of Michel de Certeau and Gaston Bachelard to discuss how media architecture, in the form of urban sound interfaces, can help us perceive the complexity of the spaces we inhabit, by exploring the history and the narratives of the places in which we live. In this pa......This paper draws on the theories of Michel de Certeau and Gaston Bachelard to discuss how media architecture, in the form of urban sound interfaces, can help us perceive the complexity of the spaces we inhabit, by exploring the history and the narratives of the places in which we live....... In this paper, three sound works are discussed in relation to the iPod, which is considered as a more private way to explore urban environments, and as a way to control the individual perception of urban spaces....
Attenborough, Keith; Horoshenkov, Kirill
2014-01-01
1. Introduction 2. The Propagation of Sound Near Ground Surfaces in a Homogeneous Medium 3. Predicting the Acoustical Properties of Outdoor Ground Surfaces 4. Measurements of the Acoustical Properties of Ground Surfaces and Comparisons with Models 5. Predicting Effects of Source Characteristics on Outdoor Sound 6. Predictions, Approximations and Empirical Results for Ground Effect Excluding Meteorological Effects 7. Influence of Source Motion on Ground Effect and Diffraction 8. Predicting Effects of Mixed Impedance Ground 9. Predicting the Performance of Outdoor Noise Barriers 10. Predicting Effects of Vegetation, Trees and Turbulence 11. Analytical Approximations including Ground Effect, Refraction and Turbulence 12. Prediction Schemes 13. Predicting Sound in an Urban Environment.
DEFF Research Database (Denmark)
Schulze, Holger
2012-01-01
How are those sounds you hear right now technically generated and post-produced, how are they aesthetically conceptualized and how culturally dependant are they really? How is your ability to hear intertwined with all the other senses and their cultural, biographical and technological constructio...... over time? And how is listening and sounding a deeply social activity – constructing our way of living together in cities as well as in apartment houses? A radio feature with Jonathan Sterne, AGF a.k.a Antye Greie, Jens Gerrit Papenburg & Holger Schulze....
Ballou, Glen
2013-01-01
Handbook for Sound Engineers is the most comprehensive reference available for audio engineers. All audio topics are explored: if you work on anything related to audio you should not be without this book! The 4th edition of this trusted reference has been updated to reflect changes in the industry since the publication of the 3rd edition in 2002 -- including new technologies like software-based recording systems such as Pro Tools and Sound Forge; digital recording using MP3, wave files and others; mobile audio devices such as iPods and MP3 players. Over 40 topic
Holman, Tomlinson
2013-01-01
Achieve professional quality sound on a limited budget! Harness all new, Hollywood style audio techniques to bring your independent film and video productions to the next level.In Sound for Digital Video, Second Edition industry experts Tomlinson Holman and Arthur Baum give you the tools and knowledge to apply recent advances in audio capture, video recording, editing workflow, and mixing to your own film or video with stunning results. This fresh edition is chockfull of techniques, tricks, and workflow secrets that you can apply to your own projects from preproduction
DEFF Research Database (Denmark)
Knakkergaard, Martin
2018-01-01
The chapter discusses expectations and imaginations vis-à-vis the concert hall of the twenty-first century. It outlines some of the central historical implications of western culture’s haven for sounding music. Based on the author’s study of the Icelandic concert-house Harpa, the chapter considers...... how these implications, together with the prime mover’s visions, have been transformed as private investors and politicians took over. The chapter furthermore investigates the objectives regarding musical sound and the far-reaching demands concerning acoustics that modern concert halls are required...
DEFF Research Database (Denmark)
Reybrouck, Mark; Brattico, Elvira
2015-01-01
Capitalizing from neuroscience knowledge on how individuals are affected by the sound environment, we propose to adopt a cybernetic and ecological point of view on the musical aesthetic experience, which includes subprocesses, such as feature extraction and integration, early affective reactions...... and motor actions, style mastering and conceptualization, emotion and proprioception, evaluation and preference. In this perspective, the role of the listener/composer/performer is seen as that of an active "agent" coping in highly individual ways with the sounds. The findings concerning the neural...
Harris, Anna
2015-11-01
Sensory experiences are often considered triggers of memory, most famously a little French cake dipped in lime blossom tea. Sense memory can also be evoked in public history research through techniques of elicitation. In this article I reflect on different social science methods for eliciting sound memories such as the use of sonic prompts, emplaced interviewing, and sound walks. I include examples from my research on medical listening. The article considers the relevance of this work for the conduct of oral histories, arguing that such methods "break the frame," allowing room for collaborative research connections and insights into the otherwise unarticulatable.
DEFF Research Database (Denmark)
Zanotto, Damiano; Turchet, Luca; Boggs, Emily Marie
2014-01-01
This paper introduces the design of SoleSound, a wearable system designed to deliver ecological, audio-tactile, underfoot feedback. The device, which primarily targets clinical applications, uses an audio-tactile footstep synthesis engine informed by the readings of pressure and inertial sensors...... embedded in the footwear to integrate enhanced feedback modalities into the authors' previously developed instrumented footwear. The synthesis models currently implemented in the SoleSound simulate different ground surface interactions. Unlike similar devices, the system presented here is fully portable...
Physics and music the science of musical sound
White, Harvey E
2014-01-01
Comprehensive and accessible, this foundational text surveys general principles of sound, musical scales, characteristics of instruments, mechanical and electronic recording devices, and many other topics. More than 300 illustrations plus questions, problems, and projects.
Identification of severe wind conditions using a Reynolds averaged Navier-Stokes solver
DEFF Research Database (Denmark)
Sørensen, Niels N.; Bechmann, Andreas; Johansen, Jeppe
2007-01-01
The present paper describes the application of a Navier-Stokes solver to predict the presence of severe flow conditions in complex terrain, capturing conditions that may be critical to the siting of wind turbines in the terrain. First it is documented that the flow solver is capable of predicting...
The SX Solver: A New Computer Program for Analyzing Solvent-Extraction Equilibria
International Nuclear Information System (INIS)
McNamara, B.K.; Rapko, B.M.; Lumetta, G.J.
1999-01-01
A new computer program, the SX Solver, has been developed to analyze solvent-extraction equilibria. The program operates out of Microsoft Excel and uses the built-in ''Solver'' function to minimize the sum of the square of the residuals between measured and calculated distribution coefficients. The extraction of nitric acid by tributylphosphate has been modeled to illustrate the program's use
The SX Solver: A Computer Program for Analyzing Solvent-Extraction Equilibria: Version 3.0
International Nuclear Information System (INIS)
Lumetta, Gregg J.
2001-01-01
A new computer program, the SX Solver, has been developed to analyze solvent-extraction equilibria. The program operates out of Microsoft Excel and uses the built-in Solver function to minimize the sum of the square of the residuals between measured and calculated distribution coefficients. The extraction of nitric acid by tributyl phosphate has been modeled to illustrate the programs use
Efficient Implementation of the Riccati Recursion for Solving Linear-Quadratic Control Problems
DEFF Research Database (Denmark)
Frison, Gianluca; Jørgensen, John Bagterp
2013-01-01
In both Active-Set (AS) and Interior-Point (IP) algorithms for Model Predictive Control (MPC), sub-problems in the form of linear-quadratic (LQ) control problems need to be solved at each iteration. The solution of these sub-problems is typically the main computational effort at each iteration....... In this paper, we compare a number of solvers for an extended formulation of the LQ control problem: a Riccati recursion based solver can be considered the best choice for the general problem with dense matrices. Furthermore, we present a novel version of the Riccati solver, that makes use of the Cholesky...... factorization of the Pn matrices to reduce the number of flops. When combined with regularization and mixed precision, this algorithm can solve large instances of the LQ control problem up to 3 times faster than the classical Riccati solver....
International Nuclear Information System (INIS)
Li, Fei; Yu, Peicheng; Xu, Xinlu; Fiuza, Frederico; Decyk, Viktor K.
2017-01-01
In this study we present a customized finite-difference-time-domain (FDTD) Maxwell solver for the particle-in-cell (PIC) algorithm. The solver is customized to effectively eliminate the numerical Cerenkov instability (NCI) which arises when a plasma (neutral or non-neutral) relativistically drifts on a grid when using the PIC algorithm. We control the EM dispersion curve in the direction of the plasma drift of a FDTD Maxwell solver by using a customized higher order finite difference operator for the spatial derivative along the direction of the drift (1^ direction). We show that this eliminates the main NCI modes with moderate |k_1|, while keeps additional main NCI modes well outside the range of physical interest with higher |k_1|. These main NCI modes can be easily filtered out along with first spatial aliasing NCI modes which are also at the edge of the fundamental Brillouin zone. The customized solver has the possible advantage of improved parallel scalability because it can be easily partitioned along 1^ which typically has many more cells than other directions for the problems of interest. We show that FFTs can be performed locally to current on each partition to filter out the main and first spatial aliasing NCI modes, and to correct the current so that it satisfies the continuity equation for the customized spatial derivative. This ensures that Gauss’ Law is satisfied. Lastly, we present simulation examples of one relativistically drifting plasma, of two colliding relativistically drifting plasmas, and of nonlinear laser wakefield acceleration (LWFA) in a Lorentz boosted frame that show no evidence of the NCI can be observed when using this customized Maxwell solver together with its NCI elimination scheme.
Efficient sound barrier calculations with the BEM
DEFF Research Database (Denmark)
Juhl, Peter Møller; Cutanda Henriquez, Vicente
2018-01-01
The Boundary Element Method has been used for calculating the effect of introducing sound barriers for some decades. The method has also been used for optimizing the shape of the barrier and in some cases the effects of introducing sound absorption. However, numerical calculations are still quite...... time consuming and inconvenient to use, which is limiting their use for many practical problems. Moreover, measurements are mostly taken in one-third or full octave bands opposed to the numerical computations at specific frequencies, which then has to be conducted using a fine density in frequencies....... This paper addresses some of the challenges and possible solutions for developing BEM into a more efficient tool for sound barrier calculations....
International Nuclear Information System (INIS)
Kim, Kun ho
2012-01-01
The International Young Physicists’ Tournament (IYPT) is a worldwide tournament that evaluates a high-school student's ability to solve various physics conundrums that have not been fully resolved in the past. The research presented here is my solution to the cup drum problem. The physics behind a cup drum has never been explored or modelled. A cup drum is a musical instrument that can generate different frequencies and amplitudes depending on the location of a cup held upside-down over, on or under a water surface. The tapping sound of a cup drum can be divided into two components: standing waves and plate vibration. By individually researching the nature of these two sounds, I arrived at conclusions that could accurately predict the frequencies in most cases. When the drum is very close to the surface, qualitative explanations are given. In addition, I examined the trend of the tapping sound amplitude at various distances and qualitatively explained the experimental results. (paper)
Development of axisymmetric lattice Boltzmann flux solver for complex multiphase flows
Wang, Yan; Shu, Chang; Yang, Li-Ming; Yuan, Hai-Zhuan
2018-05-01
This paper presents an axisymmetric lattice Boltzmann flux solver (LBFS) for simulating axisymmetric multiphase flows. In the solver, the two-dimensional (2D) multiphase LBFS is applied to reconstruct macroscopic fluxes excluding axisymmetric effects. Source terms accounting for axisymmetric effects are introduced directly into the governing equations. As compared to conventional axisymmetric multiphase lattice Boltzmann (LB) method, the present solver has the kinetic feature for flux evaluation and avoids complex derivations of external forcing terms. In addition, the present solver also saves considerable computational efforts in comparison with three-dimensional (3D) computations. The capability of the proposed solver in simulating complex multiphase flows is demonstrated by studying single bubble rising in a circular tube. The obtained results compare well with the published data.
Experimental validation of GADRAS's coupled neutron-photon inverse radiation transport solver
International Nuclear Information System (INIS)
Mattingly, John K.; Mitchell, Dean James; Harding, Lee T.
2010-01-01
Sandia National Laboratories has developed an inverse radiation transport solver that applies nonlinear regression to coupled neutron-photon deterministic transport models. The inverse solver uses nonlinear regression to fit a radiation transport model to gamma spectrometry and neutron multiplicity counting measurements. The subject of this paper is the experimental validation of that solver. This paper describes a series of experiments conducted with a 4.5 kg sphere of α-phase, weapons-grade plutonium. The source was measured bare and reflected by high-density polyethylene (HDPE) spherical shells with total thicknesses between 1.27 and 15.24 cm. Neutron and photon emissions from the source were measured using three instruments: a gross neutron counter, a portable neutron multiplicity counter, and a high-resolution gamma spectrometer. These measurements were used as input to the inverse radiation transport solver to evaluate the solver's ability to correctly infer the configuration of the source from its measured radiation signatures.
Minos: a SPN solver for core calculation in the DESCARTES system
International Nuclear Information System (INIS)
Baudron, A.M.; Lautard, J.J.
2005-01-01
This paper describes a new development of a neutronic core solver done in the context of a new generation neutronic reactor computational system, named DESCARTES. For performance reasons, the numerical method of the existing MINOS solver in the SAPHYR system has been reused in the new system. It is based on the mixed dual finite element approximation of the simplified transport equation. The solver takes into account assembly discontinuity coefficients (ADF) in the simplified transport equation (SPN) context. The solver has been rewritten in C++ programming language using an object oriented design. Its general architecture was reconsidered in order to improve its capability of evolution and its maintainability. Moreover, the performances of the old version have been improved mainly regarding the matrix construction time; this result improves significantly the performance of the solver in the context of industrial application requiring thermal hydraulic feedback and depletion calculations. (authors)
Tinnitus (Phantom Sound: Risk coming for future
Directory of Open Access Journals (Sweden)
Suresh Rewar
2015-01-01
Full Text Available The word 'tinnitus' comes from the Latin word tinnire, meaning “to ring” or “a ringing.” Tinnitus is the cognition of sound in the absence of any corresponding external sound. Tinnitus can take the form of continuous buzzing, hissing, or ringing, or a combination of these or other characteristics. Tinnitus affects 10% to 25% of the adult population. Tinnitus is classified as objective and subjective categories. Subjective tinnitus is meaningless sounds that are not associated with a physical sound and only the person who has the tinnitus can hear it. Objective tinnitus is the result of a sound that can be heard by the physician. Tinnitus is not a disease in itself but a common symptom, and because it involves the perception of sound or sounds, it is commonly associated with the hearing system. In fact, various parts of the hearing system, including the inner ear, are often responsible for this symptom. Tinnitus patients, which can lead to sleep disturbances, concentration problems, fatigue, depression, anxiety disorders, and sometimes even to suicide. The evaluation of tinnitus always begins with a thorough history and physical examination, with further testing performed when indicated. Diagnostic testing should include audiography, speech discrimination testing, computed tomography angiography, or magnetic resonance angiography should be performed. All patients with tinnitus can benefit from patient education and preventive measures, and oftentimes the physician's reassurance and assistance with the psychologic aftereffects of tinnitus can be the therapy most valuable to the patient. There are no specific medications for the treatment of tinnitus. Sedatives and some other medications may prove helpful in the early stages. The ultimate goal of neuro-imaging is to identify subtypes of tinnitus in order to better inform treatment strategies.
Workload Characterization of CFD Applications Using Partial Differential Equation Solvers
Waheed, Abdul; Yan, Jerry; Saini, Subhash (Technical Monitor)
1998-01-01
Workload characterization is used for modeling and evaluating of computing systems at different levels of detail. We present workload characterization for a class of Computational Fluid Dynamics (CFD) applications that solve Partial Differential Equations (PDEs). This workload characterization focuses on three high performance computing platforms: SGI Origin2000, EBM SP-2, a cluster of Intel Pentium Pro bases PCs. We execute extensive measurement-based experiments on these platforms to gather statistics of system resource usage, which results in workload characterization. Our workload characterization approach yields a coarse-grain resource utilization behavior that is being applied for performance modeling and evaluation of distributed high performance metacomputing systems. In addition, this study enhances our understanding of interactions between PDE solver workloads and high performance computing platforms and is useful for tuning these applications.
Extending the QUDA Library with the eigCG Solver
Energy Technology Data Exchange (ETDEWEB)
Strelchenko, Alexei [Fermilab; Stathopoulos, Andreas [William-Mary Coll.
2014-12-12
While the incremental eigCG algorithm [ 1 ] is included in many LQCD software packages, its realization on GPU micro-architectures was still missing. In this session we report our experi- ence of the eigCG implementation in the QUDA library. In particular, we will focus on how to employ the mixed precision technique to accelerate solutions of large sparse linear systems with multiple right-hand sides on GPUs. Although application of mixed precision techniques is a well-known optimization approach for linear solvers, its utilization for the eigenvector com- puting within eigCG requires special consideration. We will discuss implementation aspects of the mixed precision deflation and illustrate its numerical behavior on the example of the Wilson twisted mass fermion matrix inversions
A high order solver for the unbounded Poisson equation
DEFF Research Database (Denmark)
Hejlesen, Mads Mølholm; Rasmussen, Johannes Tophøj; Chatelain, Philippe
2013-01-01
. The method is extended to directly solve the derivatives of the solution to Poissonʼs equation. In this way differential operators such as the divergence or curl of the solution field can be solved to the same high order convergence without additional computational effort. The method, is applied......A high order converging Poisson solver is presented, based on the Greenʼs function solution to Poissonʼs equation subject to free-space boundary conditions. The high order convergence is achieved by formulating regularised integration kernels, analogous to a smoothing of the solution field...... and validated, however not restricted, to the equations of fluid mechanics, and can be used in many applications to solve Poissonʼs equation on a rectangular unbounded domain....
Visualising magnetic fields numerical equation solvers in action
Beeteson, John Stuart
2001-01-01
Visualizing Magnetic Fields: Numerical Equation Solvers in Action provides a complete description of the theory behind a new technique, a detailed discussion of the ways of solving the equations (including a software visualization of the solution algorithms), the application software itself, and the full source code. Most importantly, there is a succinct, easy-to-follow description of each procedure in the code.The physicist Michael Faraday said that the study of magnetic lines of force was greatly influential in leading him to formulate many of those concepts that are now so fundamental to our modern world, proving to him their "great utility as well as fertility." Michael Faraday could only visualize these lines in his mind's eye and, even with modern computers to help us, it has been very expensive and time consuming to plot lines of force in magnetic fields
Sound Symbolism in Basic Vocabulary
Directory of Open Access Journals (Sweden)
Søren Wichmann
2010-04-01
Full Text Available The relationship between meanings of words and their sound shapes is to a large extent arbitrary, but it is well known that languages exhibit sound symbolism effects violating arbitrariness. Evidence for sound symbolism is typically anecdotal, however. Here we present a systematic approach. Using a selection of basic vocabulary in nearly one half of the world’s languages we find commonalities among sound shapes for words referring to same concepts. These are interpreted as due to sound symbolism. Studying the effects of sound symbolism cross-linguistically is of key importance for the understanding of language evolution.
Directory of Open Access Journals (Sweden)
Denikin Anton A.
2012-12-01
Full Text Available The article considers the aesthetical and practical possibilities for sounds (sound design in video games and interactive applications. Outlines the key features of the game sound, such as simulation, representativeness, interactivity, immersion, randomization, and audio-visuality. The author defines the basic terminology in study of game audio, as well as identifies significant aesthetic differences between film sounds and sounds in video game projects. It is an attempt to determine the techniques of art analysis for the approaches in study of video games including aesthetics of their sounds. The article offers a range of research methods, considering the video game scoring as a contemporary creative practice.
Incompressible SPH (ISPH) with fast Poisson solver on a GPU
Chow, Alex D.; Rogers, Benedict D.; Lind, Steven J.; Stansby, Peter K.
2018-05-01
This paper presents a fast incompressible SPH (ISPH) solver implemented to run entirely on a graphics processing unit (GPU) capable of simulating several millions of particles in three dimensions on a single GPU. The ISPH algorithm is implemented by converting the highly optimised open-source weakly-compressible SPH (WCSPH) code DualSPHysics to run ISPH on the GPU, combining it with the open-source linear algebra library ViennaCL for fast solutions of the pressure Poisson equation (PPE). Several challenges are addressed with this research: constructing a PPE matrix every timestep on the GPU for moving particles, optimising the limited GPU memory, and exploiting fast matrix solvers. The ISPH pressure projection algorithm is implemented as 4 separate stages, each with a particle sweep, including an algorithm for the population of the PPE matrix suitable for the GPU, and mixed precision storage methods. An accurate and robust ISPH boundary condition ideal for parallel processing is also established by adapting an existing WCSPH boundary condition for ISPH. A variety of validation cases are presented: an impulsively started plate, incompressible flow around a moving square in a box, and dambreaks (2-D and 3-D) which demonstrate the accuracy, flexibility, and speed of the methodology. Fragmentation of the free surface is shown to influence the performance of matrix preconditioners and therefore the PPE matrix solution time. The Jacobi preconditioner demonstrates robustness and reliability in the presence of fragmented flows. For a dambreak simulation, GPU speed ups demonstrate up to 10-18 times and 1.1-4.5 times compared to single-threaded and 16-threaded CPU run times respectively.
Robertson, Laura; Meyer, John R.
2010-01-01
Differences in insect morphology and movement during singing provide a fascinating opportunity for students to investigate insects while learning about the characteristics of sound. In the activities described here, students use a free online computer software program to explore the songs of the major singing insects and experiment with making…
Yang, Jihee; Ihas, Gary G.; Ekdahl, Dan
2017-10-01
It is common that a physical system resonates at a particular frequency, whose frequency depends on physical parameters which may change in time. Often, one would like to automatically track this signal as the frequency changes, measuring, for example, its amplitude. In scientific research, one would also like to utilize the standard methods, such as lock-in amplifiers, to improve the signal to noise ratio. We present a complete He ii second sound system that uses positive feedback to generate a sinusoidal signal of constant amplitude via automatic gain control. This signal is used to produce temperature/entropy waves (second sound) in superfluid helium-4 (He ii). A lock-in amplifier limits the oscillation to a desirable frequency and demodulates the received sound signal. Using this tracking system, a second sound signal probed turbulent decay in He ii. We present results showing that the tracking system is more reliable than those of a conventional fixed frequency method; there is less correlation with temperature (frequency) fluctuation when the tracking system is used.
DEFF Research Database (Denmark)
Kristensen, Thomas Bjørnsten
2009-01-01
Anmeldelse af udstillingen See This Sound på Lentos Kunstmuseum Linz, Østrig, som markerer den foreløbige kulmination på et samarbejde mellem Lentos Kunstmuseum og Ludwig Boltzmann Institute Media.Art.Research. Udover den konkrete udstilling er samarbejdet tænkt som en ambitiøs, tværfaglig...
Photoacoustic Sounds from Meteors.
Energy Technology Data Exchange (ETDEWEB)
Spalding, Richard E. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Tencer, John [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Sweatt, William C. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Hogan, Roy E. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Boslough, Mark B. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Spurny, Pavel [Academy of Sciences of the Czech Republic (ASCR), Prague (Czech Republic)
2015-03-01
High-speed photometric observations of meteor fireballs have shown that they often produce high-amplitude light oscillations with frequency components in the kHz range, and in some cases exhibit strong millisecond flares. We built a light source with similar characteristics and illuminated various materials in the laboratory, generating audible sounds. Models suggest that light oscillations and pulses can radiatively heat dielectric materials, which in turn conductively heats the surrounding air on millisecond timescales. The sound waves can be heard if the illuminated material is sufficiently close to the observer’s ears. The mechanism described herein may explain many reports of meteors that appear to be audible while they are concurrently visible in the sky and too far away for sound to have propagated to the observer. This photoacoustic (PA) explanation provides an alternative to electrophonic (EP) sounds hypothesized to arise from electromagnetic coupling of plasma oscillation in the meteor wake to natural antennas in the vicinity of an observer.
DEFF Research Database (Denmark)
Groth, Sanne Krogh
2013-01-01
Med sine kun 4 år bag sig er Sound of Stockholm relativt ny i det internationale festival-landskab. Festivalen er efter sigende udsprunget af en større eller mindre frustration over, at den svenske eksperimentelle musikscenes forskellige foreninger og organisationer gik hinanden bedene, og...
Menon, Deepika; Lankford, Deanna
2016-01-01
From the earliest days of their lives, children are exposed to all kinds of sound, from soft, comforting voices to the frightening rumble of thunder. Consequently, children develop their own naïve explanations largely based upon their experiences with phenomena encountered every day. When new information does not support existing conceptions,…
DEFF Research Database (Denmark)
Grund, Cynthia M.
2015-01-01
Two, I propose that this framework allows for at least a theoretical distinction between the way in which extreme metal – e.g. black metal, doom metal, funeral doom metal, death metal – relates to its sound as music and the way in which much other music may be conceived of as being constituted...
CERN. Geneva
2013-01-01
Sound Scultor, Bill Fontana, the second winner of the Prix Ars Electronica Collide@CERN residency award, and his science inspiration partner, CERN cosmologist Subodh Patil, present their work in art and science at the CERN Globe of Science and Innovation on 4 July 2013 at 19:00.
DEFF Research Database (Denmark)
Groth, Sanne Krogh; Samson, Kristine
2013-01-01
. The article concludes that the ways in which recent sound installations work with urban ecologies vary. While two of the examples blend into the urban environment, the other transfers the concert format and its mode of listening to urban space. Last, and in accordance with recent soundscape research, we point...
Mang, Andreas; Biros, George
2017-01-01
We propose an efficient numerical algorithm for the solution of diffeomorphic image registration problems. We use a variational formulation constrained by a partial differential equation (PDE), where the constraints are a scalar transport equation. We use a pseudospectral discretization in space and second-order accurate semi-Lagrangian time stepping scheme for the transport equations. We solve for a stationary velocity field using a preconditioned, globalized, matrix-free Newton-Krylov scheme. We propose and test a two-level Hessian preconditioner. We consider two strategies for inverting the preconditioner on the coarse grid: a nested preconditioned conjugate gradient method (exact solve) and a nested Chebyshev iterative method (inexact solve) with a fixed number of iterations. We test the performance of our solver in different synthetic and real-world two-dimensional application scenarios. We study grid convergence and computational efficiency of our new scheme. We compare the performance of our solver against our initial implementation that uses the same spatial discretization but a standard, explicit, second-order Runge-Kutta scheme for the numerical time integration of the transport equations and a single-level preconditioner. Our improved scheme delivers significant speedups over our original implementation. As a highlight, we observe a 20 × speedup for a two dimensional, real world multi-subject medical image registration problem.
Gurnett, D. A.
2005-12-01
Starting in the early 1960s, spacecraft-borne plasma wave instruments revealed that space is filled with an astonishing variety of radio and plasma wave sounds, which have come to be called "sounds of space." For over forty years these sounds have been collected and played to a wide variety of audiences, often as the result of press conferences or press releases involving various NASA projects for which the University of Iowa has provided plasma wave instruments. This activity has led to many interviews on local and national radio programs, and occasionally on programs haviang world-wide coverage, such as the BBC. As a result of this media coverage, we have been approached many times by composers requesting copies of our space sounds for use in their various projects, many of which involve electronic synthesis of music. One of these collaborations led to "Sun Rings," which is a musical event produced by the Kronos Quartet that has played to large audiences all over the world. With the availability of modern computer graphic techniques we have recently been attempting to integrate some of these sound of space into an educational audio/video web site that illustrates the scientific principles involved in the origin of space plasma waves. Typically I try to emphasize that a substantial gas pressure exists everywhere in space in the form of an ionized gas called a plasma, and that this plasma can lead to a wide variety of wave phenomenon. Examples of some of this audio/video material will be presented.
"I'm Not Very Good at Solving Problems": An Exploration of Students' Problem Solving Behaviours
Muir, Tracey; Beswick, Kim; Williamson, John
2008-01-01
This paper reports one aspect of a larger study which looked at the strategies used by a selection of grade 6 students to solve six non-routine mathematical problems. The data revealed that the students exhibited many of the behaviours identified in the literature as being associated with novice and expert problem solvers. However, the categories…
Parameterizing Sound: Design Considerations for an Environmental Sound Database
2015-04-01
associated with, or produced by, a physical event or human activity and 2) sound sources that are common in the environment. Reproductions or sound...Rogers S. Confrontation naming of environmental sounds. Journal of Clinical and Experimental Neuropsychology . 2000;22(6):830–864. 14 VanDerveer NJ
Spatial resolution limits for the localization of noise sources using direct sound mapping
DEFF Research Database (Denmark)
Comesana, D. Fernandez; Holland, K. R.; Fernandez Grande, Efren
2016-01-01
the relationship between spatial resolution, noise level and geometry. The proposed expressions are validated via simulations and experiments. It is shown that particle velocity mapping yields better results for identifying closely spaced sound sources than sound pressure or sound intensity, especially...... extensively been used for many years to locate sound sources. However, it is not yet well defined when two sources should be regarded as resolved by means of direct sound mapping. This paper derives the limits of the direct representation of sound pressure, particle velocity and sound intensity by exploring......One of the main challenges arising from noise and vibration problems is how to identify the areas of a device, machine or structure that produce significant acoustic excitation, i.e. the localization of main noise sources. The direct visualization of sound, in particular sound intensity, has...
Mississippi Sound Remote Sensing Study
Atwell, B. H.
1973-01-01
The Mississippi Sound Remote Sensing Study was initiated as part of the research program of the NASA Earth Resources Laboratory. The objective of this study is development of remote sensing techniques to study near-shore marine waters. Included within this general objective are the following: (1) evaluate existing techniques and instruments used for remote measurement of parameters of interest within these waters; (2) develop methods for interpretation of state-of-the-art remote sensing data which are most meaningful to an understanding of processes taking place within near-shore waters; (3) define hardware development requirements and/or system specifications; (4) develop a system combining data from remote and surface measurements which will most efficiently assess conditions in near-shore waters; (5) conduct projects in coordination with appropriate operating agencies to demonstrate applicability of this research to environmental and economic problems.
An efficient direct solver for rarefied gas flows with arbitrary statistics
International Nuclear Information System (INIS)
Diaz, Manuel A.; Yang, Jaw-Yen
2016-01-01
A new numerical methodology associated with a unified treatment is presented to solve the Boltzmann–BGK equation of gas dynamics for the classical and quantum gases described by the Bose–Einstein and Fermi–Dirac statistics. Utilizing a class of globally-stiffly-accurate implicit–explicit Runge–Kutta scheme for the temporal evolution, associated with the discrete ordinate method for the quadratures in the momentum space and the weighted essentially non-oscillatory method for the spatial discretization, the proposed scheme is asymptotic-preserving and imposes no non-linear solver or requires the knowledge of fugacity and temperature to capture the flow structures in the hydrodynamic (Euler) limit. The proposed treatment overcomes the limitations found in the work by Yang and Muljadi (2011) [33] due to the non-linear nature of quantum relations, and can be applied in studying the dynamics of a gas with internal degrees of freedom with correct values of the ratio of specific heat for the flow regimes for all Knudsen numbers and energy wave lengths. The present methodology is numerically validated with the unified treatment by the one-dimensional shock tube problem and the two-dimensional Riemann problems for gases of arbitrary statistics. Descriptions of ideal quantum gases including rotational degrees of freedom have been successfully achieved under the proposed methodology.
A Closed Loop Inverse Kinematics Solver Intended for Offline Calculation Optimized with GA
Directory of Open Access Journals (Sweden)
Emil Dale Bjoerlykhaug
2018-01-01
Full Text Available This paper presents a simple approach to building a robotic control system. Instead of a conventional control system which solves the inverse kinematics in real-time as the robot moves, an alternative approach where the inverse kinematics is calculated ahead of time is presented. This approach reduces the complexity and code necessary for the control system. Robot control systems are usually implemented in low level programming language. This new approach enables the use of high level programming for the complex inverse kinematics problem. For our approach, we implement a program to solve the inverse kinematics, called the Inverse Kinematics Solver (IKS, in Java, with a simple graphical user interface (GUI to load a file with desired end effector poses and edit the configuration of the robot using the Denavit-Hartenberg (DH convention. The program uses the closed-loop inverse kinematics (CLIK algorithm to solve the inverse kinematics problem. As an example, the IKS was set up to solve the kinematics for a custom built serial link robot. The kinematics for the custom robot is presented, and an example of input and output files is also presented. Additionally, the gain of the loop in the IKS is optimized using a GA, resulting in almost a 50% decrease in computational time.
Scalable Nonlinear Solvers for Fully Implicit Coupled Nuclear Fuel Modeling. Final Report
International Nuclear Information System (INIS)
Cai, Xiao-Chuan; Yang, Chao; Pernice, Michael
2014-01-01
The focus of the project is on the development and customization of some highly scalable domain decomposition based preconditioning techniques for the numerical solution of nonlinear, coupled systems of partial differential equations (PDEs) arising from nuclear fuel simulations. These high-order PDEs represent multiple interacting physical fields (for example, heat conduction, oxygen transport, solid deformation), each is modeled by a certain type of Cahn-Hilliard and/or Allen-Cahn equations. Most existing approaches involve a careful splitting of the fields and the use of field-by-field iterations to obtain a solution of the coupled problem. Such approaches have many advantages such as ease of implementation since only single field solvers are needed, but also exhibit disadvantages. For example, certain nonlinear interactions between the fields may not be fully captured, and for unsteady problems, stable time integration schemes are difficult to design. In addition, when implemented on large scale parallel computers, the sequential nature of the field-by-field iterations substantially reduces the parallel efficiency. To overcome the disadvantages, fully coupled approaches have been investigated in order to obtain full physics simulations.