Mimetic finite difference method
Lipnikov, Konstantin; Manzini, Gianmarco; Shashkov, Mikhail
2014-01-01
The mimetic finite difference (MFD) method mimics fundamental properties of mathematical and physical systems including conservation laws, symmetry and positivity of solutions, duality and self-adjointness of differential operators, and exact mathematical identities of the vector and tensor calculus. This article is the first comprehensive review of the 50-year long history of the mimetic methodology and describes in a systematic way the major mimetic ideas and their relevance to academic and real-life problems. The supporting applications include diffusion, electromagnetics, fluid flow, and Lagrangian hydrodynamics problems. The article provides enough details to build various discrete operators on unstructured polygonal and polyhedral meshes and summarizes the major convergence results for the mimetic approximations. Most of these theoretical results, which are presented here as lemmas, propositions and theorems, are either original or an extension of existing results to a more general formulation using polyhedral meshes. Finally, flexibility and extensibility of the mimetic methodology are shown by deriving higher-order approximations, enforcing discrete maximum principles for diffusion problems, and ensuring the numerical stability for saddle-point systems.
Implicit and fully implicit exponential finite difference methods
Indian Academy of Sciences (India)
Burgers' equation; exponential finite difference method; implicit exponential finite difference method; ... This paper describes two new techniques which give improved exponential finite difference solutions of Burgers' equation. ... Current Issue
Hybrid finite difference/finite element immersed boundary method.
E Griffith, Boyce; Luo, Xiaoyu
2017-12-01
The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and even now, most immersed boundary methods still require Lagrangian meshes that are finer than the Eulerian grid. This work introduces a coupling scheme for the immersed boundary method to link the Lagrangian and Eulerian variables that facilitates independent spatial discretizations for the structure and background grid. This approach uses a finite element discretization of the structure while retaining a finite difference scheme for the Eulerian variables. We apply this method to benchmark problems involving elastic, rigid, and actively contracting structures, including an idealized model of the left ventricle of the heart. Our tests include cases in which, for a fixed Eulerian grid spacing, coarser Lagrangian structural meshes yield discretization errors that are as much as several orders of magnitude smaller than errors obtained using finer structural meshes. The Lagrangian-Eulerian coupling approach developed in this work enables the effective use of these coarse structural meshes with the immersed boundary method. This work also contrasts two different weak forms of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations facilitated by our coupling approach. © 2017 The Authors International Journal for Numerical Methods in Biomedical Engineering Published by John Wiley & Sons Ltd.
Finite element and finite difference methods in electromagnetic scattering
Morgan, MA
2013-01-01
This second volume in the Progress in Electromagnetic Research series examines recent advances in computational electromagnetics, with emphasis on scattering, as brought about by new formulations and algorithms which use finite element or finite difference techniques. Containing contributions by some of the world's leading experts, the papers thoroughly review and analyze this rapidly evolving area of computational electromagnetics. Covering topics ranging from the new finite-element based formulation for representing time-harmonic vector fields in 3-D inhomogeneous media using two coupled sca
Abstract Level Parallelization of Finite Difference Methods
Directory of Open Access Journals (Sweden)
Edwin Vollebregt
1997-01-01
Full Text Available A formalism is proposed for describing finite difference calculations in an abstract way. The formalism consists of index sets and stencils, for characterizing the structure of sets of data items and interactions between data items (“neighbouring relations”. The formalism provides a means for lifting programming to a more abstract level. This simplifies the tasks of performance analysis and verification of correctness, and opens the way for automaticcode generation. The notation is particularly useful in parallelization, for the systematic construction of parallel programs in a process/channel programming paradigm (e.g., message passing. This is important because message passing, unfortunately, still is the only approach that leads to acceptable performance for many more unstructured or irregular problems on parallel computers that have non-uniform memory access times. It will be shown that the use of index sets and stencils greatly simplifies the determination of which data must be exchanged between different computing processes.
Energy Technology Data Exchange (ETDEWEB)
Kim, S. [Purdue Univ., West Lafayette, IN (United States)
1994-12-31
Parallel iterative procedures based on domain decomposition techniques are defined and analyzed for the numerical solution of wave propagation by finite element and finite difference methods. For finite element methods, in a Lagrangian framework, an efficient way for choosing the algorithm parameter as well as the algorithm convergence are indicated. Some heuristic arguments for finding the algorithm parameter for finite difference schemes are addressed. Numerical results are presented to indicate the effectiveness of the methods.
Comparison of different precondtioners for nonsymmtric finite volume element methods
Energy Technology Data Exchange (ETDEWEB)
Mishev, I.D.
1996-12-31
We consider a few different preconditioners for the linear systems arising from the discretization of 3-D convection-diffusion problems with the finite volume element method. Their theoretical and computational convergence rates are compared and discussed.
Evaluation of Callable Bonds: Finite Difference Methods, Stability and Accuracy.
Buttler, Hans-Jurg
1995-01-01
The purpose of this paper is to evaluate numerically the semi-American callable bond by means of finite difference methods. This study implies three results. First, the numerical error is greater for the callable bond price than for the straight bond price, and too large for real applications Secondly, the numerical accuracy of the callable bond price computed for the relevant range of interest rates depends entirely on the finite difference scheme which is chosen for the boundary points. Thi...
Nonstandard Finite Difference Method Applied to a Linear Pharmacokinetics Model
Directory of Open Access Journals (Sweden)
Oluwaseun Egbelowo
2017-05-01
Full Text Available We extend the nonstandard finite difference method of solution to the study of pharmacokinetic–pharmacodynamic models. Pharmacokinetic (PK models are commonly used to predict drug concentrations that drive controlled intravenous (I.V. transfers (or infusion and oral transfers while pharmacokinetic and pharmacodynamic (PD interaction models are used to provide predictions of drug concentrations affecting the response of these clinical drugs. We structure a nonstandard finite difference (NSFD scheme for the relevant system of equations which models this pharamcokinetic process. We compare the results obtained to standard methods. The scheme is dynamically consistent and reliable in replicating complex dynamic properties of the relevant continuous models for varying step sizes. This study provides assistance in understanding the long-term behavior of the drug in the system, and validation of the efficiency of the nonstandard finite difference scheme as the method of choice.
Chebyshev Finite Difference Method for Fractional Boundary Value Problems
Directory of Open Access Journals (Sweden)
Boundary
2015-09-01
Full Text Available This paper presents a numerical method for fractional differential equations using Chebyshev finite difference method. The fractional derivatives are described in the Caputo sense. Numerical results show that this method is of high accuracy and is more convenient and efficient for solving boundary value problems involving fractional ordinary differential equations. AMS Subject Classification: 34A08 Keywords and Phrases: Chebyshev polynomials, Gauss-Lobatto points, fractional differential equation, finite difference 1. Introduction The idea of a derivative which interpolates between the familiar integer order derivatives was introduced many years ago and has gained increasing importance only in recent years due to the development of mathematical models of a certain situations in engineering, materials science, control theory, polymer modelling etc. For example see [20, 22, 25, 26]. Most fractional order differential equations describing real life situations, in general do not have exact analytical solutions. Several numerical and approximate analytical methods for ordinary differential equation Received: December 2014; Accepted: March 2015 57 Journal of Mathematical Extension Vol. 9, No. 3, (2015, 57-71 ISSN: 1735-8299 URL: http://www.ijmex.com Chebyshev Finite Difference Method for Fractional Boundary Value Problems H. Azizi Taft Branch, Islamic Azad University Abstract. This paper presents a numerical method for fractional differential equations using Chebyshev finite difference method. The fractional derivative
The mimetic finite difference method for elliptic problems
Veiga, Lourenço Beirão; Manzini, Gianmarco
2014-01-01
This book describes the theoretical and computational aspects of the mimetic finite difference method for a wide class of multidimensional elliptic problems, which includes diffusion, advection-diffusion, Stokes, elasticity, magnetostatics and plate bending problems. The modern mimetic discretization technology developed in part by the Authors allows one to solve these equations on unstructured polygonal, polyhedral and generalized polyhedral meshes. The book provides a practical guide for those scientists and engineers that are interested in the computational properties of the mimetic finite difference method such as the accuracy, stability, robustness, and efficiency. Many examples are provided to help the reader to understand and implement this method. This monograph also provides the essential background material and describes basic mathematical tools required to develop further the mimetic discretization technology and to extend it to various applications.
Explicit Finite Difference Methods for the Delay Pseudoparabolic Equations
Directory of Open Access Journals (Sweden)
I. Amirali
2014-01-01
Full Text Available Finite difference technique is applied to numerical solution of the initial-boundary value problem for the semilinear delay Sobolev or pseudoparabolic equation. By the method of integral identities two-level difference scheme is constructed. For the time integration the implicit rule is being used. Based on the method of energy estimates the fully discrete scheme is shown to be absolutely stable and convergent of order two in space and of order one in time. The error estimates are obtained in the discrete norm. Some numerical results confirming the expected behavior of the method are shown.
Finite-Difference Frequency-Domain Method in Nanophotonics
DEFF Research Database (Denmark)
Ivinskaya, Aliaksandra
Optics and photonics are exciting, rapidly developing fields building their success largely on use of more and more elaborate artificially made, nanostructured materials. To further advance our understanding of light-matter interactions in these complicated artificial media, numerical modeling...... is often indispensable. This thesis presents the development of rigorous finite-difference method, a very general tool to solve Maxwell’s equations in arbitrary geometries in three dimensions, with an emphasis on the frequency-domain formulation. Enhanced performance of the perfectly matched layers...... is obtained through free space squeezing technique, and nonuniform orthogonal grids are built to greatly improve the accuracy of simulations of highly heterogeneous nanostructures. Examples of the use of the finite-difference frequency-domain method in this thesis range from simulating localized modes...
Temperature Calculation of Annular Fuel Pellet by Finite Difference Method
Energy Technology Data Exchange (ETDEWEB)
Yang, Yong Sik; Bang, Je Geon; Kim, Dae Ho; Kim, Sun Ki; Lim, Ik Sung; Song, Kun Woo [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2009-10-15
KAERI has started an innovative fuel development project for applying dual-cooled annular fuel to existing PWR reactor. In fuel design, fuel temperature is the most important factor which can affect nuclear fuel integrity and safety. Many models and methodologies, which can calculate temperature distribution in a fuel pellet have been proposed. However, due to the geometrical characteristics and cooling condition differences between existing solid type fuel and dual-cooled annular fuel, current fuel temperature calculation models can not be applied directly. Therefore, the new heat conduction model of fuel pellet was established. In general, fuel pellet temperature is calculated by FDM(Finite Difference Method) or FEM(Finite Element Method), because, temperature dependency of fuel thermal conductivity and spatial dependency heat generation in the pellet due to the self-shielding should be considered. In our study, FDM is adopted due to high exactness and short calculation time.
International Nuclear Information System (INIS)
Ackroyd, R.T.
1987-01-01
A least squares principle is described which uses a penalty function treatment of boundary and interface conditions. Appropriate choices of the trial functions and vectors employed in a dual representation of an approximate solution established complementary principles for the diffusion equation. A geometrical interpretation of the principles provides weighted residual methods for diffusion theory, thus establishing a unification of least squares, variational and weighted residual methods. The complementary principles are used with either a trial function for the flux or a trial vector for the current to establish for regular meshes a connection between finite element, finite difference and nodal methods, which can be exact if the mesh pitches are chosen appropriately. Whereas the coefficients in the usual nodal equations have to be determined iteratively, those derived via the complementary principles are given explicitly in terms of the data. For the further development of the connection between finite element, finite difference and nodal methods, some hybrid variational methods are described which employ both a trial function and a trial vector. (author)
Computational electrodynamics the finite-difference time-domain method
Taflove, Allen
2005-01-01
This extensively revised and expanded third edition of the Artech House bestseller, Computational Electrodynamics: The Finite-Difference Time-Domain Method, offers engineers the most up-to-date and definitive resource on this critical method for solving Maxwell's equations. The method helps practitioners design antennas, wireless communications devices, high-speed digital and microwave circuits, and integrated optical devices with unsurpassed efficiency. There has been considerable advancement in FDTD computational technology over the past few years, and the third edition brings professionals the very latest details with entirely new chapters on important techniques, major updates on key topics, and new discussions on emerging areas such as nanophotonics. What's more, to supplement the third edition, the authors have created a Web site with solutions to problems, downloadable graphics and videos, and updates, making this new edition the ideal textbook on the subject as well.
A parallel finite-difference method for computational aerodynamics
International Nuclear Information System (INIS)
Swisshelm, J.M.
1989-01-01
A finite-difference scheme for solving complex three-dimensional aerodynamic flow on parallel-processing supercomputers is presented. The method consists of a basic flow solver with multigrid convergence acceleration, embedded grid refinements, and a zonal equation scheme. Multitasking and vectorization have been incorporated into the algorithm. Results obtained include multiprocessed flow simulations from the Cray X-MP and Cray-2. Speedups as high as 3.3 for the two-dimensional case and 3.5 for segments of the three-dimensional case have been achieved on the Cray-2. The entire solver attained a factor of 2.7 improvement over its unitasked version on the Cray-2. The performance of the parallel algorithm on each machine is analyzed. 14 refs
Modeling of NiTiHf using finite difference method
Farjam, Nazanin; Mehrabi, Reza; Karaca, Haluk; Mirzaeifar, Reza; Elahinia, Mohammad
2018-03-01
NiTiHf is a high temperature and high strength shape memory alloy with transformation temperatures above 100oC. A constitutive model based on Gibbs free energy is developed to predict the behavior of this material. Two different irrecoverable strains including transformation induced plastic strain (TRIP) and viscoplastic strain (VP) are considered when using high temperature shape memory alloys (HTSMAs). The first one happens during transformation at high levels of stress and the second one is related to the creep which is rate-dependent. The developed model is implemented for NiTiHf under uniaxial loading. Finite difference method is utilized to solve the proposed equations. The material parameters in the equations are calibrated from experimental data. Simulation results are captured to investigate the superelastic behavior of NiTiHf. The extracted results are compared with experimental tests of isobaric heating and cooling at different levels of stress and also superelastic tests at different levels of temperature. More results are generated to investigate the capability of the proposed model in the prediction of the irrecoverable strain after full transformation in HTSMAs.
High-order finite-difference methods for Poisson's equation
van Linde, Hendrik Jan
1971-01-01
In this thesis finite-difference approximations to the three boundary value problems for Poisson’s equation are given, with discretization errors of O(H^3) for the mixed boundary value problem, O(H^3 |ln(h)| for the Neumann problem and O(H^4)for the Dirichlet problem respectively . First an operator
A finite difference method for free boundary problems
Fornberg, Bengt
2010-01-01
Fornberg and Meyer-Spasche proposed some time ago a simple strategy to correct finite difference schemes in the presence of a free boundary that cuts across a Cartesian grid. We show here how this procedure can be combined with a minimax
A finite-difference contrast source inversion method
International Nuclear Information System (INIS)
Abubakar, A; Hu, W; Habashy, T M; Van den Berg, P M
2008-01-01
We present a contrast source inversion (CSI) algorithm using a finite-difference (FD) approach as its backbone for reconstructing the unknown material properties of inhomogeneous objects embedded in a known inhomogeneous background medium. Unlike the CSI method using the integral equation (IE) approach, the FD-CSI method can readily employ an arbitrary inhomogeneous medium as its background. The ability to use an inhomogeneous background medium has made this algorithm very suitable to be used in through-wall imaging and time-lapse inversion applications. Similar to the IE-CSI algorithm the unknown contrast sources and contrast function are updated alternately to reconstruct the unknown objects without requiring the solution of the full forward problem at each iteration step in the optimization process. The FD solver is formulated in the frequency domain and it is equipped with a perfectly matched layer (PML) absorbing boundary condition. The FD operator used in the FD-CSI method is only dependent on the background medium and the frequency of operation, thus it does not change throughout the inversion process. Therefore, at least for the two-dimensional (2D) configurations, where the size of the stiffness matrix is manageable, the FD stiffness matrix can be inverted using a non-iterative inversion matrix approach such as a Gauss elimination method for the sparse matrix. In this case, an LU decomposition needs to be done only once and can then be reused for multiple source positions and in successive iterations of the inversion. Numerical experiments show that this FD-CSI algorithm has an excellent performance for inverting inhomogeneous objects embedded in an inhomogeneous background medium
A finite difference method for free boundary problems
Fornberg, Bengt
2010-04-01
Fornberg and Meyer-Spasche proposed some time ago a simple strategy to correct finite difference schemes in the presence of a free boundary that cuts across a Cartesian grid. We show here how this procedure can be combined with a minimax-based optimization procedure to rapidly solve a wide range of elliptic-type free boundary value problems. © 2009 Elsevier B.V. All rights reserved.
International Nuclear Information System (INIS)
Shtromberger, N.L.
1989-01-01
To design a cyclotron magnetic system the legitimacy of two-dimensional approximations application is discussed. In all the calculations the finite difference method is used, and the linearization method with further use of the gradient conjugation method is used to solve the set of finite-difference equations. 3 refs.; 5 figs
Mesh-size errors in diffusion-theory calculations using finite-difference and finite-element methods
International Nuclear Information System (INIS)
Baker, A.R.
1982-07-01
A study has been performed of mesh-size errors in diffusion-theory calculations using finite-difference and finite-element methods. As the objective was to illuminate the issues, the study was performed for a 1D slab model of a reactor with one neutron-energy group for which analytical solutions were possible. A computer code SLAB was specially written to perform the finite-difference and finite-element calculations and also to obtain the analytical solutions. The standard finite-difference equations were obtained by starting with an expansion of the neutron current in powers of the mesh size, h, and keeping terms as far as h 2 . It was confirmed that these equations led to the well-known result that the criticality parameter varied with the square of the mesh size. An improved form of the finite-difference equations was obtained by continuing the expansion for the neutron current as far as the term in h 4 . In this case, the critical parameter varied as the fourth power of the mesh size. The finite-element solutions for 2 and 3 nodes per element revealed that the criticality parameter varied as the square and fourth power of the mesh size, respectively. Numerical results are presented for a bare reactive core of uniform composition with 2 zones of different uniform mesh and for a reactive core with an absorptive reflector. (author)
Panczak, Tim; Ring, Steve; Welch, Mark
1999-01-01
Thermal engineering has long been left out of the concurrent engineering environment dominated by CAD (computer aided design) and FEM (finite element method) software. Current tools attempt to force the thermal design process into an environment primarily created to support structural analysis, which results in inappropriate thermal models. As a result, many thermal engineers either build models "by hand" or use geometric user interfaces that are separate from and have little useful connection, if any, to CAD and FEM systems. This paper describes the development of a new thermal design environment called the Thermal Desktop. This system, while fully integrated into a neutral, low cost CAD system, and which utilizes both FEM and FD methods, does not compromise the needs of the thermal engineer. Rather, the features needed for concurrent thermal analysis are specifically addressed by combining traditional parametric surface based radiation and FD based conduction modeling with CAD and FEM methods. The use of flexible and familiar temperature solvers such as SINDA/FLUINT (Systems Improved Numerical Differencing Analyzer/Fluid Integrator) is retained.
Perfectly Matched Layer for the Wave Equation Finite Difference Time Domain Method
Miyazaki, Yutaka; Tsuchiya, Takao
2012-07-01
The perfectly matched layer (PML) is introduced into the wave equation finite difference time domain (WE-FDTD) method. The WE-FDTD method is a finite difference method in which the wave equation is directly discretized on the basis of the central differences. The required memory of the WE-FDTD method is less than that of the standard FDTD method because no particle velocity is stored in the memory. In this study, the WE-FDTD method is first combined with the standard FDTD method. Then, Berenger's PML is combined with the WE-FDTD method. Some numerical demonstrations are given for the two- and three-dimensional sound fields.
Chu, Chunlei; Stoffa, Paul L.
2012-01-01
sampled models onto vertically nonuniform grids. We use a 2D TTI salt model to demonstrate its effectiveness and show that the nonuniform grid implicit spatial finite difference method can produce highly accurate seismic modeling results with enhanced
Stability and non-standard finite difference method of the generalized Chua's circuit
Radwan, Ahmed G.; Moaddy, K.; Momani, Shaher M.
2011-01-01
In this paper, we develop a framework to obtain approximate numerical solutions of the fractional-order Chua's circuit with Memristor using a non-standard finite difference method. Chaotic response is obtained with fractional-order elements as well
ORIGINAL ARTICLE Fitted-Stable Finite Difference Method for ...
African Journals Online (AJOL)
Gemechis
two point boundary value problems with the boundary layer at one end (left or right) ... scheme (SCD Method) and its value is obtained using the theory of singular ..... Eq. (15) at the point. N iih xxi. , ,2 ,1 ,0 ,.. = = = and taking the limit as. 0. →.
Gao, Longfei
2018-02-22
We consider numerical simulation of the isotropic elastic wave equations arising from seismic applications with non-trivial land topography. The more flexible finite element method is applied to the shallow region of the simulation domain to account for the topography, and combined with the more efficient finite difference method that is applied to the deep region of the simulation domain. We demonstrate that these two discretization methods, albeit starting from different formulations of the elastic wave equation, can be joined together smoothly via weakly imposed interface conditions. Discrete energy analysis is employed to derive the proper interface treatment, leading to an overall discretization that is energy-conserving. Numerical examples are presented to demonstrate the efficacy of the proposed interface treatment.
Gao, Longfei; Keyes, David E.
2018-01-01
We consider numerical simulation of the isotropic elastic wave equations arising from seismic applications with non-trivial land topography. The more flexible finite element method is applied to the shallow region of the simulation domain to account for the topography, and combined with the more efficient finite difference method that is applied to the deep region of the simulation domain. We demonstrate that these two discretization methods, albeit starting from different formulations of the elastic wave equation, can be joined together smoothly via weakly imposed interface conditions. Discrete energy analysis is employed to derive the proper interface treatment, leading to an overall discretization that is energy-conserving. Numerical examples are presented to demonstrate the efficacy of the proposed interface treatment.
A new fitted operator finite difference method to solve systems of ...
African Journals Online (AJOL)
In recent years, fitted operator finite difference methods (FOFDMs) have been developed for numerous types of singularly perturbed ordinary differential equations. The construction of most of these methods differed though the final outcome remained similar. The most crucial aspect was how the difference operator was ...
Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics
Gedney, Stephen
2011-01-01
Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics provides a comprehensive tutorial of the most widely used method for solving Maxwell's equations -- the Finite Difference Time-Domain Method. This book is an essential guide for students, researchers, and professional engineers who want to gain a fundamental knowledge of the FDTD method. It can accompany an undergraduate or entry-level graduate course or be used for self-study. The book provides all the background required to either research or apply the FDTD method for the solution of Maxwell's equations to p
A coarse-mesh nodal method-diffusive-mesh finite difference method
International Nuclear Information System (INIS)
Joo, H.; Nichols, W.R.
1994-01-01
Modern nodal methods have been successfully used for conventional light water reactor core analyses where the homogenized, node average cross sections (XSs) and the flux discontinuity factors (DFs) based on equivalence theory can reliably predict core behavior. For other types of cores and other geometries characterized by tightly-coupled, heterogeneous core configurations, the intranodal flux shapes obtained from a homogenized nodal problem may not accurately portray steep flux gradients near fuel assembly interfaces or various reactivity control elements. This may require extreme values of DFs (either very large, very small, or even negative) to achieve a desired solution accuracy. Extreme values of DFs, however, can disrupt the convergence of the iterative methods used to solve for the node average fluxes, and can lead to a difficulty in interpolating adjacent DF values. Several attempts to remedy the problem have been made, but nothing has been satisfactory. A new coarse-mesh nodal scheme called the Diffusive-Mesh Finite Difference (DMFD) technique, as contrasted with the coarse-mesh finite difference (CMFD) technique, has been developed to resolve this problem. This new technique and the development of a few-group, multidimensional kinetics computer program are described in this paper
Wu, Zedong
2018-04-05
Numerical simulation of the acoustic wave equation in either isotropic or anisotropic media is crucial to seismic modeling, imaging and inversion. Actually, it represents the core computation cost of these highly advanced seismic processing methods. However, the conventional finite-difference method suffers from severe numerical dispersion errors and S-wave artifacts when solving the acoustic wave equation for anisotropic media. We propose a method to obtain the finite-difference coefficients by comparing its numerical dispersion with the exact form. We find the optimal finite difference coefficients that share the dispersion characteristics of the exact equation with minimal dispersion error. The method is extended to solve the acoustic wave equation in transversely isotropic (TI) media without S-wave artifacts. Numerical examples show that the method is is highly accurate and efficient.
Analysis of equilibrium in a tokamak by the finite-difference method
International Nuclear Information System (INIS)
Kim, K.E.; Jeun, G.D.
1983-01-01
Ideal magnetohydrodynamic equilibrium in a Tokamak having a small radius with an elongated rectangular cross section is studied by applying the finite-difference method to the Grad-Shafranov equation to determine possible limitations for *b=8*pPsup(2)/Bsup(2). The coupled first-order differential equations resulting from the finite-difference Grad-Shafranov equation is solved by the numarical method:1)We concluded that equilibrium consideration alone gives no limitation even for *b approx.1. 2)We have obtained the equilibrium magnetic field configuration charcterized by a set of three parameters;the aspect ratio, *b,and the safety factor. (Author)
Relative and Absolute Error Control in a Finite-Difference Method Solution of Poisson's Equation
Prentice, J. S. C.
2012-01-01
An algorithm for error control (absolute and relative) in the five-point finite-difference method applied to Poisson's equation is described. The algorithm is based on discretization of the domain of the problem by means of three rectilinear grids, each of different resolution. We discuss some hardware limitations associated with the algorithm,…
Directory of Open Access Journals (Sweden)
Lei Wang
2015-09-01
Full Text Available Based on fractal geometry, fractal medium of coalbed methane mathematical model is established by Langmuir isotherm adsorption formula, Fick's diffusion law, Laplace transform formula, considering the well bore storage effect and skin effect. The Laplace transform finite difference method is used to solve the mathematical model. With Stehfest numerical inversion, the distribution of dimensionless well bore flowing pressure and its derivative was obtained in real space. According to compare with the results from the analytical method, the result from Laplace transform finite difference method turns out to be accurate. The influence factors are analyzed, including fractal dimension, fractal index, skin factor, well bore storage coefficient, energy storage ratio, interporosity flow coefficient and the adsorption factor. The calculating error of Laplace transform difference method is small. Laplace transform difference method has advantages in well-test application since any moment simulation does not rely on other moment results and space grid.
The finite-difference time-domain method for electromagnetics with Matlab simulations
Elsherbeni, Atef Z
2016-01-01
This book introduces the powerful Finite-Difference Time-Domain method to students and interested researchers and readers. An effective introduction is accomplished using a step-by-step process that builds competence and confidence in developing complete working codes for the design and analysis of various antennas and microwave devices.
Modeling of Nanophotonic Resonators with the Finite-Difference Frequency-Domain Method
DEFF Research Database (Denmark)
Ivinskaya, Aliaksandra; Lavrinenko, Andrei; Shyroki, Dzmitry
2011-01-01
Finite-difference frequency-domain method with perfectly matched layers and free-space squeezing is applied to model open photonic resonators of arbitrary morphology in three dimensions. Treating each spatial dimension independently, nonuniform mesh of continuously varying density can be built ea...
Five-point form of the nodal diffusion method and comparison with finite-difference
International Nuclear Information System (INIS)
Azmy, Y.Y.
1988-01-01
Nodal Methods have been derived, implemented and numerically tested for several problems in physics and engineering. In the field of nuclear engineering, many nodal formalisms have been used for the neutron diffusion equation, all yielding results which were far more computationally efficient than conventional Finite Difference (FD) and Finite Element (FE) methods. However, not much effort has been devoted to theoretically comparing nodal and FD methods in order to explain the very high accuracy of the former. In this summary we outline the derivation of a simple five-point form for the lowest order nodal method and compare it to the traditional five-point, edge-centered FD scheme. The effect of the observed differences on the accuracy of the respective methods is established by considering a simple test problem. It must be emphasized that the nodal five-point scheme derived here is mathematically equivalent to previously derived lowest order nodal methods. 7 refs., 1 tab
Numerical study of water diffusion in biological tissues using an improved finite difference method
International Nuclear Information System (INIS)
Xu Junzhong; Does, Mark D; Gore, John C
2007-01-01
An improved finite difference (FD) method has been developed in order to calculate the behaviour of the nuclear magnetic resonance signal variations caused by water diffusion in biological tissues more accurately and efficiently. The algorithm converts the conventional image-based finite difference method into a convenient matrix-based approach and includes a revised periodic boundary condition which eliminates the edge effects caused by artificial boundaries in conventional FD methods. Simulated results for some modelled tissues are consistent with analytical solutions for commonly used diffusion-weighted pulse sequences, whereas the improved FD method shows improved efficiency and accuracy. A tightly coupled parallel computing approach was also developed to implement the FD methods to enable large-scale simulations of realistic biological tissues. The potential applications of the improved FD method for understanding diffusion in tissues are also discussed. (note)
Seismic wavefield modeling based on time-domain symplectic and Fourier finite-difference method
Fang, Gang; Ba, Jing; Liu, Xin-xin; Zhu, Kun; Liu, Guo-Chang
2017-06-01
Seismic wavefield modeling is important for improving seismic data processing and interpretation. Calculations of wavefield propagation are sometimes not stable when forward modeling of seismic wave uses large time steps for long times. Based on the Hamiltonian expression of the acoustic wave equation, we propose a structure-preserving method for seismic wavefield modeling by applying the symplectic finite-difference method on time grids and the Fourier finite-difference method on space grids to solve the acoustic wave equation. The proposed method is called the symplectic Fourier finite-difference (symplectic FFD) method, and offers high computational accuracy and improves the computational stability. Using acoustic approximation, we extend the method to anisotropic media. We discuss the calculations in the symplectic FFD method for seismic wavefield modeling of isotropic and anisotropic media, and use the BP salt model and BP TTI model to test the proposed method. The numerical examples suggest that the proposed method can be used in seismic modeling of strongly variable velocities, offering high computational accuracy and low numerical dispersion. The symplectic FFD method overcomes the residual qSV wave of seismic modeling in anisotropic media and maintains the stability of the wavefield propagation for large time steps.
Energy stable and high-order-accurate finite difference methods on staggered grids
O'Reilly, Ossian; Lundquist, Tomas; Dunham, Eric M.; Nordström, Jan
2017-10-01
For wave propagation over distances of many wavelengths, high-order finite difference methods on staggered grids are widely used due to their excellent dispersion properties. However, the enforcement of boundary conditions in a stable manner and treatment of interface problems with discontinuous coefficients usually pose many challenges. In this work, we construct a provably stable and high-order-accurate finite difference method on staggered grids that can be applied to a broad class of boundary and interface problems. The staggered grid difference operators are in summation-by-parts form and when combined with a weak enforcement of the boundary conditions, lead to an energy stable method on multiblock grids. The general applicability of the method is demonstrated by simulating an explosive acoustic source, generating waves reflecting against a free surface and material discontinuity.
Chu, Chunlei
2012-01-01
Discrete earth models are commonly represented by uniform structured grids. In order to ensure accurate numerical description of all wave components propagating through these uniform grids, the grid size must be determined by the slowest velocity of the entire model. Consequently, high velocity areas are always oversampled, which inevitably increases the computational cost. A practical solution to this problem is to use nonuniform grids. We propose a nonuniform grid implicit spatial finite difference method which utilizes nonuniform grids to obtain high efficiency and relies on implicit operators to achieve high accuracy. We present a simple way of deriving implicit finite difference operators of arbitrary stencil widths on general nonuniform grids for the first and second derivatives and, as a demonstration example, apply these operators to the pseudo-acoustic wave equation in tilted transversely isotropic (TTI) media. We propose an efficient gridding algorithm that can be used to convert uniformly sampled models onto vertically nonuniform grids. We use a 2D TTI salt model to demonstrate its effectiveness and show that the nonuniform grid implicit spatial finite difference method can produce highly accurate seismic modeling results with enhanced efficiency, compared to uniform grid explicit finite difference implementations. © 2011 Elsevier B.V.
Stability and non-standard finite difference method of the generalized Chua's circuit
Radwan, Ahmed G.
2011-08-01
In this paper, we develop a framework to obtain approximate numerical solutions of the fractional-order Chua\\'s circuit with Memristor using a non-standard finite difference method. Chaotic response is obtained with fractional-order elements as well as integer-order elements. Stability analysis and the condition of oscillation for the integer-order system are discussed. In addition, the stability analyses for different fractional-order cases are investigated showing a great sensitivity to small order changes indicating the poles\\' locations inside the physical s-plane. The GrnwaldLetnikov method is used to approximate the fractional derivatives. Numerical results are presented graphically and reveal that the non-standard finite difference scheme is an effective and convenient method to solve fractional-order chaotic systems, and to validate their stability. © 2011 Elsevier Ltd. All rights reserved.
A practical implicit finite-difference method: examples from seismic modelling
International Nuclear Information System (INIS)
Liu, Yang; Sen, Mrinal K
2009-01-01
We derive explicit and new implicit finite-difference formulae for derivatives of arbitrary order with any order of accuracy by the plane wave theory where the finite-difference coefficients are obtained from the Taylor series expansion. The implicit finite-difference formulae are derived from fractional expansion of derivatives which form tridiagonal matrix equations. Our results demonstrate that the accuracy of a (2N + 2)th-order implicit formula is nearly equivalent to that of a (6N + 2)th-order explicit formula for the first-order derivative, and (2N + 2)th-order implicit formula is nearly equivalent to (4N + 2)th-order explicit formula for the second-order derivative. In general, an implicit method is computationally more expensive than an explicit method, due to the requirement of solving large matrix equations. However, the new implicit method only involves solving tridiagonal matrix equations, which is fairly inexpensive. Furthermore, taking advantage of the fact that many repeated calculations of derivatives are performed by the same difference formula, several parts can be precomputed resulting in a fast algorithm. We further demonstrate that a (2N + 2)th-order implicit formulation requires nearly the same memory and computation as a (2N + 4)th-order explicit formulation but attains the accuracy achieved by a (6N + 2)th-order explicit formulation for the first-order derivative and that of a (4N + 2)th-order explicit method for the second-order derivative when additional cost of visiting arrays is not considered. This means that a high-order explicit method may be replaced by an implicit method of the same order resulting in a much improved performance. Our analysis of efficiency and numerical modelling results for acoustic and elastic wave propagation validates the effectiveness and practicality of the implicit finite-difference method
On the Stability of the Finite Difference based Lattice Boltzmann Method
El-Amin, Mohamed; Sun, Shuyu; Salama, Amgad
2013-01-01
This paper is devoted to determining the stability conditions for the finite difference based lattice Boltzmann method (FDLBM). In the current scheme, the 9-bit two-dimensional (D2Q9) model is used and the collision term of the Bhatnagar- Gross-Krook (BGK) is treated implicitly. The implicitness of the numerical scheme is removed by introducing a new distribution function different from that being used. Therefore, a new explicit finite-difference lattice Boltzmann method is obtained. Stability analysis of the resulted explicit scheme is done using Fourier expansion. Then, stability conditions in terms of time and spatial steps, relaxation time and explicitly-implicitly parameter are determined by calculating the eigenvalues of the given difference system. The determined conditions give the ranges of the parameters that have stable solutions.
On the Stability of the Finite Difference based Lattice Boltzmann Method
El-Amin, Mohamed
2013-06-01
This paper is devoted to determining the stability conditions for the finite difference based lattice Boltzmann method (FDLBM). In the current scheme, the 9-bit two-dimensional (D2Q9) model is used and the collision term of the Bhatnagar- Gross-Krook (BGK) is treated implicitly. The implicitness of the numerical scheme is removed by introducing a new distribution function different from that being used. Therefore, a new explicit finite-difference lattice Boltzmann method is obtained. Stability analysis of the resulted explicit scheme is done using Fourier expansion. Then, stability conditions in terms of time and spatial steps, relaxation time and explicitly-implicitly parameter are determined by calculating the eigenvalues of the given difference system. The determined conditions give the ranges of the parameters that have stable solutions.
Mimetic finite difference method for the stokes problem on polygonal meshes
Energy Technology Data Exchange (ETDEWEB)
Lipnikov, K [Los Alamos National Laboratory; Beirao Da Veiga, L [DIPARTIMENTO DI MATE; Gyrya, V [PENNSYLVANIA STATE UNIV; Manzini, G [ISTIUTO DI MATEMATICA
2009-01-01
Various approaches to extend the finite element methods to non-traditional elements (pyramids, polyhedra, etc.) have been developed over the last decade. Building of basis functions for such elements is a challenging task and may require extensive geometry analysis. The mimetic finite difference (MFD) method has many similarities with low-order finite element methods. Both methods try to preserve fundamental properties of physical and mathematical models. The essential difference is that the MFD method uses only the surface representation of discrete unknowns to build stiffness and mass matrices. Since no extension inside the mesh element is required, practical implementation of the MFD method is simple for polygonal meshes that may include degenerate and non-convex elements. In this article, we develop a MFD method for the Stokes problem on arbitrary polygonal meshes. The method is constructed for tensor coefficients, which will allow to apply it to the linear elasticity problem. The numerical experiments show the second-order convergence for the velocity variable and the first-order for the pressure.
Wang, Yi
2016-07-21
Velocity of fluid flow in underground porous media is 6~12 orders of magnitudes lower than that in pipelines. If numerical errors are not carefully controlled in this kind of simulations, high distortion of the final results may occur [1-4]. To fit the high accuracy demands of fluid flow simulations in porous media, traditional finite difference methods and numerical integration methods are discussed and corresponding high-accurate methods are developed. When applied to the direct calculation of full-tensor permeability for underground flow, the high-accurate finite difference method is confirmed to have numerical error as low as 10-5% while the high-accurate numerical integration method has numerical error around 0%. Thus, the approach combining the high-accurate finite difference and numerical integration methods is a reliable way to efficiently determine the characteristics of general full-tensor permeability such as maximum and minimum permeability components, principal direction and anisotropic ratio. Copyright © Global-Science Press 2016.
International Nuclear Information System (INIS)
Lee, Byeong Hae
1992-02-01
This book gives descriptions of basic finite element method, which includes basic finite element method and data, black box, writing of data, definition of VECTOR, definition of matrix, matrix and multiplication of matrix, addition of matrix, and unit matrix, conception of hardness matrix like spring power and displacement, governed equation of an elastic body, finite element method, Fortran method and programming such as composition of computer, order of programming and data card and Fortran card, finite element program and application of nonelastic problem.
Implementation of compact finite-difference method to parabolized Navier-Stokes equations
International Nuclear Information System (INIS)
Esfahanian, V.; Hejranfar, K.; Darian, H.M.
2005-01-01
The numerical simulation of the Parabolized Navier-Stokes (PNS) equations for supersonic/hypersonic flow field is obtained by using the fourth-order compact finite-difference method. The PNS equations in the general curvilinear coordinates are solved by using the implicit finite-difference algorithm of Beam and Warming. A shock fitting procedure is utilized to obtain the accurate solution in the vicinity of the shock. The computations are performed for hypersonic axisymmetric flow over a blunt cone. The present results for the flow field along with those of the second-order method are presented and accuracy analysis is performed to insure the fourth-order accuracy of the method. (author)
Agarwal, P.; El-Sayed, A. A.
2018-06-01
In this paper, a new numerical technique for solving the fractional order diffusion equation is introduced. This technique basically depends on the Non-Standard finite difference method (NSFD) and Chebyshev collocation method, where the fractional derivatives are described in terms of the Caputo sense. The Chebyshev collocation method with the (NSFD) method is used to convert the problem into a system of algebraic equations. These equations solved numerically using Newton's iteration method. The applicability, reliability, and efficiency of the presented technique are demonstrated through some given numerical examples.
Elastic frequency-domain finite-difference contrast source inversion method
International Nuclear Information System (INIS)
He, Qinglong; Chen, Yong; Han, Bo; Li, Yang
2016-01-01
In this work, we extend the finite-difference contrast source inversion (FD-CSI) method to the frequency-domain elastic wave equations, where the parameters describing the subsurface structure are simultaneously reconstructed. The FD-CSI method is an iterative nonlinear inversion method, which exhibits several strengths. First, the finite-difference operator only relies on the background media and the given angular frequency, both of which are unchanged during inversion. Therefore, the matrix decomposition is performed only once at the beginning of the iteration if a direct solver is employed. This makes the inversion process relatively efficient in terms of the computational cost. In addition, the FD-CSI method automatically normalizes different parameters, which could avoid the numerical problems arising from the difference of the parameter magnitude. We exploit a parallel implementation of the FD-CSI method based on the domain decomposition method, ensuring a satisfactory scalability for large-scale problems. A simple numerical example with a homogeneous background medium is used to investigate the convergence of the elastic FD-CSI method. Moreover, the Marmousi II model proposed as a benchmark for testing seismic imaging methods is presented to demonstrate the performance of the elastic FD-CSI method in an inhomogeneous background medium. (paper)
Solving the Schroedinger equation using the finite difference time domain method
International Nuclear Information System (INIS)
Sudiarta, I Wayan; Geldart, D J Wallace
2007-01-01
In this paper, we solve the Schroedinger equation using the finite difference time domain (FDTD) method to determine energies and eigenfunctions. In order to apply the FDTD method, the Schroedinger equation is first transformed into a diffusion equation by the imaginary time transformation. The resulting time-domain diffusion equation is then solved numerically by the FDTD method. The theory and an algorithm are provided for the procedure. Numerical results are given for illustrative examples in one, two and three dimensions. It is shown that the FDTD method accurately determines eigenfunctions and energies of these systems
Directory of Open Access Journals (Sweden)
Xinfeng Ruan
2013-01-01
Full Text Available We study option pricing with risk-minimization criterion in an incomplete market where the dynamics of the risky underlying asset is governed by a jump diffusion equation with stochastic volatility. We obtain the Radon-Nikodym derivative for the minimal martingale measure and a partial integro-differential equation (PIDE of European option. The finite difference method is employed to compute the European option valuation of PIDE.
Research on GPU-accelerated algorithm in 3D finite difference neutron diffusion calculation method
International Nuclear Information System (INIS)
Xu Qi; Yu Ganglin; Wang Kan; Sun Jialong
2014-01-01
In this paper, the adaptability of the neutron diffusion numerical algorithm on GPUs was studied, and a GPU-accelerated multi-group 3D neutron diffusion code based on finite difference method was developed. The IAEA 3D PWR benchmark problem was calculated in the numerical test. The results demonstrate both high efficiency and adequate accuracy of the GPU implementation for neutron diffusion equation. (authors)
Lei Wang; Hongjun Yin; Xiaoshuang Yang; Chuncheng Yang; Jing Fu
2015-01-01
Based on fractal geometry, fractal medium of coalbed methane mathematical model is established by Langmuir isotherm adsorption formula, Fick's diffusion law, Laplace transform formula, considering the well bore storage effect and skin effect. The Laplace transform finite difference method is used to solve the mathematical model. With Stehfest numerical inversion, the distribution of dimensionless well bore flowing pressure and its derivative was obtained in real space. According to compare wi...
Stability analysis of single-phase thermosyphon loops by finite difference numerical methods
International Nuclear Information System (INIS)
Ambrosini, W.
1998-01-01
In this paper, examples of the application of finite difference numerical methods in the analysis of stability of single-phase natural circulation loops are reported. The problem is here addressed for its relevance for thermal-hydraulic system code applications, in the aim to point out the effect of truncation error on stability prediction. The methodology adopted for analysing in a systematic way the effect of various finite difference discretization can be considered the numerical analogue of the usual techniques adopted for PDE stability analysis. Three different single-phase loop configurations are considered involving various kinds of boundary conditions. In one of these cases, an original dimensionless form of the governing equations is proposed, adopting the Reynolds number as a flow variable. This allows for an appropriate consideration of transition between laminar and turbulent regimes, which is not possible with other dimensionless forms, thus enlarging the field of validity of model assumptions. (author). 14 refs., 8 figs
Analysis of multi lobe journal bearings with surface roughness using finite difference method
PhaniRaja Kumar, K.; Bhaskar, SUdaya; Manzoor Hussain, M.
2018-04-01
Multi lobe journal bearings are used for high operating speeds and high loads in machines. In this paper symmetrical multi lobe journal bearings are analyzed to find out the effect of surface roughnessduring non linear loading. Using the fourth order RungeKutta method, time transient analysis was performed to calculate and plot the journal centre trajectories. Flow factor method is used to evaluate the roughness and the finite difference method (FDM) is used to predict the pressure distribution over the bearing surface. The Transient analysis is done on the multi lobe journal bearings for threedifferent surface roughness orientations. Longitudinal surface roughness is more effective when compared with isotopic and traverse surface roughness.
Modelling migration in multilayer systems by a finite difference method: the spherical symmetry case
International Nuclear Information System (INIS)
Hojbota, C I; Toşa, V; Mercea, P V
2013-01-01
We present a numerical model based on finite differences to solve the problem of chemical impurity migration within a multilayer spherical system. Migration here means diffusion of chemical species in conditions of concentration partitioning at layer interfaces due to different solubilities of the migrant in different layers. We detail here the numerical model and discuss the results of its implementation. To validate the method we compare it with cases where an analytic solution exists. We also present an application of our model to a practical problem in which we compute the migration of caprolactam from the packaging multilayer foil into the food
Finite difference applied to the reconstruction method of the nuclear power density distribution
International Nuclear Information System (INIS)
Pessoa, Paulo O.; Silva, Fernando C.; Martinez, Aquilino S.
2016-01-01
Highlights: • A method for reconstruction of the power density distribution is presented. • The method uses discretization by finite differences of 2D neutrons diffusion equation. • The discretization is performed homogeneous meshes with dimensions of a fuel cell. • The discretization is combined with flux distributions on the four node surfaces. • The maximum errors in reconstruction occur in the peripheral water region. - Abstract: In this reconstruction method the two-dimensional (2D) neutron diffusion equation is discretized by finite differences, employed to two energy groups (2G) and meshes with fuel-pin cell dimensions. The Nodal Expansion Method (NEM) makes use of surface discontinuity factors of the node and provides for reconstruction method the effective multiplication factor of the problem and the four surface average fluxes in homogeneous nodes with size of a fuel assembly (FA). The reconstruction process combines the discretized 2D diffusion equation by finite differences with fluxes distribution on four surfaces of the nodes. These distributions are obtained for each surfaces from a fourth order one-dimensional (1D) polynomial expansion with five coefficients to be determined. The conditions necessary for coefficients determination are three average fluxes on consecutive surfaces of the three nodes and two fluxes in corners between these three surface fluxes. Corner fluxes of the node are determined using a third order 1D polynomial expansion with four coefficients. This reconstruction method uses heterogeneous nuclear parameters directly providing the heterogeneous neutron flux distribution and the detailed nuclear power density distribution within the FAs. The results obtained with this method has good accuracy and efficiency when compared with reference values.
DEFF Research Database (Denmark)
Santillan, Arturo Orozco
2011-01-01
The aim of the work described in this paper has been to investigate the use of the finite-difference time-domain method to describe the interactions between a moving object and a sound field. The main objective was to simulate oscillational instabilities that appear in single-axis acoustic...... levitation devices and to describe their evolution in time to further understand the physical mechanism involved. The study shows that the method gives accurate results for steady state conditions, and that it is a promising tool for simulations with a moving object....
Jinghai, Zhou; Tianbei, Kang; Fengchi, Wang; Xindong, Wang
2017-11-01
Eight less stirrups in the core area frame joints are simulated by ABAQUS finite element numerical software. The composite reinforcement method is strengthened with carbon fiber and increasing column section, the axial compression ratio of reinforced specimens is 0.3, 0.45 and 0.6 respectively. The results of the load-displacement curve, ductility and stiffness are analyzed, and it is found that the different axial compression ratio has great influence on the bearing capacity of increasing column section strengthening method, and has little influence on carbon fiber reinforcement method. The different strengthening schemes improve the ultimate bearing capacity and ductility of frame joints in a certain extent, composite reinforcement joints strengthening method to improve the most significant, followed by increasing column section, reinforcement method of carbon fiber reinforced joints to increase the minimum.
A mimetic finite difference method for the Stokes problem with elected edge bubbles
Energy Technology Data Exchange (ETDEWEB)
Lipnikov, K [Los Alamos National Laboratory; Berirao, L [DIPARTMENTO DI MATERMATICA
2009-01-01
A new mimetic finite difference method for the Stokes problem is proposed and analyzed. The unstable P{sub 1}-P{sub 0} discretization is stabilized by adding a small number of bubble functions to selected mesh edges. A simple strategy for selecting such edges is proposed and verified with numerical experiments. The discretizations schemes for Stokes and Navier-Stokes equations must satisfy the celebrated inf-sup (or the LBB) stability condition. The stability condition implies a balance between discrete spaces for velocity and pressure. In finite elements, this balance is frequently achieved by adding bubble functions to the velocity space. The goal of this article is to show that the stabilizing edge bubble functions can be added only to a small set of mesh edges. This results in a smaller algebraic system and potentially in a faster calculations. We employ the mimetic finite difference (MFD) discretization technique that works for general polyhedral meshes and can accomodate non-uniform distribution of stabilizing bubbles.
A study of unstable rock failures using finite difference and discrete element methods
Garvey, Ryan J.
Case histories in mining have long described pillars or faces of rock failing violently with an accompanying rapid ejection of debris and broken material into the working areas of the mine. These unstable failures have resulted in large losses of life and collapses of entire mine panels. Modern mining operations take significant steps to reduce the likelihood of unstable failure, however eliminating their occurrence is difficult in practice. Researchers over several decades have supplemented studies of unstable failures through the application of various numerical methods. The direction of the current research is to extend these methods and to develop improved numerical tools with which to study unstable failures in underground mining layouts. An extensive study is first conducted on the expression of unstable failure in discrete element and finite difference methods. Simulated uniaxial compressive strength tests are run on brittle rock specimens. Stable or unstable loading conditions are applied onto the brittle specimens by a pair of elastic platens with ranging stiffnesses. Determinations of instability are established through stress and strain histories taken for the specimen and the system. Additional numerical tools are then developed for the finite difference method to analyze unstable failure in larger mine models. Instability identifiers are established for assessing the locations and relative magnitudes of unstable failure through measures of rapid dynamic motion. An energy balance is developed which calculates the excess energy released as a result of unstable equilibria in rock systems. These tools are validated through uniaxial and triaxial compressive strength tests and are extended to models of coal pillars and a simplified mining layout. The results of the finite difference simulations reveal that the instability identifiers and excess energy calculations provide a generalized methodology for assessing unstable failures within potentially complex
Finite difference method calculations of X-ray absorption fine structure for copper
Energy Technology Data Exchange (ETDEWEB)
Bourke, J.D. [School of Physics, University of Melbourne, Parkville, Vic 3010 (Australia); Chantler, C.T. [School of Physics, University of Melbourne, Parkville, Vic 3010 (Australia)]. E-mail: chantler@physics.unimelb.edu.au; Witte, C. [School of Physics, University of Melbourne, Parkville, Vic 3010 (Australia)
2007-01-15
The finite difference method is extended to calculate X-ray absorption fine structure (XAFS) for solid state copper. These extensions include the incorporation of a Monte Carlo frozen phonon technique to simulate the effect of thermal vibrations under a correlated Debye-Waller model, and the inclusion of broadening effects from inelastic processes. Spectra are obtained over an energy range in excess of 300 eV above the K absorption edge-more than twice the greatest energy range previously reported for a solid state calculation using this method. We find this method is highly sensitive to values of the photoelectron inelastic mean free path, allowing us to probe the accuracy of current models of this parameter, particularly at low energies. We therefore find that experimental data for the photoelectron inelastic mean free path can be obtained by this method. Our results compare favourably with high precision measurements of the X-ray mass attenuation coefficient for copper, reaching agreement to within 3%, and improving previous results using the finite difference method by an order of magnitude.
Mustapha, K.
2017-06-03
Anomalous diffusion is a phenomenon that cannot be modeled accurately by second-order diffusion equations, but is better described by fractional diffusion models. The nonlocal nature of the fractional diffusion operators makes substantially more difficult the mathematical analysis of these models and the establishment of suitable numerical schemes. This paper proposes and analyzes the first finite difference method for solving {\\\\em variable-coefficient} fractional differential equations, with two-sided fractional derivatives, in one-dimensional space. The proposed scheme combines first-order forward and backward Euler methods for approximating the left-sided fractional derivative when the right-sided fractional derivative is approximated by two consecutive applications of the first-order backward Euler method. Our finite difference scheme reduces to the standard second-order central difference scheme in the absence of fractional derivatives. The existence and uniqueness of the solution for the proposed scheme are proved, and truncation errors of order $h$ are demonstrated, where $h$ denotes the maximum space step size. The numerical tests illustrate the global $O(h)$ accuracy of our scheme, except for nonsmooth cases which, as expected, have deteriorated convergence rates.
Mustapha, K.; Furati, K.; Knio, Omar; Maitre, O. Le
2017-01-01
Anomalous diffusion is a phenomenon that cannot be modeled accurately by second-order diffusion equations, but is better described by fractional diffusion models. The nonlocal nature of the fractional diffusion operators makes substantially more difficult the mathematical analysis of these models and the establishment of suitable numerical schemes. This paper proposes and analyzes the first finite difference method for solving {\\em variable-coefficient} fractional differential equations, with two-sided fractional derivatives, in one-dimensional space. The proposed scheme combines first-order forward and backward Euler methods for approximating the left-sided fractional derivative when the right-sided fractional derivative is approximated by two consecutive applications of the first-order backward Euler method. Our finite difference scheme reduces to the standard second-order central difference scheme in the absence of fractional derivatives. The existence and uniqueness of the solution for the proposed scheme are proved, and truncation errors of order $h$ are demonstrated, where $h$ denotes the maximum space step size. The numerical tests illustrate the global $O(h)$ accuracy of our scheme, except for nonsmooth cases which, as expected, have deteriorated convergence rates.
A moving mesh finite difference method for equilibrium radiation diffusion equations
Energy Technology Data Exchange (ETDEWEB)
Yang, Xiaobo, E-mail: xwindyb@126.com [Department of Mathematics, College of Science, China University of Mining and Technology, Xuzhou, Jiangsu 221116 (China); Huang, Weizhang, E-mail: whuang@ku.edu [Department of Mathematics, University of Kansas, Lawrence, KS 66045 (United States); Qiu, Jianxian, E-mail: jxqiu@xmu.edu.cn [School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing, Xiamen University, Xiamen, Fujian 361005 (China)
2015-10-01
An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor–corrector and lagged diffusion strategy. Moreover, the nonnegativity of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation.
A moving mesh finite difference method for equilibrium radiation diffusion equations
International Nuclear Information System (INIS)
Yang, Xiaobo; Huang, Weizhang; Qiu, Jianxian
2015-01-01
An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor–corrector and lagged diffusion strategy. Moreover, the nonnegativity of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation
Slat Noise Predictions Using Higher-Order Finite-Difference Methods on Overset Grids
Housman, Jeffrey A.; Kiris, Cetin
2016-01-01
Computational aeroacoustic simulations using the structured overset grid approach and higher-order finite difference methods within the Launch Ascent and Vehicle Aerodynamics (LAVA) solver framework are presented for slat noise predictions. The simulations are part of a collaborative study comparing noise generation mechanisms between a conventional slat and a Krueger leading edge flap. Simulation results are compared with experimental data acquired during an aeroacoustic test in the NASA Langley Quiet Flow Facility. Details of the structured overset grid, numerical discretization, and turbulence model are provided.
New way for determining electron energy levels in quantum dots arrays using finite difference method
Dujardin, F.; Assaid, E.; Feddi, E.
2018-06-01
Electronic states are investigated in quantum dots arrays, depending on the type of cubic Bravais lattice (primitive, body centered or face centered) according to which the dots are arranged, the size of the dots and the interdot distance. It is shown that the ground state energy level can undergo significant variations when these parameters are modified. The results were obtained by means of finite difference method which has proved to be easily adaptable, efficient and precise. The symmetry properties of the lattice have been used to reduce the size of the Hamiltonian matrix.
Jia, Shouqing; La, Dongsheng; Ma, Xuelian
2018-04-01
The finite difference time domain (FDTD) algorithm and Green function algorithm are implemented into the numerical simulation of electromagnetic waves in Schwarzschild space-time. FDTD method in curved space-time is developed by filling the flat space-time with an equivalent medium. Green function in curved space-time is obtained by solving transport equations. Simulation results validate both the FDTD code and Green function code. The methods developed in this paper offer a tool to solve electromagnetic scattering problems.
International Nuclear Information System (INIS)
Potemki, Valeri G.; Borisevich, Valentine D.; Yupatov, Sergei V.
1996-01-01
This paper describes the the next evolution step in development of the direct method for solving systems of Nonlinear Algebraic Equations (SNAE). These equations arise from the finite difference approximation of original nonlinear partial differential equations (PDE). This method has been extended on the SNAE with three variables. The solving SNAE bases on Reiterating General Singular Value Decomposition of rectangular matrix pencils (RGSVD-algorithm). In contrast to the computer algebra algorithm in integer arithmetic based on the reduction to the Groebner's basis that algorithm is working in floating point arithmetic and realizes the reduction to the Kronecker's form. The possibilities of the method are illustrated on the example of solving the one-dimensional diffusion equation for 3-component model isotope mixture in a ga centrifuge. The implicit scheme for the finite difference equations without simplifying the nonlinear properties of the original equations is realized. The technique offered provides convergence to the solution for the single run. The Toolbox SNAE is developed in the framework of the high performance numeric computation and visualization software MATLAB. It includes more than 30 modules in MATLAB language for solving SNAE with two and three variables. (author)
International Nuclear Information System (INIS)
Li Bihong; Shuang Na; Liu Qingcheng
2006-01-01
The principle of finite difference method is introduced, and the radon field distribution over sandstone-type uranium deposit is narrated. The radon field distribution theory equation is established. To solve radon field distribution equation using finite difference algorithm is to provide the value computational method for forward calculation about radon field over sandstone-type uranium mine. Study on 2-D finite difference method on the center of either high anomaly radon fields in view of the character of radon field over sandstone-type uranium provide an algorithm for further research. (authors)
GPU-accelerated 3D neutron diffusion code based on finite difference method
Energy Technology Data Exchange (ETDEWEB)
Xu, Q.; Yu, G.; Wang, K. [Dept. of Engineering Physics, Tsinghua Univ. (China)
2012-07-01
Finite difference method, as a traditional numerical solution to neutron diffusion equation, although considered simpler and more precise than the coarse mesh nodal methods, has a bottle neck to be widely applied caused by the huge memory and unendurable computation time it requires. In recent years, the concept of General-Purpose computation on GPUs has provided us with a powerful computational engine for scientific research. In this study, a GPU-Accelerated multi-group 3D neutron diffusion code based on finite difference method was developed. First, a clean-sheet neutron diffusion code (3DFD-CPU) was written in C++ on the CPU architecture, and later ported to GPUs under NVIDIA's CUDA platform (3DFD-GPU). The IAEA 3D PWR benchmark problem was calculated in the numerical test, where three different codes, including the original CPU-based sequential code, the HYPRE (High Performance Pre-conditioners)-based diffusion code and CITATION, were used as counterpoints to test the efficiency and accuracy of the GPU-based program. The results demonstrate both high efficiency and adequate accuracy of the GPU implementation for neutron diffusion equation. A speedup factor of about 46 times was obtained, using NVIDIA's Geforce GTX470 GPU card against a 2.50 GHz Intel Quad Q9300 CPU processor. Compared with the HYPRE-based code performing in parallel on an 8-core tower server, the speedup of about 2 still could be observed. More encouragingly, without any mathematical acceleration technology, the GPU implementation ran about 5 times faster than CITATION which was speeded up by using the SOR method and Chebyshev extrapolation technique. (authors)
GPU-accelerated 3D neutron diffusion code based on finite difference method
International Nuclear Information System (INIS)
Xu, Q.; Yu, G.; Wang, K.
2012-01-01
Finite difference method, as a traditional numerical solution to neutron diffusion equation, although considered simpler and more precise than the coarse mesh nodal methods, has a bottle neck to be widely applied caused by the huge memory and unendurable computation time it requires. In recent years, the concept of General-Purpose computation on GPUs has provided us with a powerful computational engine for scientific research. In this study, a GPU-Accelerated multi-group 3D neutron diffusion code based on finite difference method was developed. First, a clean-sheet neutron diffusion code (3DFD-CPU) was written in C++ on the CPU architecture, and later ported to GPUs under NVIDIA's CUDA platform (3DFD-GPU). The IAEA 3D PWR benchmark problem was calculated in the numerical test, where three different codes, including the original CPU-based sequential code, the HYPRE (High Performance Pre-conditioners)-based diffusion code and CITATION, were used as counterpoints to test the efficiency and accuracy of the GPU-based program. The results demonstrate both high efficiency and adequate accuracy of the GPU implementation for neutron diffusion equation. A speedup factor of about 46 times was obtained, using NVIDIA's Geforce GTX470 GPU card against a 2.50 GHz Intel Quad Q9300 CPU processor. Compared with the HYPRE-based code performing in parallel on an 8-core tower server, the speedup of about 2 still could be observed. More encouragingly, without any mathematical acceleration technology, the GPU implementation ran about 5 times faster than CITATION which was speeded up by using the SOR method and Chebyshev extrapolation technique. (authors)
Directory of Open Access Journals (Sweden)
M.H.R. Ghoreishy
2008-02-01
Full Text Available This research work is devoted to the footprint analysis of a steel-belted radial tyre (185/65R14 under vertical static load using finite element method. Two models have been developed in which in the first model the tread patterns were replaced by simple ribs while the second model was consisted of details of the tread blocks. Linear elastic and hyper elastic (Arruda-Boyce material models were selected to describe the mechanical behavior of the reinforcing and rubbery parts, respectively. The above two finite element models of the tyre were analyzed under inflation pressure and vertical static loads. The second model (with detailed tread patterns was analyzed with and without friction effect between tread and contact surfaces. In every stage of the analysis, the results were compared with the experimental data to confirm the accuracy and applicability of the model. Results showed that neglecting the tread pattern design not only reduces the computational cost and effort but also the differences between computed deformations do not show significant changes. However, more complicated variables such as shape and area of the footprint zone and contact pressure are affected considerably by the finite element model selected for the tread blocks. In addition, inclusion of friction even in static state changes these variables significantly.
Non-linear analysis of skew thin plate by finite difference method
International Nuclear Information System (INIS)
Kim, Chi Kyung; Hwang, Myung Hwan
2012-01-01
This paper deals with a discrete analysis capability for predicting the geometrically nonlinear behavior of skew thin plate subjected to uniform pressure. The differential equations are discretized by means of the finite difference method which are used to determine the deflections and the in-plane stress functions of plates and reduced to several sets of linear algebraic simultaneous equations. For the geometrically non-linear, large deflection behavior of the plate, the non-linear plate theory is used for the analysis. An iterative scheme is employed to solve these quasi-linear algebraic equations. Several problems are solved which illustrate the potential of the method for predicting the finite deflection and stress. For increasing lateral pressures, the maximum principal tensile stress occurs at the center of the plate and migrates toward the corners as the load increases. It was deemed important to describe the locations of the maximum principal tensile stress as it occurs. The load-deflection relations and the maximum bending and membrane stresses for each case are presented and discussed
Simulation of acoustic streaming by means of the finite-difference time-domain method
DEFF Research Database (Denmark)
Santillan, Arturo Orozco
2012-01-01
Numerical simulations of acoustic streaming generated by a standing wave in a narrow twodimensional cavity are presented. In this case, acoustic streaming arises from the viscous boundary layers set up at the surfaces of the walls. It is known that streaming vortices inside the boundary layer have...... directions of rotation that are opposite to those of the outer streaming vortices (Rayleigh streaming). The general objective of the work described in this paper has been to study the extent to which it is possible to simulate both the outer streaming vortices and the inner boundary layer vortices using...... the finite-difference time-domain method. To simplify the problem, thermal effects are not considered. The motivation of the described investigation has been the possibility of using the numerical method to study acoustic streaming, particularly under non-steady conditions. Results are discussed for channels...
Contact Stress Analysis for Gears of Different Helix Angle Using Finite Element Method
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Patil Santosh
2014-07-01
Full Text Available The gear contact stress problem has been a great point of interest for many years, but still an extensive research is required to understand the various parameters affecting this stress. Among such parameters, helix angle is one which has played a crucial role in variation of contact stress. Numerous studies have been carried out on spur gear for contact stress variation. Hence, the present work is an attempt to study the contact stresses among the helical gear pairs, under static conditions, by using a 3D finite element method. The helical gear pairs on which the analysis is carried are 0, 5, 15, 25 degree helical gear sets. The Lagrange multiplier algorithm has been used between the contacting pairs to determine the stresses. The helical gear contact stress is evaluated using FE model and results have also been found at different coefficient of friction, varying from 0.0 to 0.3. The FE results have been further compared with the analytical calculations. The analytical calculations are based upon Hertz and AGMA equations, which are modified to include helix angle. The commercial finite element software was used in the study and it was shown that this approach can be applied to gear design efficiently. The contact stress results have shown a decreasing trend, with increase in helix angle.
Use of the finite-difference time-domain method in electromagnetic dosimetry
International Nuclear Information System (INIS)
Sullivan, D.M.
1987-01-01
Although there are acceptable methods for calculating whole body electromagnetic absorption, no completely acceptable method for calculating the local specific absorption rate (SAR) at points within the body has been developed. Frequency domain methods, such as the method of moments (MoM) have achieved some success; however, the MoM requires computer storage on the order of (3N) 2 , and computation time on the order of (3N) 3 where N is the number of cells. The finite-difference time-domain (FDTD) method has been employed extensively in calculating the scattering from metallic objects, and recently is seeing some use in calculating the interaction of EM fields with complex, lossy dielectric bodies. Since the FDTD method has storage and time requirements proportional to N, it presents an attractive alternative to calculating SAR distribution in large bodies. This dissertation describes the FDTD method and evaluates it by comparing its results with analytic solutions in 2 and 3 dimensions. The results obtained demonstrate that the FDTD method is capable of calculating internal SAR distribution with acceptable accuracy. The construction of a data base to provide detailed, inhomogeneous man models for use with the FDTD method is described. Using this construction method, a model of 40,000 1.31 cm. cells is developed for use at 350 MHz, and another model consisting of 5000 2.62 cm. cells is developed for use at 100 MHz. To add more realism to the problem, a ground plane is added to the FDTD software. The needed changes to the software are described, along with a test which confirms its accuracy. Using the CRAY II supercomputer, SAR distributions in human models are calculated using incident frequencies of 100 MHz and 350 MHz for three different cases: (1) A homogeneous man model in free space, (2) an inhomogeneous man model in free space, and (3) an inhomogeneous man model standing on a ground plane
DETERMINATION OF MOISTURE DIFFUSION COEFFICIENT OF LARCH BOARD WITH FINITE DIFFERENCE METHOD
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Qiaofang Zhou
2011-04-01
Full Text Available This paper deals with the moisture diffusion coefficient of Dahurian Larch (Larix gmelinii Rupr. by use of the Finite Difference Method (FDM. To obtain moisture distributions the dimensional boards of Dahurian Larch were dried, from which test samples were cut and sliced evenly into 9 pieces in different drying periods, so that moisture distributions at different locations and times across the thickness of Dahurian Larch were obtained with a weighing method. With these experimental data, FDM was used to solve Fick’s one-dimensional unsteady-state diffusion equation, and the moisture diffusion coefficient across the thickness at specified time was obtained. Results indicated that the moisture diffusion coefficient decreased from the surface to the center of the Dahurian Larch wood, and it decreased with decreasing moisture content at constant wood temperature; as the wood temperature increased, the moisture diffusion coefficient increased, and the effect of the wood temperature on the moisture diffusion coefficient was more significant than that of moisture content. Moisture diffusion coefficients were different for the two experiments due to differing diffusivity of the specimens.
Thermal Analysis of Ball screw Systems by Explicit Finite Difference Method
Energy Technology Data Exchange (ETDEWEB)
Min, Bog Ki [Hanyang Univ., Seoul (Korea, Republic of); Park, Chun Hong; Chung, Sung Chong [KIMM, Daejeon (Korea, Republic of)
2016-01-15
Friction generated from balls and grooves incurs temperature rise in the ball screw system. Thermal deformation due to the heat degrades positioning accuracy of the feed drive system. To compensate for the thermal error, accurate prediction of the temperature distribution is required first. In this paper, to predict the temperature distribution according to the rotational speed, solid and hollow cylinders are applied for analysis of the ball screw shaft and nut, respectively. Boundary conditions such as the convective heat transfer coefficient, friction torque, and thermal contact conductance (TCC) between balls and grooves are formulated according to operating and fabrication conditions of the ball screw. Explicit FDM (finite difference method) is studied for development of a temperature prediction simulator. Its effectiveness is verified through numerical analysis.
Directory of Open Access Journals (Sweden)
Beltrán-Prieto Juan Carlos
2016-01-01
Full Text Available The mathematical modelling of diffusion of a bleaching agent into a porous material is studied in the present paper. Law of mass conservation was applied to analize the mass transfer of a reactant from the bulk into the external surface of a solid geometrically described as a flat plate. After diffusion of the reactant, surface reaction following kinetics of first order was considered to take place. The solution of the differential equation that described the process leaded to an equation that represents the concentration profile in function of distance, porosity and Thiele modulus. The case of interfacial mass resistance is also discused. In this case, finite difference method was used for the solution of the differential equation taking into account the respective boundary conditions. The profile of concentration can be obtained after numerical especification of Thiele modulus and Biot number.
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Mohammad Hadi Jalali
2018-01-01
Full Text Available Elastic stress analysis of rotating variable thickness annular disk made of functionally graded material (FGM is presented. Elasticity modulus, density, and thickness of the disk are assumed to vary radially according to a power-law function. Radial stress, circumferential stress, and radial deformation of the rotating FG annular disk of variable thickness with clamped-clamped (C-C, clamped-free (C-F, and free-free (F-F boundary conditions are obtained using the numerical finite difference method, and the effects of the graded index, thickness variation, and rotating speed on the stresses and deformation are evaluated. It is shown that using FG material could decrease the value of radial stress and increase the radial displacement in a rotating thin disk. It is also demonstrated that increasing the rotating speed can strongly increase the stress in the FG annular disk.
International Nuclear Information System (INIS)
Park, Beom Woo; Joo, Han Gyu
2015-01-01
Highlights: • The stiffness confinement method is combined with multigroup CMFD with SENM nodal kernel. • The systematic methods for determining the shape and amplitude frequencies are established. • Eigenvalue problems instead of fixed source problems are solved in the transient calculation. • It is demonstrated that much larger time step sizes can be used with the SCM–CMFD method. - Abstract: An improved Stiffness Confinement Method (SCM) is formulated within the framework of the coarse mesh finite difference (CMFD) formulation for efficient multigroup spatial kinetics calculation. The algorithm for searching for the amplitude frequency that makes the dynamic eigenvalue unity is developed in a systematic way along with the methods for determining the shape and precursor frequencies. A nodal calculation scheme is established within the CMFD framework to incorporate the cross section changes due to thermal feedback and dynamic frequency update. The conditional nodal update scheme is employed such that the transient calculation is performed mostly with the CMFD formulation and the CMFD parameters are conditionally updated by intermittent nodal calculations. A quadratic representation of amplitude frequency is introduced as another improvement. The performance of the improved SCM within the CMFD framework is assessed by comparing the solution accuracy and computing times for the NEACRP control rod ejection benchmark problems with those obtained with the Crank–Nicholson method with exponential transform (CNET). It is demonstrated that the improved SCM is beneficial for large time step size calculations with stability and accuracy enhancement
A finite difference method for off-fault plasticity throughout the earthquake cycle
Erickson, Brittany A.; Dunham, Eric M.; Khosravifar, Arash
2017-12-01
We have developed an efficient computational framework for simulating multiple earthquake cycles with off-fault plasticity. The method is developed for the classical antiplane problem of a vertical strike-slip fault governed by rate-and-state friction, with inertial effects captured through the radiation-damping approximation. Both rate-independent plasticity and viscoplasticity are considered, where stresses are constrained by a Drucker-Prager yield condition. The off-fault volume is discretized using finite differences and tectonic loading is imposed by displacing the remote side boundaries at a constant rate. Time-stepping combines an adaptive Runge-Kutta method with an incremental solution process which makes use of an elastoplastic tangent stiffness tensor and the return-mapping algorithm. Solutions are verified by convergence tests and comparison to a finite element solution. We quantify how viscosity, isotropic hardening, and cohesion affect the magnitude and off-fault extent of plastic strain that develops over many ruptures. If hardening is included, plastic strain saturates after the first event and the response during subsequent ruptures is effectively elastic. For viscoplasticity without hardening, however, successive ruptures continue to generate additional plastic strain. In all cases, coseismic slip in the shallow sub-surface is diminished compared to slip accumulated at depth during interseismic loading. The evolution of this slip deficit with each subsequent event, however, is dictated by the plasticity model. Integration of the off-fault plastic strain from the viscoplastic model reveals that a significant amount of tectonic offset is accommodated by inelastic deformation ( ∼ 0.1 m per rupture, or ∼ 10% of the tectonic deformation budget).
Directory of Open Access Journals (Sweden)
Tsugio Fukuchi
2014-06-01
Full Text Available The finite difference method (FDM based on Cartesian coordinate systems can be applied to numerical analyses over any complex domain. A complex domain is usually taken to mean that the geometry of an immersed body in a fluid is complex; here, it means simply an analytical domain of arbitrary configuration. In such an approach, we do not need to treat the outer and inner boundaries differently in numerical calculations; both are treated in the same way. Using a method that adopts algebraic polynomial interpolations in the calculation around near-wall elements, all the calculations over irregular domains reduce to those over regular domains. Discretization of the space differential in the FDM is usually derived using the Taylor series expansion; however, if we use the polynomial interpolation systematically, exceptional advantages are gained in deriving high-order differences. In using the polynomial interpolations, we can numerically solve the Poisson equation freely over any complex domain. Only a particular type of partial differential equation, Poisson's equations, is treated; however, the arguments put forward have wider generality in numerical calculations using the FDM.
Ping, Jing
2017-05-19
Optimal management of subsurface processes requires the characterization of the uncertainty in reservoir description and reservoir performance prediction. For fractured reservoirs, the location and orientation of fractures are crucial for predicting production characteristics. With the help of accurate and comprehensive knowledge of fracture distributions, early water/CO 2 breakthrough can be prevented and sweep efficiency can be improved. However, since the rock property fields are highly non-Gaussian in this case, it is a challenge to estimate fracture distributions by conventional history matching approaches. In this work, a method that combines vector-based level-set parameterization technique and ensemble Kalman filter (EnKF) for estimating fracture distributions is presented. Performing the necessary forward modeling is particularly challenging. In addition to the large number of forward models needed, each model is used for sampling of randomly located fractures. Conventional mesh generation for such systems would be time consuming if possible at all. For these reasons, we rely on a novel polyhedral mesh method using the mimetic finite difference (MFD) method. A discrete fracture model is adopted that maintains the full geometry of the fracture network. By using a cut-cell paradigm, a computational mesh for the matrix can be generated quickly and reliably. In this research, we apply this workflow on 2D two-phase fractured reservoirs. The combination of MFD approach, level-set parameterization, and EnKF provides an effective solution to address the challenges in the history matching problem of highly non-Gaussian fractured reservoirs.
International Nuclear Information System (INIS)
Tokuda, Shinji; Watanabe, Tomoko.
1996-08-01
The matching problem in resistive MagnetoHydroDynamic stability analysis by the asymptotic matching method has been reformulated as an initial-boundary value problem for the inner-layer equations describing the plasma dynamics in the thin layer around a rational surface. The third boundary conditions at boundaries of a finite interval are imposed on the inner layer equations in the formulation instead of asymptotic conditions at infinities. The finite difference method for this problem has been applied to model equations whose solutions are known in a closed form. It has been shown that the initial value problem and the associated eigenvalue problem for the model equations can be solved by the finite difference method with numerical stability. The formulation presented here enables the asymptotic matching method to be a practical method for the resistive MHD stability analysis. (author)
Methods for compressible fluid simulation on GPUs using high-order finite differences
Pekkilä, Johannes; Väisälä, Miikka S.; Käpylä, Maarit J.; Käpylä, Petri J.; Anjum, Omer
2017-08-01
We focus on implementing and optimizing a sixth-order finite-difference solver for simulating compressible fluids on a GPU using third-order Runge-Kutta integration. Since graphics processing units perform well in data-parallel tasks, this makes them an attractive platform for fluid simulation. However, high-order stencil computation is memory-intensive with respect to both main memory and the caches of the GPU. We present two approaches for simulating compressible fluids using 55-point and 19-point stencils. We seek to reduce the requirements for memory bandwidth and cache size in our methods by using cache blocking and decomposing a latency-bound kernel into several bandwidth-bound kernels. Our fastest implementation is bandwidth-bound and integrates 343 million grid points per second on a Tesla K40t GPU, achieving a 3 . 6 × speedup over a comparable hydrodynamics solver benchmarked on two Intel Xeon E5-2690v3 processors. Our alternative GPU implementation is latency-bound and achieves the rate of 168 million updates per second.
Chiranjeevi, C.; Srinivas, T.
2017-11-01
Humidifier is an important component in air humidification-dehumidification desalination plant for fresh water production. Liquid to air flow rate ratio is optimization is reported for an industrial cooling towers but for an air humidifier it is not addressed. The current work is focused on the design and analysis of an air humidifier for solar desalination plant to maximize the yield with better humidification, using finite difference method (FDM). The outlet conditions of air from the humidifier are theoretically predicted by FDM with the given inlet conditions, which will be further used in the design calculation of the humidifier. Hot water to air flow rate ratio and inlet hot water temperature are identified as key operating parameters to evaluate the humidifier performance. The maximum and optimal values of mass flow rate ratio of water to air are found to be 2.15 and 1.5 respectively using packing function and Merkel Integral. The height of humidifier is constrained to 1.5 m and the diameter of the humidifier is found as 0.28m. The performance of humidifier and outlet conditions of air are simulated using FDM and compared with experimental results. The obtained results are within an agreeable range of deviation.
Pressure transient analysis in single and two-phase water by finite difference methods
International Nuclear Information System (INIS)
Berry, G.F.; Daley, J.G.
1977-01-01
An important consideration in the design of LMFBR steam generators is the possibility of leakage from a steam generator water tube. The ensuing sodium/water reaction will be largely controlled by the amount of water available at the leak site, thus analysis methods treating this event must have the capability of accurately modeling pressure transients through all states of water occurring in a steam generator, whether single or two-phase. The equation systems of the present model consist of the conservation equations together with an equation of state for one-dimensional homogeneous flow. These equations are then solved using finite difference techniques with phase considerations and non-equilibrium effects being treated through the equation of state. The basis for water property computation is Keenan's 'fundamental equation of state' which is applicable to single-phase water at pressures less than 1000 bars and temperatures less than 1300 0 C. This provides formulations allowing computation of any water property to any desired precision. Two-phase properties are constructed from values on the saturation line. The use of formulations permits the direct calculation of any thermodynamic property (or property derivative) to great precision while requiring very little computer storage, but does involve considerable computation time. For this reason an optional calculation scheme based on the method of 'transfinite interpolation' is included to give rapid computation in selected regions with decreased precision. The conservation equations were solved using the second order Lax-Wendroff scheme which includes wall friction, allows the formation of shocks and locally supersonic flow. Computational boundary conditions were found from a method-of-characteristics solution at the reservoir and receiver ends. The local characteristics were used to interpolate data from inside the pipe to the boundary
Rotational degree-of-freedom synthesis: An optimised finite difference method for non-exact data
Gibbons, T. J.; Öztürk, E.; Sims, N. D.
2018-01-01
Measuring the rotational dynamic behaviour of a structure is important for many areas of dynamics such as passive vibration control, acoustics, and model updating. Specialist and dedicated equipment is often needed, unless the rotational degree-of-freedom is synthesised based upon translational data. However, this involves numerically differentiating the translational mode shapes to approximate the rotational modes, for example using a finite difference algorithm. A key challenge with this approach is choosing the measurement spacing between the data points, an issue which has often been overlooked in the published literature. The present contribution will for the first time prove that the use of a finite difference approach can be unstable when using non-exact measured data and a small measurement spacing, for beam-like structures. Then, a generalised analytical error analysis is used to propose an optimised measurement spacing, which balances the numerical error of the finite difference equation with the propagation error from the perturbed data. The approach is demonstrated using both numerical and experimental investigations. It is shown that by obtaining a small number of test measurements it is possible to optimise the measurement accuracy, without any further assumptions on the boundary conditions of the structure.
Emoto, K.; Saito, T.; Shiomi, K.
2017-12-01
Short-period (2 s) seismograms. We found that the energy of the coda of long-period seismograms shows a spatially flat distribution. This phenomenon is well known in short-period seismograms and results from the scattering by small-scale heterogeneities. We estimate the statistical parameters that characterize the small-scale random heterogeneity by modelling the spatiotemporal energy distribution of long-period seismograms. We analyse three moderate-size earthquakes that occurred in southwest Japan. We calculate the spatial distribution of the energy density recorded by a dense seismograph network in Japan at the period bands of 8-16 s, 4-8 s and 2-4 s and model them by using 3-D finite difference (FD) simulations. Compared to conventional methods based on statistical theories, we can calculate more realistic synthetics by using the FD simulation. It is not necessary to assume a uniform background velocity, body or surface waves and scattering properties considered in general scattering theories. By taking the ratio of the energy of the coda area to that of the entire area, we can separately estimate the scattering and the intrinsic absorption effects. Our result reveals the spectrum of the random inhomogeneity in a wide wavenumber range including the intensity around the corner wavenumber as P(m) = 8πε2a3/(1 + a2m2)2, where ε = 0.05 and a = 3.1 km, even though past studies analysing higher-frequency records could not detect the corner. Finally, we estimate the intrinsic attenuation by modelling the decay rate of the energy. The method proposed in this study is suitable for quantifying the statistical properties of long-wavelength subsurface random inhomogeneity, which leads the way to characterizing a wider wavenumber range of spectra, including the corner wavenumber.
DEFF Research Database (Denmark)
Amini Afshar, Mostafa; Bingham, Harry B.
2017-01-01
. Frequency-domain results are then obtained from a Fourier transform of the force and motion signals. In order to make a robust Fourier transform, and capture the response around the critical frequency, the tail of the force signal is asymptotically extrapolated assuming a linear decay rate. Fourth......The linearized potential flow approximation for the forward speed radiation problem is solved in the time domain using a high-order finite difference method. The finite-difference discretization is developed on overlapping, curvilinear body-fitted grids. To ensure numerical stability...
Raeli, Alice; Bergmann, Michel; Iollo, Angelo
2018-02-01
We consider problems governed by a linear elliptic equation with varying coefficients across internal interfaces. The solution and its normal derivative can undergo significant variations through these internal boundaries. We present a compact finite-difference scheme on a tree-based adaptive grid that can be efficiently solved using a natively parallel data structure. The main idea is to optimize the truncation error of the discretization scheme as a function of the local grid configuration to achieve second-order accuracy. Numerical illustrations are presented in two and three-dimensional configurations.
Domain-adaptive finite difference methods for collapsing annular liquid jets
Ramos, J. I.
1993-01-01
rate increases as the Weber number, nozzle exit angle, gas concentration at the nozzle exit, and temperature of the gases enclosed by the annular liquid jet are increased, but it decreases as the Froude and Peclet numbers, and annular liquid jet's thickness-to-radius ratio at the nozzle exit are increased. It is also shown that the annular liquid jet's collapse rate increases as the Weber number, nozzle exit angle, temperature of the gases enclosed by the annular liquid jet, and pressure of the gases which surround the jet are increased, but decreases as the Froude and Peclet numbers, and annular liquid jet's thickness-toradius ratio at the nozzle exit are increased. It is also shown that both the ratio of the initial pressure of the gas enclosed by the jet to the pressure of the gas surrounding the jet and the ratio of solubilities at the annular liquid jet's inner and outer interfaces play an important role on both the steady state mass absorption rate and the jet collapse. If the product of these ratios is greater or less than one, both the pressure and the mass of the gas enclosed by the annular liquid jet decrease or increase, respectively, with time. It is also shown that the numerical results obtained with the conservative, domain-adaptive method of lines technique presented in this paper are in excellent agreement with those of a domain-adaptive, iterative, non-conservative, block-bidiagonal, finite difference method which uncouples the solution of the fluid dynamics equations from that of the convergence length.
Transient analysis of printed lines using finite-difference time-domain method
Energy Technology Data Exchange (ETDEWEB)
Ahmed, Shahid [Thomas Jefferson National Accelerator Facility, 12050 Jefferson Avenue, Suite 704, Newport News, VA, 23606, USA
2012-03-29
Comprehensive studies of ultra-wideband pulses and electromagnetic coupling on printed coupled lines have been performed using full-wave 3D finite-difference time-domain analysis. Effects of unequal phase velocities of coupled modes, coupling between line traces, and the frequency dispersion on the waveform fidelity and crosstalk have been investigated in detail. To discriminate the contributions of different mechanisms into pulse evolution, single and coupled microstrip lines without (ϵ_{r} = 1) and with (ϵ_{r} > 1) dielectric substrates have been examined. To consistently compare the performance of the coupled lines with substrates of different permittivities and transients of different characteristic times, a generic metric similar to the electrical wavelength has been introduced. The features of pulse propagation on coupled lines with layered and pedestal substrates and on the irregular traces have been explored. Finally, physical interpretations of the simulation results are discussed in the paper.
Simulation model of stratified thermal energy storage tank using finite difference method
Waluyo, Joko
2016-06-01
Stratified TES tank is normally used in the cogeneration plant. The stratified TES tanks are simple, low cost, and equal or superior in thermal performance. The advantage of TES tank is that it enables shifting of energy usage from off-peak demand for on-peak demand requirement. To increase energy utilization in a stratified TES tank, it is required to build a simulation model which capable to simulate the charging phenomenon in the stratified TES tank precisely. This paper is aimed to develop a novel model in addressing the aforementioned problem. The model incorporated chiller into the charging of stratified TES tank system in a closed system. The model was developed in one-dimensional type involve with heat transfer aspect. The model covers the main factors affect to degradation of temperature distribution namely conduction through the tank wall, conduction between cool and warm water, mixing effect on the initial flow of the charging as well as heat loss to surrounding. The simulation model is developed based on finite difference method utilizing buffer concept theory and solved in explicit method. Validation of the simulation model is carried out using observed data obtained from operating stratified TES tank in cogeneration plant. The temperature distribution of the model capable of representing S-curve pattern as well as simulating decreased charging temperature after reaching full condition. The coefficient of determination values between the observed data and model obtained higher than 0.88. Meaning that the model has capability in simulating the charging phenomenon in the stratified TES tank. The model is not only capable of generating temperature distribution but also can be enhanced for representing transient condition during the charging of stratified TES tank. This successful model can be addressed for solving the limitation temperature occurs in charging of the stratified TES tank with the absorption chiller. Further, the stratified TES tank can be
Directory of Open Access Journals (Sweden)
Taohua Liu
2017-01-01
Full Text Available Fractional advection-dispersion equations, as generalizations of classical integer-order advection-dispersion equations, are used to model the transport of passive tracers carried by fluid flow in a porous medium. In this paper, we develop an implicit finite difference method for fractional advection-dispersion equations with fractional derivative boundary conditions. First-order consistency, solvability, unconditional stability, and first-order convergence of the method are proven. Then, we present a fast iterative method for the implicit finite difference scheme, which only requires storage of O(K and computational cost of O(KlogK. Traditionally, the Gaussian elimination method requires storage of O(K2 and computational cost of O(K3. Finally, the accuracy and efficiency of the method are checked with a numerical example.
Castaldo, Raffaele; Tizzani, Pietro
2016-04-01
Many numerical models have been developed to simulate the deformation and stress changes associated to the faulting process. This aspect is an important topic in fracture mechanism. In the proposed study, we investigate the impact of the deep fault geometry and tectonic setting on the co-seismic ground deformation pattern associated to different earthquake phenomena. We exploit the impact of the structural-geological data in Finite Element environment through an optimization procedure. In this framework, we model the failure processes in a physical mechanical scenario to evaluate the kinematics associated to the Mw 6.1 L'Aquila 2009 earthquake (Italy), the Mw 5.9 Ferrara and Mw 5.8 Mirandola 2012 earthquake (Italy) and the Mw 8.3 Gorkha 2015 earthquake (Nepal). These seismic events are representative of different tectonic scenario: the normal, the reverse and thrust faulting processes, respectively. In order to simulate the kinematic of the analyzed natural phenomena, we assume, under the plane stress approximation (is defined to be a state of stress in which the normal stress, sz, and the shear stress sxz and syz, directed perpendicular to x-y plane are assumed to be zero), the linear elastic behavior of the involved media. The performed finite element procedure consist of through two stages: (i) compacting under the weight of the rock successions (gravity loading), the deformation model reaches a stable equilibrium; (ii) the co-seismic stage simulates, through a distributed slip along the active fault, the released stresses. To constrain the models solution, we exploit the DInSAR deformation velocity maps retrieved by satellite data acquired by old and new generation sensors, as ENVISAT, RADARSAT-2 and SENTINEL 1A, encompassing the studied earthquakes. More specifically, we first generate 2D several forward mechanical models, then, we compare these with the recorded ground deformation fields, in order to select the best boundaries setting and parameters. Finally
Acceleration of Linear Finite-Difference Poisson-Boltzmann Methods on Graphics Processing Units.
Qi, Ruxi; Botello-Smith, Wesley M; Luo, Ray
2017-07-11
Electrostatic interactions play crucial roles in biophysical processes such as protein folding and molecular recognition. Poisson-Boltzmann equation (PBE)-based models have emerged as widely used in modeling these important processes. Though great efforts have been put into developing efficient PBE numerical models, challenges still remain due to the high dimensionality of typical biomolecular systems. In this study, we implemented and analyzed commonly used linear PBE solvers for the ever-improving graphics processing units (GPU) for biomolecular simulations, including both standard and preconditioned conjugate gradient (CG) solvers with several alternative preconditioners. Our implementation utilizes the standard Nvidia CUDA libraries cuSPARSE, cuBLAS, and CUSP. Extensive tests show that good numerical accuracy can be achieved given that the single precision is often used for numerical applications on GPU platforms. The optimal GPU performance was observed with the Jacobi-preconditioned CG solver, with a significant speedup over standard CG solver on CPU in our diversified test cases. Our analysis further shows that different matrix storage formats also considerably affect the efficiency of different linear PBE solvers on GPU, with the diagonal format best suited for our standard finite-difference linear systems. Further efficiency may be possible with matrix-free operations and integrated grid stencil setup specifically tailored for the banded matrices in PBE-specific linear systems.
Comparison of SAR calculation algorithms for the finite-difference time-domain method
International Nuclear Information System (INIS)
Laakso, Ilkka; Uusitupa, Tero; Ilvonen, Sami
2010-01-01
Finite-difference time-domain (FDTD) simulations of specific-absorption rate (SAR) have several uncertainty factors. For example, significantly varying SAR values may result from the use of different algorithms for determining the SAR from the FDTD electric field. The objective of this paper is to rigorously study the divergence of SAR values due to different SAR calculation algorithms and to examine if some SAR calculation algorithm should be preferred over others. For this purpose, numerical FDTD results are compared to analytical solutions in a one-dimensional layered model and a three-dimensional spherical object. Additionally, the implications of SAR calculation algorithms for dosimetry of anatomically realistic whole-body models are studied. The results show that the trapezium algorithm-based on the trapezium integration rule-is always conservative compared to the analytic solution, making it a good choice for worst-case exposure assessment. In contrast, the mid-ordinate algorithm-named after the mid-ordinate integration rule-usually underestimates the analytic SAR. The linear algorithm-which is approximately a weighted average of the two-seems to be the most accurate choice overall, typically giving the best fit with the shape of the analytic SAR distribution. For anatomically realistic models, the whole-body SAR difference between different algorithms is relatively independent of the used body model, incident direction and polarization of the plane wave. The main factors affecting the difference are cell size and frequency. The choice of the SAR calculation algorithm is an important simulation parameter in high-frequency FDTD SAR calculations, and it should be explained to allow intercomparison of the results between different studies. (note)
Double-grid finite-difference frequency-domain (DG-FDFD) method for scattering from chiral objects
Alkan, Erdogan; Elsherbeni, Atef
2013-01-01
This book presents the application of the overlapping grids approach to solve chiral material problems using the FDFD method. Due to the two grids being used in the technique, we will name this method as Double-Grid Finite Difference Frequency-Domain (DG-FDFD) method. As a result of this new approach the electric and magnetic field components are defined at every node in the computation space. Thus, there is no need to perform averaging during the calculations as in the aforementioned FDFD technique [16]. We formulate general 3D frequency-domain numerical methods based on double-grid
Directory of Open Access Journals (Sweden)
Navnit Jha
2014-04-01
Full Text Available An efficient numerical method based on quintic nonpolynomial spline basis and high order finite difference approximations has been presented. The scheme deals with the space containing hyperbolic and polynomial functions as spline basis. With the help of spline functions we derive consistency conditions and high order discretizations of the differential equation with the significant first order derivative. The error analysis of the new method is discussed briefly. The new method is analyzed for its efficiency using the physical problems. The order and accuracy of the proposed method have been analyzed in terms of maximum errors and root mean square errors.
International Nuclear Information System (INIS)
Lu Jia; Zhou Huaichun
2016-01-01
To deal with the staircase approximation problem in the standard finite-difference time-domain (FDTD) simulation, the two-dimensional boundary condition equations (BCE) method is proposed in this paper. In the BCE method, the standard FDTD algorithm can be used as usual, and the curved surface is treated by adding the boundary condition equations. Thus, while maintaining the simplicity and computational efficiency of the standard FDTD algorithm, the BCE method can solve the staircase approximation problem. The BCE method is validated by analyzing near field and far field scattering properties of the PEC and dielectric cylinders. The results show that the BCE method can maintain a second-order accuracy by eliminating the staircase approximation errors. Moreover, the results of the BCE method show good accuracy for cylinder scattering cases with different permittivities. (paper)
DEFF Research Database (Denmark)
Shyroki, Dzmitry; Lavrinenko, Andrei
2007-01-01
A complex-coordinate method known under the guise of the perfectly matched layer (PML) method for treating unbounded domains in computational electrodynamics is related to similar techniques in fluid dynamics and classical quantum theory. It may also find use in electronic-structure finite......-difference simulations. Straightforward transfer of the PML formulation to other fields does not seem feasible, however, since it is a unique feature of electrodynamics - the natural invariance - that allows analytic trick of complex coordinate scaling to be represented as pure modification of local material parameters...
Group foliation of finite difference equations
Thompson, Robert; Valiquette, Francis
2018-06-01
Using the theory of equivariant moving frames, a group foliation method for invariant finite difference equations is developed. This method is analogous to the group foliation of differential equations and uses the symmetry group of the equation to decompose the solution process into two steps, called resolving and reconstruction. Our constructions are performed algorithmically and symbolically by making use of discrete recurrence relations among joint invariants. Applications to invariant finite difference equations that approximate differential equations are given.
Khanday, M A; Hussain, Fida
2015-02-01
During cold exposure, peripheral tissues undergo vasoconstriction to minimize heat loss to preserve the maintenance of a normal core temperature. However, vasoconstricted tissues exposed to cold temperatures are susceptible to freezing and frostbite-related tissue damage. Therefore, it is imperative to establish a mathematical model for the estimation of tissue necrosis due to cold stress. To this end, an explicit formula of finite difference method has been used to obtain the solution of Pennes' bio-heat equation with appropriate boundary conditions to estimate the temperature profiles of dermal and subdermal layers when exposed to severe cold temperatures. The discrete values of nodal temperature were calculated at the interfaces of skin and subcutaneous tissues with respect to the atmospheric temperatures of 25 °C, 20 °C, 15 °C, 5 °C, -5 °C and -10 °C. The results obtained were used to identify the scenarios under which various degrees of frostbite occur on the surface of skin as well as the dermal and subdermal areas. The explicit formula of finite difference method proposed in this model provides more accurate predictions as compared to other numerical methods. This model of predicting tissue temperatures provides researchers with a more accurate prediction of peripheral tissue temperature and, hence, the susceptibility to frostbite during severe cold exposure. Copyright © 2014 Elsevier Ltd. All rights reserved.
International Nuclear Information System (INIS)
Dai, Hao; Si, Gangquan; Jia, Lixin; Zhang, Yanbin
2014-01-01
This paper investigates the problem of finite-time generalized function matrix projective lag synchronization between two different coupled dynamical networks with different dimensions of network nodes. The double power function nonlinear feedback control method is proposed in this paper to guarantee that the state trajectories of the response network converge to the state trajectories of the drive network according to a function matrix in a given finite time. Furthermore, in comparison with the traditional nonlinear feedback control method, the new method improves the synchronization efficiency, and shortens the finite synchronization time. Numerical simulation results are presented to illustrate the effectiveness of this method. (papers)
Simulation for light extraction in light emitting diode using finite domain time difference method
International Nuclear Information System (INIS)
Hong, Jun Hee; Park, Si Hyun
2008-01-01
InGaN based LEDs are indispensable to traffic light, full color displays, back lights in liquid crystals, and general lighting. The demand for high efficiency LEDs is on the increase. Recently we have reported the improvement of the light extraction efficiency of InGaN based LED. In this paper we show suitable a three dimensional (3 D)FDTD simulation method for LED simulation and we apply our FDTD simulation to our PNS LED structures, comparing the simulation results with the experimental results. For real FDTD simulation, we first must consider the spatial and temporal grid size. In order to obtain an accurate result, the spatial grid size must be so small that the feature of the field can be resolved. We computed the field power at each time at the surface 0.3mm away from the surface between GaN and air and integrate over surface. The calculations were conducted for the PNS LEDs employing the different height of SiO_2 columns, that is, h=160nm, h=350nm, h=550nm, h=750nm, and h=950nm. Simulation results according to different height is shown in Fig. 1(a,b). All simulation curves follow rough trend that it increases with column height and reaches the maximum at about 600nm height and then decreases with height. And this is a consistent with the trend from our experiments. Our FDTD simulation gives a possibility for design of LED structures of high extraction efficiency
Gerke, Kirill M.
2018-01-17
Permeability is one of the fundamental properties of porous media and is required for large-scale Darcian fluid flow and mass transport models. Whilst permeability can be measured directly at a range of scales, there are increasing opportunities to evaluate permeability from pore-scale fluid flow simulations. We introduce the free software Finite-Difference Method Stokes Solver (FDMSS) that solves Stokes equation using a finite-difference method (FDM) directly on voxelized 3D pore geometries (i.e. without meshing). Based on explicit convergence studies, validation on sphere packings with analytically known permeabilities, and comparison against lattice-Boltzmann and other published FDM studies, we conclude that FDMSS provides a computationally efficient and accurate basis for single-phase pore-scale flow simulations. By implementing an efficient parallelization and code optimization scheme, permeability inferences can now be made from 3D images of up to 109 voxels using modern desktop computers. Case studies demonstrate the broad applicability of the FDMSS software for both natural and artificial porous media.
Gerke, Kirill M.; Vasilyev, Roman V.; Khirevich, Siarhei; Collins, Daniel; Karsanina, Marina V.; Sizonenko, Timofey O.; Korost, Dmitry V.; Lamontagne, Sébastien; Mallants, Dirk
2018-05-01
Permeability is one of the fundamental properties of porous media and is required for large-scale Darcian fluid flow and mass transport models. Whilst permeability can be measured directly at a range of scales, there are increasing opportunities to evaluate permeability from pore-scale fluid flow simulations. We introduce the free software Finite-Difference Method Stokes Solver (FDMSS) that solves Stokes equation using a finite-difference method (FDM) directly on voxelized 3D pore geometries (i.e. without meshing). Based on explicit convergence studies, validation on sphere packings with analytically known permeabilities, and comparison against lattice-Boltzmann and other published FDM studies, we conclude that FDMSS provides a computationally efficient and accurate basis for single-phase pore-scale flow simulations. By implementing an efficient parallelization and code optimization scheme, permeability inferences can now be made from 3D images of up to 109 voxels using modern desktop computers. Case studies demonstrate the broad applicability of the FDMSS software for both natural and artificial porous media.
Directory of Open Access Journals (Sweden)
Pedram Iranmanesh
2014-01-01
Full Text Available Introduction: In the present study, the finite element method (FEM was used to investigate the effects of prosthesis material types on stress distribution of the bone surrounding implants and to evaluate stress distribution in three-unit implant-supported fixed dental prosthesis (FDP. Materials and Methods: A three-dimensional (3D finite element FDP model of the maxillary second premolar to the second molar was designed. Three load conditions were statically applied on the functional cusps in horizontal (57.0 N, vertical (200.0 N, and oblique (400.0 N, θ = 120° directions. Four standard framework materials were evaluated: Polymethyl methacrylate (PMMA, base-metal, porcelain fused to metal, andporcelain. Results: The maximum of von Mises stress in the oblique direction was higher than the vertical and horizontal directions in all conditions. In the bone-crestal section, the maximum von Mises stress (53.78 MPa was observed in PMMA within oblique load. In FDPs, the maximum stress was generated at the connector region in all conditions. Conclusion: A noticeable difference was not observed in the bone stress distribution pattern with different prosthetic materials. Although, higher stress value could be seen in polymethyl methacrylate, all types of prosthesis yielded the same stress distribution pattern in FDP. More clinical studies are needed to evaluate the survival rate of these materials.
Hajipour, Mojtaba; Jajarmi, Amin
2018-02-01
Using the Pontryagin's maximum principle for a time-delayed optimal control problem results in a system of coupled two-point boundary-value problems (BVPs) involving both time-advance and time-delay arguments. The analytical solution of this advance-delay two-point BVP is extremely difficult, if not impossible. This paper provides a discrete general form of the numerical solution for the derived advance-delay system by applying a finite difference θ-method. This method is also implemented for the infinite-time horizon time-delayed optimal control problems by using a piecewise version of the θ-method. A matrix formulation and the error analysis of the suggested technique are provided. The new scheme is accurate, fast and very effective for the optimal control of linear and nonlinear time-delay systems. Various types of finite- and infinite-time horizon problems are included to demonstrate the accuracy, validity and applicability of the new technique.
Directory of Open Access Journals (Sweden)
Treena Basu
2015-10-01
Full Text Available This paper proposes an approach for the space-fractional diffusion equation in one dimension. Since fractional differential operators are non-local, two main difficulties arise after discretization and solving using Gaussian elimination: how to handle the memory requirement of O(N2 for storing the dense or even full matrices that arise from application of numerical methods and how to manage the significant computational work count of O(N3 per time step, where N is the number of spatial grid points. In this paper, a fast iterative finite difference method is developed, which has a memory requirement of O(N and a computational cost of O(N logN per iteration. Finally, some numerical results are shown to verify the accuracy and efficiency of the new method.
International Nuclear Information System (INIS)
Morisaki, T.; Ono, H.
2005-01-01
A laser-induced liquid-crystal lens is formed by large optical non-linearity and anisotropic complex refractive indices in guest-host liquid crystals. We obtained light wave propagation characteristics of the laser-induced LC lens. Three analytical methods were used to obtain light wave propagation characteristics. Analysis by 3-dimensional heat conduction was applied to determine the refractive index in the liquid-crystal layer. Another method used was to determine light wave propagation characteristics in the laser-induced lens by means of the finite-difference tune domain (FDTD) method and diffraction theory. In this study, we draw a parallel between the experimental results and FDTD. Copyright (2003) AD-TECH - International Foundation for the Advancement of Technology Ltd
Directory of Open Access Journals (Sweden)
Polshkov Yulian M.
2013-11-01
Full Text Available The article considers data on the gross domestic product, consumer expenditures, gross investments and volume of foreign trade for the national economy. It is assumed that time is a discrete variable with one year iteration. The article uses finite-difference equations. It considers models with a high degree of the regulatory function of the state with respect to the consumer market. The econometric component is based on the hypothesis that each of the above said macro-economic indicators for this year depends on the gross domestic product for the previous time periods. Such an assumption gives a possibility to engage the least-squares method for building up linear models of the pair regression. The article obtains the time series model, which allows building point and interval forecasts for the gross domestic product for the next year based on the values of the gross domestic product for the current and previous years. The article draws a conclusion that such forecasts could be considered justified at least in the short-term prospect. From the mathematical point of view the built model is a heterogeneous finite-difference equation of the second order with constant ratios. The article describes specific features of such equations. It illustrates graphically the analytical view of solutions of the finite-difference equation. This gives grounds to differentiate national economies as sustainable growth economies, one-sided, weak or being in the stage of successful re-formation. The article conducts comparison of the listed types with specific economies of modern states.
Beyond Euler's Method: Implicit Finite Differences in an Introductory ODE Course
Kull, Trent C.
2011-01-01
A typical introductory course in ordinary differential equations (ODEs) exposes students to exact solution methods. However, many differential equations must be approximated with numerical methods. Textbooks commonly include explicit methods such as Euler's and Improved Euler's. Implicit methods are typically introduced in more advanced courses…
Energy Technology Data Exchange (ETDEWEB)
Yang, Fan; Yang, Haicheng; Guo, Xueyan; Ren Dai [University of Shanghai for Science and Technology, Shanghai (China); Yan, Yonghua [Shanghai Key Laboratory of Multiphase Flow and Heat Transfer in Power Engineering, Shanghai (China); Liu, Chaoqun [University of Texas at Arlington, Arlington (United States)
2017-06-15
Natural convection heat transfer in an inclined polar cavity was studied using a Finite-difference lattice Boltzmann method (FDLBM) based on a double-population approach for body-fitted coordinates. A D2G9 model coupled with the simplest TD2Q4 lattice model was applied to determine the velocity field and temperature field. For both velocity and temperature fields, the discrete spatial derivatives were obtained by combining the upwind scheme with the central scheme, and the discrete temporal term is obtained using a fourth-order Runge-Kutta scheme. Studies were carried out for different Rayleigh numbers and different inclination angles. The results in terms of streamlines, isotherms, and Nusselt numbers explain the heat transfer mechanism of natural convection in an inclined polar cavity due to the change of Rayleigh number and inclination angle.
International Nuclear Information System (INIS)
Deupree, R.G.
1977-01-01
Finite difference techniques were used to examine the coupling of radial pulsation and convection in stellar models having comparable time scales. Numerical procedures are emphasized, including diagnostics to help determine the range of free parameters
Directory of Open Access Journals (Sweden)
Arezoo Jahanbin
2014-01-01
Full Text Available Background. The aim of this study was to evaluate root displacement of the lower incisors fixed with FRC in different positions versus FSW retainers using the finite element method. Materials and Methods. 3D finite element models were designed for a mandibular anterior segment: Model 1: flexible spiral wire bonded to the lingual teeth surfaces, Model 2: FRC bonded to the upper third of lingual teeth surfaces, and Model 3: FRC bonded to the middle third. FE analysis was performed for three models and then tooth displacements were evaluated. Results. In contrast to lateral incisors and canines, the FSW retainer caused the central teeth to move more than the teeth bonded with FRC in both loadings. Comparison between Models 2 and 3 (in vertical loading showed that FRC retainers that bonded at the upper third of lingual teeth surfaces made central and canine teeth move less than FRC retainers bonded at the middle third; however, for lateral teeth it was the opposite. Conclusion. FRC retainers bonded at the upper third of lingual teeth surfaces make central and canine teeth move less than FRC retainers bonded at the middle third in vertical loading; however, for lateral teeth it was the opposite.
International Nuclear Information System (INIS)
Wang Yue; Wang Jian-Guo; Chen Zai-Gao
2015-01-01
Based on conformal construction of physical model in a three-dimensional Cartesian grid, an integral-based conformal convolutional perfectly matched layer (CPML) is given for solving the truncation problem of the open port when the enlarged cell technique conformal finite-difference time-domain (ECT-CFDTD) method is used to simulate the wave propagation inside a perfect electric conductor (PEC) waveguide. The algorithm has the same numerical stability as the ECT-CFDTD method. For the long-time propagation problems of an evanescent wave in a waveguide, several numerical simulations are performed to analyze the reflection error by sweeping the constitutive parameters of the integral-based conformal CPML. Our numerical results show that the integral-based conformal CPML can be used to efficiently truncate the open port of the waveguide. (paper)
DEFF Research Database (Denmark)
Hattel, Jesper; Hansen, Preben
1995-01-01
This paper presents a novel control volume based FD method for solving the equilibrium equations in terms of displacements, i.e. the generalized Navier equations. The method is based on the widely used cv-FDM solution of heat conduction and fluid flow problems involving a staggered grid formulati....... The resulting linear algebraic equations are solved by line-Gauss-Seidel....
Directory of Open Access Journals (Sweden)
Oleg Kudryavtsev
2013-01-01
factorization identity. Notice that our algorithm has the same complexity as the ones which use the explicit-implicit scheme, with a tridiagonal matrix. However, our method is more accurate. We support the advantage of the new method in terms of accuracy and convergence by using numerical experiments.
Convergency analysis of the high-order mimetic finite difference method
Energy Technology Data Exchange (ETDEWEB)
Lipnikov, Konstantin [Los Alamos National Laboratory; Veiga Da Beirao, L [UNIV DEGLI STUDI; Manzini, G [NON LANL
2008-01-01
We prove second-order convergence of the conservative variable and its flux in the high-order MFD method. The convergence results are proved for unstructured polyhedral meshes and full tensor diffusion coefficients. For the case of non-constant coefficients, we also develop a new family of high-order MFD methods. Theoretical result are confirmed through numerical experiments.
Colera, Manuel; Pérez-Saborid, Miguel
2017-09-01
A finite differences scheme is proposed in this work to compute in the time domain the compressible, subsonic, unsteady flow past an aerodynamic airfoil using the linearized potential theory. It improves and extends the original method proposed in this journal by Hariharan, Ping and Scott [1] by considering: (i) a non-uniform mesh, (ii) an implicit time integration algorithm, (iii) a vectorized implementation and (iv) the coupled airfoil dynamics and fluid dynamic loads. First, we have formulated the method for cases in which the airfoil motion is given. The scheme has been tested on well known problems in unsteady aerodynamics -such as the response to a sudden change of the angle of attack and to a harmonic motion of the airfoil- and has been proved to be more accurate and efficient than other finite differences and vortex-lattice methods found in the literature. Secondly, we have coupled our method to the equations governing the airfoil dynamics in order to numerically solve problems where the airfoil motion is unknown a priori as happens, for example, in the cases of the flutter and the divergence of a typical section of a wing or of a flexible panel. Apparently, this is the first self-consistent and easy-to-implement numerical analysis in the time domain of the compressible, linearized coupled dynamics of the (generally flexible) airfoil-fluid system carried out in the literature. The results for the particular case of a rigid airfoil show excellent agreement with those reported by other authors, whereas those obtained for the case of a cantilevered flexible airfoil in compressible flow seem to be original or, at least, not well-known.
Peridynamic Multiscale Finite Element Methods
Energy Technology Data Exchange (ETDEWEB)
Costa, Timothy [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Bond, Stephen D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Littlewood, David John [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Moore, Stan Gerald [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2015-12-01
The problem of computing quantum-accurate design-scale solutions to mechanics problems is rich with applications and serves as the background to modern multiscale science research. The prob- lem can be broken into component problems comprised of communicating across adjacent scales, which when strung together create a pipeline for information to travel from quantum scales to design scales. Traditionally, this involves connections between a) quantum electronic structure calculations and molecular dynamics and between b) molecular dynamics and local partial differ- ential equation models at the design scale. The second step, b), is particularly challenging since the appropriate scales of molecular dynamic and local partial differential equation models do not overlap. The peridynamic model for continuum mechanics provides an advantage in this endeavor, as the basic equations of peridynamics are valid at a wide range of scales limiting from the classical partial differential equation models valid at the design scale to the scale of molecular dynamics. In this work we focus on the development of multiscale finite element methods for the peridynamic model, in an effort to create a mathematically consistent channel for microscale information to travel from the upper limits of the molecular dynamics scale to the design scale. In particular, we first develop a Nonlocal Multiscale Finite Element Method which solves the peridynamic model at multiple scales to include microscale information at the coarse-scale. We then consider a method that solves a fine-scale peridynamic model to build element-support basis functions for a coarse- scale local partial differential equation model, called the Mixed Locality Multiscale Finite Element Method. Given decades of research and development into finite element codes for the local partial differential equation models of continuum mechanics there is a strong desire to couple local and nonlocal models to leverage the speed and state of the
Wu, Zedong; Alkhalifah, Tariq Ali
2018-01-01
Numerical simulation of the acoustic wave equation in either isotropic or anisotropic media is crucial to seismic modeling, imaging and inversion. Actually, it represents the core computation cost of these highly advanced seismic processing methods
Calculation of large ion densities under HVdc transmission lines by the finite difference method
International Nuclear Information System (INIS)
Suda, Tomotaka; Sunaga, Yoshitaka
1995-01-01
A calculation method for large ion densities (charged aerosols) under HVdc transmission lines was developed considering both the charging mechanism of aerosols by small ions and the drifting process by wind. Large ion densities calculated by this method agreed well with the ones measured under the Shiobara HVdc test line on the lateral profiles at ground level up to about 70m downwind from the line. Measured values decreased more quickly than calculated ones farther downwind from the line. Considering the effect of point discharge from ground cover (earth corona) improved the agreement in the farther downwind region
Programming the finite element method
Smith, I M; Margetts, L
2013-01-01
Many students, engineers, scientists and researchers have benefited from the practical, programming-oriented style of the previous editions of Programming the Finite Element Method, learning how to develop computer programs to solve specific engineering problems using the finite element method. This new fifth edition offers timely revisions that include programs and subroutine libraries fully updated to Fortran 2003, which are freely available online, and provides updated material on advances in parallel computing, thermal stress analysis, plasticity return algorithms, convection boundary c
de Graaf, C.S.L.; Kandhai, D.; Sloot, P.M.A.
According to Basel III, financial institutions have to charge a credit valuation adjustment (CVA) to account for a possible counterparty default. Calculating this measure and its sensitivities is one of the biggest challenges in risk management. Here, we introduce an efficient method for the
C.S.L. de Graaf (Kees); B.D. Kandhai; P.M.A. Sloot
2017-01-01
htmlabstractAccording to Basel III, financial institutions have to charge a credit valuation adjustment (CVA) to account for a possible counterparty default. Calculating this measure and its sensitivities is one of the biggest challenges in risk management. Here, we introduce an efficient method
Ping, Jing; Al-Hinai, Omar; Wheeler, Mary F.
2017-01-01
-Gaussian in this case, it is a challenge to estimate fracture distributions by conventional history matching approaches. In this work, a method that combines vector-based level-set parameterization technique and ensemble Kalman filter (EnKF) for estimating fracture
Czech Academy of Sciences Publication Activity Database
Papáček, Š.; Matonoha, Ctirad; Štumbauer, V.; Štys, D.
2012-01-01
Roč. 82, č. 10 (2012), s. 2022-2032 ISSN 0378-4754. [Modelling 2009. IMACS Conference on Mathematical Modelling and Computational Methods in Applied Sciences and Engineering /4./. Rožnov pod Radhoštěm, 22.06.2009-26.06.2009] Grant - others:CENAKVA(CZ) CZ.1.05/2.1.00/01.0024; GA JU(CZ) 152//2010/Z Institutional research plan: CEZ:AV0Z10300504 Keywords : multiscale modelling * distributed parameter system * boundary value problem * random walk * photosynthetic factory Subject RIV: EI - Biotechnology ; Bionics Impact factor: 0.836, year: 2012
Directory of Open Access Journals (Sweden)
Koichi Narahara
2012-01-01
Full Text Available Nonlinear transmission lines, which define transmission lines periodically loaded with nonlinear devices such as varactors, diodes, and transistors, are modeled in the framework of finite-difference time-domain (FDTD method. Originally, some root-finding routine is needed to evaluate the contributions of nonlinear device currents appropriately to the temporally advanced electrical fields. Arbitrary nonlinear transmission lines contain large amount of nonlinear devices; therefore, it costs too much time to complete calculations. To reduce the calculation time, we recently developed a simple model of diodes to eliminate root-finding routines in an FDTD solver. Approximating the diode current-voltage relation by a piecewise-linear function, an extended Ampere's law is solved in a closed form for the time-advanced electrical fields. In this paper, we newly develop an FDTD model of field-effect transistors (FETs, together with several numerical examples that demonstrate pulse-shortening phenomena in a traveling-wave FET.
Directory of Open Access Journals (Sweden)
Alexandre Bambina
2018-01-01
Full Text Available Limitation of the cloak-size reduction is investigated numerically by a finite-difference time-domain (FDTD method. A metallic pole that imitates an antenna is cloaked with an anisotropic and parameter-gradient medium against electromagnetic-wave propagation in microwave range. The cloaking structure is a metamaterial submerged in a plasma confined in a vacuum chamber made of glass. The smooth-permittivity plasma can be compressed in the radial direction, which enables us to decrease the size of the cloak. Theoretical analysis is performed numerically by comparing scattering waves in various cases; there exists a high reduction of the scattering wave when the radius of the cloak is larger than a quarter of one wavelength. This result indicates that the required size of the cloaking layer is more than an object scale in the Rayleigh scattering regime.
A conservative finite difference method for the numerical solution of plasma fluid equations
International Nuclear Information System (INIS)
Colella, P.; Dorr, M.R.; Wake, D.D.
1999-01-01
This paper describes a numerical method for the solution of a system of plasma fluid equations. The fluid model is similar to those employed in the simulation of high-density, low-pressure plasmas used in semiconductor processing. The governing equations consist of a drift-diffusion model of the electrons, together with an internal energy equation, coupled via Poisson's equation to a system of Euler equations for each ion species augmented with electrostatic force, collisional, and source/sink terms. The time integration of the full system is performed using an operator splitting that conserves space charge and avoids dielectric relaxation timestep restrictions. The integration of the individual ion species and electrons within the time-split advancement is achieved using a second-order Godunov discretization of the hyperbolic terms, modified to account for the significant role of the electric field in the propagation of acoustic waves, combined with a backward Euler discretization of the parabolic terms. Discrete boundary conditions are employed to accommodate the plasma sheath boundary layer on underresolved grids. The algorithm is described for the case of a single Cartesian grid as the first step toward an implementation on a locally refined grid hierarchy in which the method presented here may be applied on each refinement level
DeBonis, James R.
2013-01-01
A computational fluid dynamics code that solves the compressible Navier-Stokes equations was applied to the Taylor-Green vortex problem to examine the code s ability to accurately simulate the vortex decay and subsequent turbulence. The code, WRLES (Wave Resolving Large-Eddy Simulation), uses explicit central-differencing to compute the spatial derivatives and explicit Low Dispersion Runge-Kutta methods for the temporal discretization. The flow was first studied and characterized using Bogey & Bailley s 13-point dispersion relation preserving (DRP) scheme. The kinetic energy dissipation rate, computed both directly and from the enstrophy field, vorticity contours, and the energy spectra are examined. Results are in excellent agreement with a reference solution obtained using a spectral method and provide insight into computations of turbulent flows. In addition the following studies were performed: a comparison of 4th-, 8th-, 12th- and DRP spatial differencing schemes, the effect of the solution filtering on the results, the effect of large-eddy simulation sub-grid scale models, and the effect of high-order discretization of the viscous terms.
International Nuclear Information System (INIS)
Kraus, H.G.; Jones, J.L.
1986-01-01
The problem of non-linear superconducting magnet and electrical protection circuit system transients is formulated. To enable studying the effects of coil normalization transients, coil distortion (due to imbalanced magnetic forces), internal coil arcs and shorts, and other normal and off-normal circuit element responses, the following capabilities are included: temporal, voltage and current-dependent voltage sources, current sources, resistors, capacitors and inductors. The concept of self-mutual inductance, and the form of the associated inductance matrix, is discussed for internally shorted coils. This is a Kirchhoff's voltage loop law and Kirchhoff's current node law formulation. The non-linear integrodifferential equation set is solved via a unique hybrid finite difference/integral finite element technique. (author)
Zhu, D.; Zhu, H.; Luo, Y.; Chen, X.
2008-12-01
We use a new finite difference method (FDM) and the slip-weakening law to model the rupture dynamics of a non-planar fault embedded in a 3-D elastic media with free surface. The new FDM, based on boundary- conforming grid, sets up the mapping equations between the curvilinear coordinate and the Cartesian coordinate and transforms irregular physical space to regular computational space; it also employs a higher- order non-staggered DRP/opt MacCormack scheme which is of low dispersion and low dissipation so that the high accuracy and stability of our rupture modeling are guaranteed. Compared with the previous methods, not only we can compute the spontaneous rupture of an arbitrarily shaped fault, but also can model the influence of the surface topography on the rupture process of earthquake. In order to verify the feasibility of this method, we compared our results and other previous results, and found out they matched perfectly. Thanks to the boundary-conforming FDM, problems such as dynamic rupture with arbitrary dip, strike and rake over an arbitrary curved plane can be handled; and supershear or subshear rupture can be simulated with different parameters such as the initial stresses and the critical slip displacement Dc. Besides, our rupture modeling is economical to be implemented owing to its high efficiency and does not suffer from displacement leakage. With the help of inversion data of rupture by field observations, this method is convenient to model rupture processes and seismograms of natural earthquakes.
Finite-difference methods in multi-dimensional two-phase flow
International Nuclear Information System (INIS)
Travis, J.R.
1977-01-01
In the summer of 1974, the Theoretical Division of the Los Alamos Scientific Laboratory began several research programs in the area of reactor safety for the United States Nuclear Regulatory Commission. Research efforts were started in the Liquid Metal Fast Breeder (LMFBR) and the Light Water Reactor (LWR) safety programs. The character of the Theoretical Division was to develop computer codes for the safety analysis of these reactor systems. The question of whether or not, during the course of a hypothetical accident sequence in an LMFBR, the core will subside to a coolable configuration without secondary critical bursts has never been resolved. To aid the study of this question, a computer program called SIMMER (S/sub N/, Implicit, Multified, Multicomponent, Eulerian Recriticality) was to be developed to predict the dynamics of extreme hypothetical accident sequences during which extended core motion is expected. This time-dependent computer code called for combining an advanced multidimensional, multiphase fluid dynamic methodology with multidimensional neutron transport theory and improved equation-of-state technology. In the LWR program, the research emphasis was to push forward in two areas: (1) the development of advanced multiphase fluid dynamic methods and computer programs for performing basic research and analyzing areas in thermal hydraulics important to the safety of water reactors, and (2) the development of an advanced ''best estimate'' systems code called TRAC (Transient Reactor Analysis Code) for analyzing loss-of-coolant accidents and anticipated-transients-without-scram in light water reactors
Investigation of a natural convection in a small slot using a finite difference method
International Nuclear Information System (INIS)
Schira, P.; Guenther, C.; Mueller, U.
1984-07-01
Experimental results by Koster who studied natural convection processes in slender Hele-Shaw cells are simulated with an existing two-dimensional natural convection code. This investigation yields the following results: The basic model of the calculations, which assumes a constant temperature across the gap (smallest extent of the Hele-Shaw cell) and thus without heat exchange with the Plexiglas windows, leads to an underestimation of the experimentally obtained critical Rayleigh numbers (onset of convection, onset of oscillatory convection) by one order of magnitude and an overestimation of the nondimensional period compared to experimental findings. Another version of the code, which permits heat exchange with the windows reveals an overestimation of the critical Rayleigh numbers and smaller dimensionless periods than the experiments. By these two different approaches a twoside bounding the Koster's experiments are achieved. As the modified version overestimates the real heat transfer from and to the windows it may be concluded that using a suitably adapted heat transfer coefficient for the thermal coupling of the fluid and the windows numerical simulation would also reproduce quantitatively the results of Koster. The reason for the break down of the steady flow solution and the onset of transient flow was studied numerically by examining a model proposed by Howard. At this time no really satisfying answer to this question is available. (orig./GL) [de
Finite difference order doubling in two dimensions
International Nuclear Information System (INIS)
Killingbeck, John P; Jolicard, Georges
2008-01-01
An order doubling process previously used to obtain eighth-order eigenvalues from the fourth-order Numerov method is applied to the perturbed oscillator in two dimensions. A simple method of obtaining high order finite difference operators is reported and an odd parity boundary condition is found to be effective in facilitating the smooth operation of the order doubling process
Sun, Qiang; Wu, Guo Xiong
2013-03-01
A mathematical model and a numerical solution procedure are developed to simulate flow field through a 3D permeable vessel with multibranches embedded in a solid tumour. The model is based on Poisseuille's law for the description of the flow through the vessels, Darcy's law for the fluid field inside the tumour interstitium, and Starling's law for the flux transmitted across the vascular walls. The solution procedure is based on a coupled method, in which the finite difference method is used for the flow in the vessels and the boundary element method is used for the flow in the tumour. When vessels meet each other at a junction, the pressure continuity and mass conservation are imposed at the junction. Three typical representative structures within the tumour vasculature, symmetrical dichotomous branching, asymmetrical bifurcation with uneven radius of daughter vessels and trifurcation, are investigated in detail as case studies. These results have demonstrated the features of tumour flow environment by the pressure distributions and flow velocity field. Copyright © 2012 John Wiley & Sons, Ltd.
Electron-phonon coupling from finite differences
Monserrat, Bartomeu
2018-02-01
The interaction between electrons and phonons underlies multiple phenomena in physics, chemistry, and materials science. Examples include superconductivity, electronic transport, and the temperature dependence of optical spectra. A first-principles description of electron-phonon coupling enables the study of the above phenomena with accuracy and material specificity, which can be used to understand experiments and to predict novel effects and functionality. In this topical review, we describe the first-principles calculation of electron-phonon coupling from finite differences. The finite differences approach provides several advantages compared to alternative methods, in particular (i) any underlying electronic structure method can be used, and (ii) terms beyond the lowest order in the electron-phonon interaction can be readily incorporated. But these advantages are associated with a large computational cost that has until recently prevented the widespread adoption of this method. We describe some recent advances, including nondiagonal supercells and thermal lines, that resolve these difficulties, and make the calculation of electron-phonon coupling from finite differences a powerful tool. We review multiple applications of the calculation of electron-phonon coupling from finite differences, including the temperature dependence of optical spectra, superconductivity, charge transport, and the role of defects in semiconductors. These examples illustrate the advantages of finite differences, with cases where semilocal density functional theory is not appropriate for the calculation of electron-phonon coupling and many-body methods such as the GW approximation are required, as well as examples in which higher-order terms in the electron-phonon interaction are essential for an accurate description of the relevant phenomena. We expect that the finite difference approach will play a central role in future studies of the electron-phonon interaction.
A three-point backward finite-difference method has been derived for a system of mixed hyperbolic¯¯parabolic (convection¯¯diffusion) partial differential equations (mixed PDEs). The method resorts to the three-point backward differenci...
International Nuclear Information System (INIS)
Garcia-Herranz, Nuria; Cabellos, Oscar; Aragones, Jose M.; Ahnert, Carol
2003-01-01
In order to take into account in a more effective and accurate way the intranodal heterogeneities in coarse-mesh finite-difference (CMFD) methods, a new equivalent parameter generation methodology has been developed and tested. This methodology accounts for the dependence of the nodal homogeneized two-group cross sections and nodal coupling factors, with interface flux discontinuity (IFD) factors that account for heterogeneities on the flux-spectrum and burnup intranodal distributions as well as on neighbor effects.The methodology has been implemented in an analytic CMFD method, rigorously obtained for homogeneous nodes with transverse leakage and generalized now for heterogeneous nodes by including IFD heterogeneity factors. When intranodal mesh node heterogeneity vanishes, the heterogeneous solution tends to the analytic homogeneous nodal solution. On the other hand, when intranodal heterogeneity increases, a high accuracy is maintained since the linear and nonlinear feedbacks on equivalent parameters have been shown to be as a very effective way of accounting for heterogeneity effects in two-group multidimensional coarse-mesh diffusion calculations
Iterative methods for 3D implicit finite-difference migration using the complex Padé approximation
International Nuclear Information System (INIS)
Costa, Carlos A N; Campos, Itamara S; Costa, Jessé C; Neto, Francisco A; Schleicher, Jörg; Novais, Amélia
2013-01-01
Conventional implementations of 3D finite-difference (FD) migration use splitting techniques to accelerate performance and save computational cost. However, such techniques are plagued with numerical anisotropy that jeopardises the correct positioning of dipping reflectors in the directions not used for the operator splitting. We implement 3D downward continuation FD migration without splitting using a complex Padé approximation. In this way, the numerical anisotropy is eliminated at the expense of a computationally more intensive solution of a large-band linear system. We compare the performance of the iterative stabilized biconjugate gradient (BICGSTAB) and that of the multifrontal massively parallel direct solver (MUMPS). It turns out that the use of the complex Padé approximation not only stabilizes the solution, but also acts as an effective preconditioner for the BICGSTAB algorithm, reducing the number of iterations as compared to the implementation using the real Padé expansion. As a consequence, the iterative BICGSTAB method is more efficient than the direct MUMPS method when solving a single term in the Padé expansion. The results of both algorithms, here evaluated by computing the migration impulse response in the SEG/EAGE salt model, are of comparable quality. (paper)
Directory of Open Access Journals (Sweden)
Richasanty Septima S
2017-03-01
Full Text Available The research in this thesis was done to examine the model of traffic flow of volcanic disaster evacuation path for uphill and downhill roads. The assessment was focused on the area of disaster evacuation path from the Pante Raya Bener Meriah intersection to Takengon. This model is assessed for two different types of time when which a disaster occurs; the disaster occurred at night and the disaster occurred during the day, especially during peak hours (working hours. The model was developed with attention to the exixtence of inflow and outflow along the evacuation route. Furthermore, the model obtained is solved numerically by using finite difference method. The chosen approach of this method is upwind scheme with time and space steps using forward difference and backward difference. The solution of this model in the form of simulated vehicle density along evacuation pathways. The research conducted is in the form of a model of traffic flow on evacuation paths and restricted to the inflow and outflow without alternative path as well as the conditions of the road which are uphill and downhill, showed a high density of vehicles either at night or during the day. Uphill road conditions resulted in decreased vehicle speed and vehicle density will increase, while downhill road conditions resulted in increased vehicle speed and vehicle density will decrease, meaning that the road conditions which are uphill and downhill will greatly affect the process of evacuation. Degree vehicles of evacuation efficiency occuring at night without an alternative pathway produces a high efficiency so that it can be interpreted that the evacuation process in the evening was successful and runs better than the evacuation process during the day, and this is caused by the existence of vehicles on the road evacuation process started thus affecting the efficiency levels.
Moriyama, Eduardo H.; Zangaro, Renato A.; Lobo, Paulo D. d. C.; Villaverde, Antonio G. J. B.; Watanabe-Sei, Ii; Pacheco, Marcos T. T.; Otsuka, Daniel K.
2002-06-01
Thermal damage in dental pulp during Nd:YAG laser irradiation have been studied by several researchers; but due to dentin inhomogeneous structure, laser interaction with dentin in the hypersensitivity treatment are not fully understood. In this work, heat distribution profile on human dentine samples irradiated with Nd:YAG laser was simulated at surface and subjacent layers. Calculations were carried out using the Crank-Nicolson's finite difference method. Sixteen dentin samples with 1,5 mm of thickness were evenly distributed into four groups and irradiated with Nd:YAG laser pulses, according to the following scheme: (I) 1 pulse of 900 mJ, (II) 2 pulses of 450 mJ, (III) 3 pulses of 300 mJ, (IV) 6 pulses of 150 mJ; corresponding to a total laser energy of 900 mJ. The pulse interval was 300ms, the pulse duration of 900 ms and irradiated surface area of 0,005 mm2. Laser induced morphological changes in dentin were observed for all the irradiated samples. The heat distribution throughout the dentin layer, from the external dentin surface to the pulpal chamber wall, was calculated for each case, in order to obtain further information about the pulsed Nd:YAG laser-oral hard tissue interaction. The simulation showed significant differences in the final temperature at the pulpal chamber, depending on the exposition time and the energy contained in the laser pulse.
Coco, Armando; Russo, Giovanni
2018-05-01
In this paper we propose a second-order accurate numerical method to solve elliptic problems with discontinuous coefficients (with general non-homogeneous jumps in the solution and its gradient) in 2D and 3D. The method consists of a finite-difference method on a Cartesian grid in which complex geometries (boundaries and interfaces) are embedded, and is second order accurate in the solution and the gradient itself. In order to avoid the drop in accuracy caused by the discontinuity of the coefficients across the interface, two numerical values are assigned on grid points that are close to the interface: a real value, that represents the numerical solution on that grid point, and a ghost value, that represents the numerical solution extrapolated from the other side of the interface, obtained by enforcing the assigned non-homogeneous jump conditions on the solution and its flux. The method is also extended to the case of matrix coefficient. The linear system arising from the discretization is solved by an efficient multigrid approach. Unlike the 1D case, grid points are not necessarily aligned with the normal derivative and therefore suitable stencils must be chosen to discretize interface conditions in order to achieve second order accuracy in the solution and its gradient. A proper treatment of the interface conditions will allow the multigrid to attain the optimal convergence factor, comparable with the one obtained by Local Fourier Analysis for rectangular domains. The method is robust enough to handle large jump in the coefficients: order of accuracy, monotonicity of the errors and good convergence factor are maintained by the scheme.
Determination of finite-difference weights using scaled binomial windows
Chu, Chunlei; Stoffa, Paul L.
2012-01-01
The finite-difference method evaluates a derivative through a weighted summation of function values from neighboring grid nodes. Conventional finite-difference weights can be calculated either from Taylor series expansions or by Lagrange interpolation polynomials. The finite-difference method can be interpreted as a truncated convolutional counterpart of the pseudospectral method in the space domain. For this reason, we also can derive finite-difference operators by truncating the convolution series of the pseudospectral method. Various truncation windows can be employed for this purpose and they result in finite-difference operators with different dispersion properties. We found that there exists two families of scaled binomial windows that can be used to derive conventional finite-difference operators analytically. With a minor change, these scaled binomial windows can also be used to derive optimized finite-difference operators with enhanced dispersion properties. © 2012 Society of Exploration Geophysicists.
Determination of finite-difference weights using scaled binomial windows
Chu, Chunlei
2012-05-01
The finite-difference method evaluates a derivative through a weighted summation of function values from neighboring grid nodes. Conventional finite-difference weights can be calculated either from Taylor series expansions or by Lagrange interpolation polynomials. The finite-difference method can be interpreted as a truncated convolutional counterpart of the pseudospectral method in the space domain. For this reason, we also can derive finite-difference operators by truncating the convolution series of the pseudospectral method. Various truncation windows can be employed for this purpose and they result in finite-difference operators with different dispersion properties. We found that there exists two families of scaled binomial windows that can be used to derive conventional finite-difference operators analytically. With a minor change, these scaled binomial windows can also be used to derive optimized finite-difference operators with enhanced dispersion properties. © 2012 Society of Exploration Geophysicists.
Energy Technology Data Exchange (ETDEWEB)
Sasaki, Y [Kyushu University, Fukuoka (Japan). Faculty of Engineering
1997-05-27
To enhance the reliability of electromagnetic/magnetotelluric (MT) survey, calculation results of finite-element methods (FEMs) and finite difference methods (FDMs) were compared. Accuracy of individual methods and convergence of repitition solution were examined. As a result of the investigation, it was found that appropriate accuracy can be obtained from the edge FEM and FDM for the example of vertical magnetic dipole, and that the best accuracy can be obtained from the FDM among four methods for the example of MT survey. It was revealed that the ICBCG (incomplete Cholesky bi-conjugate gradient) method is an excellent method as a solution method of simultaneous equations from the viewpoint of accuracy and calculation time. For the joint FEM, solutions of SOR method converged for both the examples. It was concluded that the cause of error is not due to the error of numerical calculation, but due to the consideration without discontinuity of electric field. The conditions of coefficient matrix increased with decreasing the frequency, which resulted in the unstable numerical calculation. It would be required to incorporate the constraint in a certain form. 4 refs., 12 figs.
A new time–space domain high-order finite-difference method for the acoustic wave equation
Liu, Yang; Sen, Mrinal K.
2009-01-01
A new unified methodology was proposed in Finkelstein and Kastner (2007) [39] to derive spatial finite-difference (FD) coefficients in the joint time-space domain to reduce numerical dispersion. The key idea of this method is that the dispersion relation is completely satisfied at several designated frequencies. We develop this new time-space domain FD method further for 1D, 2D and 3D acoustic wave modeling using a plane wave theory and the Taylor series expansion. New spatial FD coefficients are frequency independent though they lead to a frequency dependent numerical solution. We prove that the modeling accuracy is 2nd-order when the conventional (2 M)th-order space domain FD and the 2nd-order time domain FD stencils are directly used to solve the acoustic wave equation. However, under the same discretization, the new 1D method can reach (2 M)th-order accuracy and is always stable. The 2D method can reach (2 M)th-order accuracy along eight directions and has better stability. Similarly, the 3D method can reach (2 M)th-order accuracy along 48 directions and also has better stability than the conventional FD method. The advantages of the new method are also demonstrated by the results of dispersion analysis and numerical modeling of acoustic wave equation for homogeneous and inhomogeneous acoustic models. In addition, we study the influence of the FD stencil length on numerical modeling for 1D inhomogeneous media, and derive an optimal FD stencil length required to balance the accuracy and efficiency of modeling. A new time-space domain high-order staggered-grid FD method for the 1D acoustic wave equation with variable densities is also developed, which has similar advantages demonstrated by dispersion analysis, stability analysis and modeling experiments. The methodology presented in this paper can be easily extended to solve similar partial difference equations arising in other fields of science and engineering. © 2009 Elsevier Inc.
A new time–space domain high-order finite-difference method for the acoustic wave equation
Liu, Yang
2009-12-01
A new unified methodology was proposed in Finkelstein and Kastner (2007) [39] to derive spatial finite-difference (FD) coefficients in the joint time-space domain to reduce numerical dispersion. The key idea of this method is that the dispersion relation is completely satisfied at several designated frequencies. We develop this new time-space domain FD method further for 1D, 2D and 3D acoustic wave modeling using a plane wave theory and the Taylor series expansion. New spatial FD coefficients are frequency independent though they lead to a frequency dependent numerical solution. We prove that the modeling accuracy is 2nd-order when the conventional (2 M)th-order space domain FD and the 2nd-order time domain FD stencils are directly used to solve the acoustic wave equation. However, under the same discretization, the new 1D method can reach (2 M)th-order accuracy and is always stable. The 2D method can reach (2 M)th-order accuracy along eight directions and has better stability. Similarly, the 3D method can reach (2 M)th-order accuracy along 48 directions and also has better stability than the conventional FD method. The advantages of the new method are also demonstrated by the results of dispersion analysis and numerical modeling of acoustic wave equation for homogeneous and inhomogeneous acoustic models. In addition, we study the influence of the FD stencil length on numerical modeling for 1D inhomogeneous media, and derive an optimal FD stencil length required to balance the accuracy and efficiency of modeling. A new time-space domain high-order staggered-grid FD method for the 1D acoustic wave equation with variable densities is also developed, which has similar advantages demonstrated by dispersion analysis, stability analysis and modeling experiments. The methodology presented in this paper can be easily extended to solve similar partial difference equations arising in other fields of science and engineering. © 2009 Elsevier Inc.
Energy Technology Data Exchange (ETDEWEB)
Oh, Jae-Yong, E-mail: tylor@kaeri.re.kr [Korea Atomic Energy Research Institute, Daedeok-daero 1045, Yuseong, Daejeon 305-353 (Korea, Republic of); Koo, Yang-Hyun; Lee, Byung-Ho; Tahk, Young-Wook [Korea Atomic Energy Research Institute, Daedeok-daero 1045, Yuseong, Daejeon 305-353 (Korea, Republic of)
2011-07-15
This paper evaluated the effects of porosity on the effective thermal conductivity of UO{sub 2} fuel by combining the Potts model and the finite difference method (FDM). Two types of microstructures representing irradiated UO{sub 2} microstructures were simulated by the Potts model in the three dimensional cubic system. One represented very small intragranular bubbles and a few intergranular bubbles under a low temperature condition. The other represented large intergranular bubbles under a high temperature or annealing condition. For the simulated microstructures, the effective thermal conductivities were determined by FDM calculation of the temperature distributions under steady state condition. They were compared with an experimental equation and the effect of bubble morphology was investigated by fitting a porosity shape factor in the Maxwell-Eucken equation. The simulation results showed a good agreement with an experimental equation and demonstrated the capability of the Potts model to provide information on microstructure for calculating the effective thermal conductivity of UO{sub 2} fuel.
The finite-difference and finite-element modeling of seismic wave propagation and earthquake motion
International Nuclear Information System (INIS)
Moszo, P.; Kristek, J.; Galis, M.; Pazak, P.; Balazovijech, M.
2006-01-01
Numerical modeling of seismic wave propagation and earthquake motion is an irreplaceable tool in investigation of the Earth's structure, processes in the Earth, and particularly earthquake phenomena. Among various numerical methods, the finite-difference method is the dominant method in the modeling of earthquake motion. Moreover, it is becoming more important in the seismic exploration and structural modeling. At the same time we are convinced that the best time of the finite-difference method in seismology is in the future. This monograph provides tutorial and detailed introduction to the application of the finite-difference, finite-element, and hybrid finite-difference-finite-element methods to the modeling of seismic wave propagation and earthquake motion. The text does not cover all topics and aspects of the methods. We focus on those to which we have contributed. (Author)
Finite element methods a practical guide
Whiteley, Jonathan
2017-01-01
This book presents practical applications of the finite element method to general differential equations. The underlying strategy of deriving the finite element solution is introduced using linear ordinary differential equations, thus allowing the basic concepts of the finite element solution to be introduced without being obscured by the additional mathematical detail required when applying this technique to partial differential equations. The author generalizes the presented approach to partial differential equations which include nonlinearities. The book also includes variations of the finite element method such as different classes of meshes and basic functions. Practical application of the theory is emphasised, with development of all concepts leading ultimately to a description of their computational implementation illustrated using Matlab functions. The target audience primarily comprises applied researchers and practitioners in engineering, but the book may also be beneficial for graduate students.
High-Order Entropy Stable Finite Difference Schemes for Nonlinear Conservation Laws: Finite Domains
Fisher, Travis C.; Carpenter, Mark H.
2013-01-01
Developing stable and robust high-order finite difference schemes requires mathematical formalism and appropriate methods of analysis. In this work, nonlinear entropy stability is used to derive provably stable high-order finite difference methods with formal boundary closures for conservation laws. Particular emphasis is placed on the entropy stability of the compressible Navier-Stokes equations. A newly derived entropy stable weighted essentially non-oscillatory finite difference method is used to simulate problems with shocks and a conservative, entropy stable, narrow-stencil finite difference approach is used to approximate viscous terms.
Finite elements methods in mechanics
Eslami, M Reza
2014-01-01
This book covers all basic areas of mechanical engineering, such as fluid mechanics, heat conduction, beams, and elasticity with detailed derivations for the mass, stiffness, and force matrices. It is especially designed to give physical feeling to the reader for finite element approximation by the introduction of finite elements to the elevation of elastic membrane. A detailed treatment of computer methods with numerical examples are provided. In the fluid mechanics chapter, the conventional and vorticity transport formulations for viscous incompressible fluid flow with discussion on the method of solution are presented. The variational and Galerkin formulations of the heat conduction, beams, and elasticity problems are also discussed in detail. Three computer codes are provided to solve the elastic membrane problem. One of them solves the Poisson’s equation. The second computer program handles the two dimensional elasticity problems, and the third one presents the three dimensional transient heat conducti...
International Nuclear Information System (INIS)
O'Dell, R.D.; Stepanek, J.; Wagner, M.R.
1983-01-01
The aim of the present work is to compare and discuss the three of the most advanced two dimensional transport methods, the finite difference and nodal discrete ordinates and surface flux method, incorporated into the transport codes TWODANT, TWOTRAN-NODAL, MULTIMEDIUM and SURCU. For intercomparison the eigenvalue and the neutron flux distribution are calculated using these codes in the LWR pool reactor benchmark problem. Additionally the results are compared with some results obtained by French collision probability transport codes MARSYAS and TRIDENT. Because the transport solution of this benchmark problem is close to its diffusion solution some results obtained by the finite element diffusion code FINELM and the finite difference diffusion code DIFF-2D are included
Energy Technology Data Exchange (ETDEWEB)
Dattoli, Giuseppe; Torre, Amalia [ENEA, Centro Ricerche Frascati, Rome (Italy). Dipt. Innovazione; Ottaviani, Pier Luigi [ENEA, Centro Ricerche Bologna (Italy); Vasquez, Luis [Madris, Univ. Complutense (Spain). Dept. de Matemateca Aplicado
1997-10-01
The finite-difference based integration method for evolution-line equations is discussed in detail and framed within the general context of the evolution operator picture. Exact analytical methods are described to solve evolution-like equations in a quite general physical context. The numerical technique based on the factorization formulae of exponential operator is then illustrated and applied to the evolution-operator in both classical and quantum framework. Finally, the general view to the finite differencing schemes is provided, displaying the wide range of applications from the classical Newton equation of motion to the quantum field theory.
Directory of Open Access Journals (Sweden)
Mir Hamid Reza Ghoreishy
2014-10-01
Full Text Available This research work is devoted to the simulation of a steel-belted radial tire under different static loads. The nonlinear finite element calculations were performed using the MSC.MARC code, installed on a computer system equipped with a parallel processing technology. Hybrid elements in conjunction with two hyperelastic models, namely Marlow and Yeoh, and rebar layer implemented in surface elements were used for the modeling of rubbery and reinforcing parts, respectively. Linear elastic material models were also used for the modeling of the reinforcing elements including steel cord in belts, polyester cord in carcass and nylon cord in cap ply section. Two-dimensional axisymmetric elements were used for the modeling of rim-mounting and inflation and three-dimensional models were developed for the application of the radial, tangential, lateral and torsional loads. Different finite element models were developed, in which both linear and quadratic elements were used in conjunction with different mesh densities in order to find the optimum finite element model. Based on the results of the load deflection (displacement data, the tire stiffness under radial, tangential, lateral and torsional loads were calculated and compared with their corresponding experimentally measured values. The comparison was verified by the accuracy of the measured radial stiffness. However, due to the neglecting of the stiffness in shear and bending modes in cord-rubber composites, modeled with rebar layer methodology, the difference between computed values and real data are not small enough so that a more robust material models and element formulation are required to be developed.
Yu, Guojun
2012-10-01
In this article, comparative studies on computational accuracies and convergence rates of triangular and quadrilateral meshes are carried out in the frame work of the finite-volume method. By theoretical analysis, we conclude that the number of triangular cells needs to be 4/3 times that of quadrilateral cells to obtain similar accuracy. The conclusion is verified by a number of numerical examples. In addition, the convergence rates of the triangular meshes are found to be slower than those of the quadrilateral meshes when the same accuracy is obtained with these two mesh types. © 2012 Taylor and Francis Group, LLC.
Yu, Guojun; Yu, Bo; Sun, Shuyu; Tao, Wenquan
2012-01-01
In this article, comparative studies on computational accuracies and convergence rates of triangular and quadrilateral meshes are carried out in the frame work of the finite-volume method. By theoretical analysis, we conclude that the number of triangular cells needs to be 4/3 times that of quadrilateral cells to obtain similar accuracy. The conclusion is verified by a number of numerical examples. In addition, the convergence rates of the triangular meshes are found to be slower than those of the quadrilateral meshes when the same accuracy is obtained with these two mesh types. © 2012 Taylor and Francis Group, LLC.
Directory of Open Access Journals (Sweden)
Min-Jhong Gu
2014-08-01
Full Text Available This article describes the development of a suite of programs that is capable of simulating the radiation properties of a random rough surface (RRS. The fundamental approach involves the generation, by fast Fourier transform (FFT built with rigorous finite difference time domain (FDTD, as the theoretical basis for the simulation of a bidirectional reflectance distribution function (BRDF of the RRS. The results are compared with the measurements and modeling of existing work to verify the feasibility of customized programming. It was found that the results of this study were a better match to the measurement data than those achieved in other modeling work.
Automation of finite element methods
Korelc, Jože
2016-01-01
New finite elements are needed as well in research as in industry environments for the development of virtual prediction techniques. The design and implementation of novel finite elements for specific purposes is a tedious and time consuming task, especially for nonlinear formulations. The automation of this process can help to speed up this process considerably since the generation of the final computer code can be accelerated by order of several magnitudes. This book provides the reader with the required knowledge needed to employ modern automatic tools like AceGen within solid mechanics in a successful way. It covers the range from the theoretical background, algorithmic treatments to many different applications. The book is written for advanced students in the engineering field and for researchers in educational and industrial environments.
Du, Liang; Yang, Yi; Harley, Ronald Gordon; Habetler, Thomas G.; He, Dawei
2016-08-09
A system is for a plurality of different electric load types. The system includes a plurality of sensors structured to sense a voltage signal and a current signal for each of the different electric loads; and a processor. The processor acquires a voltage and current waveform from the sensors for a corresponding one of the different electric load types; calculates a power or current RMS profile of the waveform; quantizes the power or current RMS profile into a set of quantized state-values; evaluates a state-duration for each of the quantized state-values; evaluates a plurality of state-types based on the power or current RMS profile and the quantized state-values; generates a state-sequence that describes a corresponding finite state machine model of a generalized load start-up or transient profile for the corresponding electric load type; and identifies the corresponding electric load type.
Nonlinear Conservation Laws and Finite Volume Methods
Leveque, Randall J.
Introduction Software Notation Classification of Differential Equations Derivation of Conservation Laws The Euler Equations of Gas Dynamics Dissipative Fluxes Source Terms Radiative Transfer and Isothermal Equations Multi-dimensional Conservation Laws The Shock Tube Problem Mathematical Theory of Hyperbolic Systems Scalar Equations Linear Hyperbolic Systems Nonlinear Systems The Riemann Problem for the Euler Equations Numerical Methods in One Dimension Finite Difference Theory Finite Volume Methods Importance of Conservation Form - Incorrect Shock Speeds Numerical Flux Functions Godunov's Method Approximate Riemann Solvers High-Resolution Methods Other Approaches Boundary Conditions Source Terms and Fractional Steps Unsplit Methods Fractional Step Methods General Formulation of Fractional Step Methods Stiff Source Terms Quasi-stationary Flow and Gravity Multi-dimensional Problems Dimensional Splitting Multi-dimensional Finite Volume Methods Grids and Adaptive Refinement Computational Difficulties Low-Density Flows Discrete Shocks and Viscous Profiles Start-Up Errors Wall Heating Slow-Moving Shocks Grid Orientation Effects Grid-Aligned Shocks Magnetohydrodynamics The MHD Equations One-Dimensional MHD Solving the Riemann Problem Nonstrict Hyperbolicity Stiffness The Divergence of B Riemann Problems in Multi-dimensional MHD Staggered Grids The 8-Wave Riemann Solver Relativistic Hydrodynamics Conservation Laws in Spacetime The Continuity Equation The 4-Momentum of a Particle The Stress-Energy Tensor Finite Volume Methods Multi-dimensional Relativistic Flow Gravitation and General Relativity References
The overlapped radial basis function-finite difference (RBF-FD) method: A generalization of RBF-FD
Shankar, Varun
2017-08-01
We present a generalization of the RBF-FD method that computes RBF-FD weights in finite-sized neighborhoods around the centers of RBF-FD stencils by introducing an overlap parameter δ ∈ (0 , 1 ] such that δ = 1 recovers the standard RBF-FD method and δ = 0 results in a full decoupling of stencils. We provide experimental evidence to support this generalization, and develop an automatic stabilization procedure based on local Lebesgue functions for the stable selection of stencil weights over a wide range of δ values. We provide an a priori estimate for the speedup of our method over RBF-FD that serves as a good predictor for the true speedup. We apply our method to parabolic partial differential equations with time-dependent inhomogeneous boundary conditions - Neumann in 2D, and Dirichlet in 3D. Our results show that our method can achieve as high as a 60× speedup in 3D over existing RBF-FD methods in the task of forming differentiation matrices.
International Nuclear Information System (INIS)
Uusitupa, T M; Ilvonen, S A; Laakso, I M; Nikoskinen, K I
2008-01-01
In this paper, the anatomically realistic body model Zubal is exposed to a plane wave. A finite-difference time-domain (FDTD) method is used to obtain field data for specific-absorption-rate (SAR) computation. It is investigated how the FDTD resolution, power-loss computation method and positioning of the material voxels in the FDTD grid affect the SAR results. The results enable one to estimate the effects due to certain fundamental choices made in the SAR simulation
Directory of Open Access Journals (Sweden)
B. U. Musa
2017-04-01
Full Text Available The C++ programming language was used to implement three-dimensional (3-D finite-difference time-domain (FDTD technique to simulate radiation of high frequency electromagnetic waves in free space. To achieve any meaningful results the computational domain of interest should have to be truncated in some way and this is achieved by applying absorbing boundary conditions. A uniaxial perfectly matched layer (UPML absorbing boundary condition is used in this work. The discretised equations of the UPML in FDTD time stepping scheme were derived and has been successfully implemented using the computer program. Simulation results showed that the UPML behaves as an absorber. This was confirmed by comparing the results with another boundary condition, the Mur ABC.
Gyrya, V.; Lipnikov, K.
2017-11-01
We present the arbitrary order mimetic finite difference (MFD) discretization for the diffusion equation with non-symmetric tensorial diffusion coefficient in a mixed formulation on general polygonal meshes. The diffusion tensor is assumed to be positive definite. The asymmetry of the diffusion tensor requires changes to the standard MFD construction. We present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities. The numerically observed convergence rate for the scalar quantity matches the predicted one in the case of the lowest order mimetic scheme. For higher orders schemes, we observed super-convergence by one order for the scalar variable which is consistent with the previously published result for a symmetric diffusion tensor. The new scheme was also tested on a time-dependent problem modeling the Hall effect in the resistive magnetohydrodynamics.
Finite difference time domain analysis of a chiro plasma
International Nuclear Information System (INIS)
Torres-Silva, H.; Obligado, A.; Reggiani, N.; Sakanaka, P.H.
1995-01-01
The finite difference time-domain (FDTD) method is one of the most widely used computational methods in electromagnetics. Using FDTD, Maxwell's equations are solved directly in the time domain via finite differences and time stepping. The basic approach is relatively easy to understand and is an alternative to the more usual frequency-domain approaches. (author). 5 refs
Schultz, A.
2010-12-01
describe our ongoing efforts to achieve massive parallelization on a novel hybrid GPU testbed machine currently configured with 12 Intel Westmere Xeon CPU cores (or 24 parallel computational threads) with 96 GB DDR3 system memory, 4 GPU subsystems which in aggregate contain 960 NVidia Tesla GPU cores with 16 GB dedicated DDR3 GPU memory, and a second interleved bank of 4 GPU subsystems containing in aggregate 1792 NVidia Fermi GPU cores with 12 GB dedicated DDR5 GPU memory. We are applying domain decomposition methods to a modified version of Weiss' (2001) 3D frequency domain full physics EM finite difference code, an open source GPL licensed f90 code available for download from www.OpenEM.org. This will be the core of a new hybrid 3D inversion that parallelizes frequencies across CPUs and individual forward solutions across GPUs. We describe progress made in modifying the code to use direct solvers in GPU cores dedicated to each small subdomain, iteratively improving the solution by matching adjacent subdomain boundary solutions, rather than iterative Krylov space sparse solvers as currently applied to the whole domain.
Crack Propagation by Finite Element Method
Directory of Open Access Journals (Sweden)
Luiz Carlos H. Ricardo
2018-01-01
Full Text Available Crack propagation simulation began with the development of the finite element method; the analyses were conducted to obtain a basic understanding of the crack growth. Today structural and materials engineers develop structures and materials properties using this technique. The aim of this paper is to verify the effect of different crack propagation rates in determination of crack opening and closing stress of an ASTM specimen under a standard suspension spectrum loading from FDandE SAE Keyhole Specimen Test Load Histories by finite element analysis. To understand the crack propagation processes under variable amplitude loading, retardation effects are observed
Solving hyperbolic equations with finite volume methods
Vázquez-Cendón, M Elena
2015-01-01
Finite volume methods are used in numerous applications and by a broad multidisciplinary scientific community. The book communicates this important tool to students, researchers in training and academics involved in the training of students in different science and technology fields. The selection of content is based on the author’s experience giving PhD and master courses in different universities. In the book the introduction of new concepts and numerical methods go together with simple exercises, examples and applications that contribute to reinforce them. In addition, some of them involve the execution of MATLAB codes. The author promotes an understanding of common terminology with a balance between mathematical rigor and physical intuition that characterizes the origin of the methods. This book aims to be a first contact with finite volume methods. Once readers have studied it, they will be able to follow more specific bibliographical references and use commercial programs or open source software withi...
Directory of Open Access Journals (Sweden)
E. A. Levchuk
2018-01-01
Full Text Available Numerical modeling of electronic state evolution due to non-uniform external electric field in the structure metal-insulator-semiconductor with solitary donor center is carried out. Considering a nanometer disc-shaped gate as a source of the electric field, the problem for the Laplace equation in multilayered medium is solved numerically to determine the distribution of the gate potential. The energy spectrum of a bound electron is calculated from the problem for the stationary Schrödinger equation. Finite difference schemes are constructed to solve both the problems. Difference scheme for the Schrödinger equation takes into account cusp condition for the wave function at the donor location. To solve the problem for the Laplace equation, asymptotic boundary conditions for approximating the external field potential at large distances from the gate in different layers are suggested. These conditions allow to reduce the calculation domain for the electrostatic problem essentially. The effect of the boundary conditions on the accuracy of calculating the potential and energies is investigated. Using the developed difference schemes, the dependences of the energy spectrum of the bound electron on the gate potential are calculated, and the values of critical potential at which the wave function of the electron is relocated are determined. It has been found on the basis of calculation results, that governing parameter for the description of electronic behavior is the potential difference between the donor and semiconductor surface. It has been shown that critical potential difference does not depend on dielectric thickness and permittivity.
International Nuclear Information System (INIS)
Aruchunan, E.
2015-01-01
In this paper, we have examined the effectiveness of the quarter-sweep iteration concept on conjugate gradient normal residual (CGNR) iterative method by using composite Simpson's (CS) and finite difference (FD) discretization schemes in solving Fredholm integro-differential equations. For comparison purposes, Gauss- Seidel (GS) and the standard or full- and half-sweep CGNR methods namely FSCGNR and HSCGNR are also presented. To validate the efficacy of the proposed method, several analyses were carried out such as computational complexity and percentage reduction on the proposed and existing methods. (author)
International Nuclear Information System (INIS)
Fujii, A; Hayashi, S; Fujii, S; Yanagi, K
2014-01-01
This paper deals with the functional performance of optical surface texture measuring instruments on the market. It is well known that their height response curves against certain referential geometry are not always identical to each other. So, a more precise study on the optical instrument's characteristics is greatly needed. Firstly, we developed a new simulation tool using a finite-difference time-domain technique, which enables the prediction of the height response curve against the fundamental surface geometry in the case of the confocal laser scanning microscope. Secondly, by utilizing this new simulation tool, measurement results, including outliers, were compared with the analytical simulation results. The comparison showed the consistency, which indicates that necessary conditions of surface measurement standards for verifying the instrument performance can be established. Consequently, we suggest that the maximum measurable slope angle must be added to evaluation subjects as significant metrological characteristics of measuring instruments, along with the lateral period limit. Finally, we propose a procedure to determine the lateral period limit in an ISO standard. (paper)
Merritt, M.L.
1993-01-01
The simulation of the transport of injected freshwater in a thin brackish aquifer, overlain and underlain by confining layers containing more saline water, is shown to be influenced by the choice of the finite-difference approximation method, the algorithm for representing vertical advective and dispersive fluxes, and the values assigned to parametric coefficients that specify the degree of vertical dispersion and molecular diffusion that occurs. Computed potable water recovery efficiencies will differ depending upon the choice of algorithm and approximation method, as will dispersion coefficients estimated based on the calibration of simulations to match measured data. A comparison of centered and backward finite-difference approximation methods shows that substantially different transition zones between injected and native waters are depicted by the different methods, and computed recovery efficiencies vary greatly. Standard and experimental algorithms and a variety of values for molecular diffusivity, transverse dispersivity, and vertical scaling factor were compared in simulations of freshwater storage in a thin brackish aquifer. Computed recovery efficiencies vary considerably, and appreciable differences are observed in the distribution of injected freshwater in the various cases tested. The results demonstrate both a qualitatively different description of transport using the experimental algorithms and the interrelated influences of molecular diffusion and transverse dispersion on simulated recovery efficiency. When simulating natural aquifer flow in cross-section, flushing of the aquifer occurred for all tested coefficient choices using both standard and experimental algorithms. ?? 1993.
Structural modeling techniques by finite element method
International Nuclear Information System (INIS)
Kang, Yeong Jin; Kim, Geung Hwan; Ju, Gwan Jeong
1991-01-01
This book includes introduction table of contents chapter 1 finite element idealization introduction summary of the finite element method equilibrium and compatibility in the finite element solution degrees of freedom symmetry and anti symmetry modeling guidelines local analysis example references chapter 2 static analysis structural geometry finite element models analysis procedure modeling guidelines references chapter 3 dynamic analysis models for dynamic analysis dynamic analysis procedures modeling guidelines and modeling guidelines.
Crack Propagation by Finite Element Method
H. Ricardo, Luiz Carlos
2017-01-01
Crack propagation simulation began with the development of the finite element method; the analyses were conducted to obtain a basic understanding of the crack growth. Today structural and materials engineers develop structures and materials properties using this technique. The aim of this paper is to verify the effect of different crack propagation rates in determination of crack opening and closing stress of an ASTM specimen under a standard suspension spectrum loading from FD&E SAE Keyh...
Domain decomposition methods for mortar finite elements
Energy Technology Data Exchange (ETDEWEB)
Widlund, O.
1996-12-31
In the last few years, domain decomposition methods, previously developed and tested for standard finite element methods and elliptic problems, have been extended and modified to work for mortar and other nonconforming finite element methods. A survey will be given of work carried out jointly with Yves Achdou, Mario Casarin, Maksymilian Dryja and Yvon Maday. Results on the p- and h-p-version finite elements will also be discussed.
Iterative solutions of finite difference diffusion equations
International Nuclear Information System (INIS)
Menon, S.V.G.; Khandekar, D.C.; Trasi, M.S.
1981-01-01
The heterogeneous arrangement of materials and the three-dimensional character of the reactor physics problems encountered in the design and operation of nuclear reactors makes it necessary to use numerical methods for solution of the neutron diffusion equations which are based on the linear Boltzmann equation. The commonly used numerical method for this purpose is the finite difference method. It converts the diffusion equations to a system of algebraic equations. In practice, the size of this resulting algebraic system is so large that the iterative methods have to be used. Most frequently used iterative methods are discussed. They include : (1) basic iterative methods for one-group problems, (2) iterative methods for eigenvalue problems, and (3) iterative methods which use variable acceleration parameters. Application of Chebyshev theorem to iterative methods is discussed. The extension of the above iterative methods to multigroup neutron diffusion equations is also considered. These methods are applicable to elliptic boundary value problems in reactor design studies in particular, and to elliptic partial differential equations in general. Solution of sample problems is included to illustrate their applications. The subject matter is presented in as simple a manner as possible. However, a working knowledge of matrix theory is presupposed. (M.G.B.)
Syed, S. A.; Chiappetta, L. M.
1985-01-01
A methodological evaluation for two-finite differencing schemes for computer-aided gas turbine design is presented. The two computational schemes include; a Bounded Skewed Finite Differencing Scheme (BSUDS); and a Quadratic Upwind Differencing Scheme (QSDS). In the evaluation, the derivations of the schemes were incorporated into two-dimensional and three-dimensional versions of the Teaching Axisymmetric Characteristics Heuristically (TEACH) computer code. Assessments were made according to performance criteria for the solution of problems of turbulent, laminar, and coannular turbulent flow. The specific performance criteria used in the evaluation were simplicity, accuracy, and computational economy. It is found that the BSUDS scheme performed better with respect to the criteria than the QUDS. Some of the reasons for the more successful performance BSUDS are discussed.
Hydrothermal analysis in engineering using control volume finite element method
Sheikholeslami, Mohsen
2015-01-01
Control volume finite element methods (CVFEM) bridge the gap between finite difference and finite element methods, using the advantages of both methods for simulation of multi-physics problems in complex geometries. In Hydrothermal Analysis in Engineering Using Control Volume Finite Element Method, CVFEM is covered in detail and applied to key areas of thermal engineering. Examples, exercises, and extensive references are used to show the use of the technique to model key engineering problems such as heat transfer in nanofluids (to enhance performance and compactness of energy systems),
International Nuclear Information System (INIS)
Su Xiaoxing; Zhang Chuanzeng; Ma Tianxue; Wang Yuesheng
2012-01-01
When three-dimensional (3D) phononic band structures are calculated by using the finite difference time domain (FDTD) method with a relatively small number of iterations, the results can be effectively improved by post-processing the FDTD time series (FDTD-TS) based on the filter diagonalization method (FDM), instead of the classical fast Fourier transform. In this paper, we propose a way to further improve the performance of the FDM-based post-processing method by introducing a relatively large number of observing points to record the FDTD-TS. To this end, the existing scheme of FDTD-TS preprocessing is modified. With the new preprocessing scheme, the processing efficiency of a single FDTD-TS can be improved significantly, and thus the entire post-processing method can have sufficiently high efficiency even when a relatively large number of observing points are used. The feasibility of the proposed method for improvement is verified by the numerical results.
Finite element analysis of thermal stress distribution in different ...
African Journals Online (AJOL)
Nigerian Journal of Clinical Practice • Jan-Feb 2016 • Vol 19 • Issue 1. Abstract ... Key words: Amalgam, finite element method, glass ionomer cement, resin composite, thermal stress ... applications for force analysis and assessment of different.
Energy Technology Data Exchange (ETDEWEB)
Sudiarta, I. Wayan; Angraini, Lily Maysari, E-mail: lilyangraini@unram.ac.id [Physics Study Program, University of Mataram, Jln. Majapahit 62 Mataram, NTB (Indonesia)
2016-04-19
We have applied the finite difference time domain (FDTD) method with the supersymmetric quantum mechanics (SUSY-QM) procedure to determine excited energies of one dimensional quantum systems. The theoretical basis of FDTD, SUSY-QM, a numerical algorithm and an illustrative example for a particle in a one dimensional square-well potential were given in this paper. It was shown that the numerical results were in excellent agreement with theoretical results. Numerical errors produced by the SUSY-QM procedure was due to errors in estimations of superpotentials and supersymmetric partner potentials.
Velivelli, A. C.; Bryden, K. M.
2006-03-01
Lattice Boltzmann methods are gaining recognition in the field of computational fluid dynamics due to their computational efficiency. In order to quantify the computational efficiency and accuracy of the lattice Boltzmann method, it is compared with efficient traditional finite difference methods such as the alternating direction implicit scheme. The lattice Boltzmann algorithm implemented in previous studies does not approach peak performance for simulations where the data involved in computation per time step is more than the cache size. Due to this, data is obtained from the main memory and this access is much slower than access to cache memory. Using a cache-optimized lattice Boltzmann algorithm, this paper takes into account the full computational strength of the lattice Boltzmann method. The com parison is performed on both a single processor and multiple processors.
Finite difference computation of Casimir forces
International Nuclear Information System (INIS)
Pinto, Fabrizio
2016-01-01
In this Invited paper, we begin by a historical introduction to provide a motivation for the classical problems of interatomic force computation and associated challenges. This analysis will lead us from early theoretical and experimental accomplishments to the integration of these fascinating interactions into the operation of realistic, next-generation micro- and nanodevices both for the advanced metrology of fundamental physical processes and in breakthrough industrial applications. Among several powerful strategies enabling vastly enhanced performance and entirely novel technological capabilities, we shall specifically consider Casimir force time-modulation and the adoption of non-trivial geometries. As to the former, the ability to alter the magnitude and sign of the Casimir force will be recognized as a crucial principle to implement thermodynamical nano-engines. As to the latter, we shall first briefly review various reported computational approaches. We shall then discuss the game-changing discovery, in the last decade, that standard methods of numerical classical electromagnetism can be retooled to formulate the problem of Casimir force computation in arbitrary geometries. This remarkable development will be practically illustrated by showing that such an apparently elementary method as standard finite-differencing can be successfully employed to numerically recover results known from the Lifshitz theory of dispersion forces in the case of interacting parallel-plane slabs. Other geometries will be also be explored and consideration given to the potential of non-standard finite-difference methods. Finally, we shall introduce problems at the computational frontier, such as those including membranes deformed by Casimir forces and the effects of anisotropic materials. Conclusions will highlight the dramatic transition from the enduring perception of this field as an exotic application of quantum electrodynamics to the recent demonstration of a human climbing
Implicit finite-difference simulations of seismic wave propagation
Chu, Chunlei; Stoffa, Paul L.
2012-01-01
We propose a new finite-difference modeling method, implicit both in space and in time, for the scalar wave equation. We use a three-level implicit splitting time integration method for the temporal derivative and implicit finite-difference operators of arbitrary order for the spatial derivatives. Both the implicit splitting time integration method and the implicit spatial finite-difference operators require solving systems of linear equations. We show that it is possible to merge these two sets of linear systems, one from implicit temporal discretizations and the other from implicit spatial discretizations, to reduce the amount of computations to develop a highly efficient and accurate seismic modeling algorithm. We give the complete derivations of the implicit splitting time integration method and the implicit spatial finite-difference operators, and present the resulting discretized formulas for the scalar wave equation. We conduct a thorough numerical analysis on grid dispersions of this new implicit modeling method. We show that implicit spatial finite-difference operators greatly improve the accuracy of the implicit splitting time integration simulation results with only a slight increase in computational time, compared with explicit spatial finite-difference operators. We further verify this conclusion by both 2D and 3D numerical examples. © 2012 Society of Exploration Geophysicists.
Implicit finite-difference simulations of seismic wave propagation
Chu, Chunlei
2012-03-01
We propose a new finite-difference modeling method, implicit both in space and in time, for the scalar wave equation. We use a three-level implicit splitting time integration method for the temporal derivative and implicit finite-difference operators of arbitrary order for the spatial derivatives. Both the implicit splitting time integration method and the implicit spatial finite-difference operators require solving systems of linear equations. We show that it is possible to merge these two sets of linear systems, one from implicit temporal discretizations and the other from implicit spatial discretizations, to reduce the amount of computations to develop a highly efficient and accurate seismic modeling algorithm. We give the complete derivations of the implicit splitting time integration method and the implicit spatial finite-difference operators, and present the resulting discretized formulas for the scalar wave equation. We conduct a thorough numerical analysis on grid dispersions of this new implicit modeling method. We show that implicit spatial finite-difference operators greatly improve the accuracy of the implicit splitting time integration simulation results with only a slight increase in computational time, compared with explicit spatial finite-difference operators. We further verify this conclusion by both 2D and 3D numerical examples. © 2012 Society of Exploration Geophysicists.
Energy Technology Data Exchange (ETDEWEB)
Noguchi, K; Endo, M [Waseda University, Tokyo (Japan). School of Science and Engineering
1997-10-22
Study is made on the theory of three-dimensional modelling of TDEM (Time Domain Electromagnetic) method based on the theory of Wang and Hohmann. A difference scheme is built and investigation is conducted about calculation accuracy with attention paid especially to space and time division, and the obtained optimum value is compared with the analytical solution for a homogeneous medium. As the result, it becomes possible to have a high-accuracy TDEM response thanks to the obtained optimum parameter. In an example, a response is determined in the case of a high-resistivity body in presence near the ground surface. Calculation is performed under the given conditions of a medium 100 ohm/m in resistivity, anomalous bodies 200, 500, 1000, 2000,5000, and 10,000 ohm/m in resistivity, respectively, and a distance in the direction of depth of 20m. The result indicates that it is possible to estimate the effect of the ground surface terrain on a TDEM response. Since the effect of the ground surface terrain emerges at the initial part of a response, it is inferred that consideration of terrain is mandatory in building a model if it is for interpreting the subsurface structure in detail. 5 refs., 7 figs.
Topology optimization using the finite volume method
DEFF Research Database (Denmark)
in this presentation is focused on a prototype model for topology optimization of steady heat diffusion. This allows for a study of the basic ingredients in working with FVM methods when dealing with topology optimization problems. The FVM and FEM based formulations differ both in how one computes the design...... derivative of the system matrix K and in how one computes the discretized version of certain objective functions. Thus for a cost function for minimum dissipated energy (like minimum compliance for an elastic structure) one obtains an expression c = u^\\T \\tilde{K}u $, where \\tilde{K} is different from K...... the well known Reuss lower bound. [1] Bendsøe, M.P.; Sigmund, O. 2004: Topology Optimization - Theory, Methods, and Applications. Berlin Heidelberg: Springer Verlag [2] Versteeg, H. K.; W. Malalasekera 1995: An introduction to Computational Fluid Dynamics: the Finite Volume Method. London: Longman...
International Nuclear Information System (INIS)
Lee, Deokjung; Downar, Thomas J.; Kim, Yonghee
2004-01-01
An innovative hybrid spatial discretization method is proposed to improve the computational efficiency of pin-wise heterogeneous three-dimensional light water reactor (LWR) core neutronics analysis. The newly developed method employs the standard finite difference method in the x and y directions and the well-known nodal methods [nodal expansion method (NEM) and analytic nodal method (ANM) as needed] in the z direction. Four variants of the hybrid method are investigated depending on the axial nodal methodologies: HYBRID A, NEM with the conventional quadratic transverse leakage; HYBRID B, the conventional NEM method except that the transverse-leakage shapes are obtained from a fine-mesh local problem (FMLP) around the control rod tip; HYBRID C, the same as HYBRID B except that ANM with a high-order transverse leakage obtained from the FMLP is used in the vicinity of the control rod tip; and HYBRID D, the same as HYBRID C except that the transverse leakage is determined using the buckling approximation instead of the FMLP around the control rod tip. Benchmark calculations demonstrate that all the hybrid algorithms are consistent and stable and that the HYBRID C method provides the best numerical performance in the case of rodded LWR problems with pin-wise homogenized cross sections
Generalized multiscale finite element methods: Oversampling strategies
Efendiev, Yalchin R.; Galvis, Juan; Li, Guanglian; Presho, Michael
2014-01-01
In this paper, we propose oversampling strategies in the generalized multiscale finite element method (GMsFEM) framework. The GMsFEM, which has been recently introduced in Efendiev et al. (2013b) [Generalized Multiscale Finite Element Methods, J. Comput. Phys., vol. 251, pp. 116-135, 2013], allows solving multiscale parameter-dependent problems at a reduced computational cost by constructing a reduced-order representation of the solution on a coarse grid. The main idea of the method consists of (1) the construction of snapshot space, (2) the construction of the offline space, and (3) construction of the online space (the latter for parameter-dependent problems). In Efendiev et al. (2013b) [Generalized Multiscale Finite Element Methods, J. Comput. Phys., vol. 251, pp. 116-135, 2013], it was shown that the GMsFEM provides a flexible tool to solve multiscale problems with a complex input space by generating appropriate snapshot, offline, and online spaces. In this paper, we develop oversampling techniques to be used in this context (see Hou and Wu (1997) where oversampling is introduced for multiscale finite element methods). It is known (see Hou and Wu (1997)) that the oversampling can improve the accuracy of multiscale methods. In particular, the oversampling technique uses larger regions (larger than the target coarse block) in constructing local basis functions. Our motivation stems from the analysis presented in this paper, which shows that when using oversampling techniques in the construction of the snapshot space and offline space, GMsFEM will converge independent of small scales and high contrast under certain assumptions. We consider the use of a multiple eigenvalue problems to improve the convergence and discuss their relation to single spectral problems that use oversampled regions. The oversampling procedures proposed in this paper differ from those in Hou and Wu (1997). In particular, the oversampling domains are partially used in constructing local
International Nuclear Information System (INIS)
Civalek, Oemer
2005-01-01
The nonlinear dynamic response of doubly curved shallow shells resting on Winkler-Pasternak elastic foundation has been studied for step and sinusoidal loadings. Dynamic analogues of Von Karman-Donnel type shell equations are used. Clamped immovable and simply supported immovable boundary conditions are considered. The governing nonlinear partial differential equations of the shell are discretized in space and time domains using the harmonic differential quadrature (HDQ) and finite differences (FD) methods, respectively. The accuracy of the proposed HDQ-FD coupled methodology is demonstrated by numerical examples. The shear parameter G of the Pasternak foundation and the stiffness parameter K of the Winkler foundation have been found to have a significant influence on the dynamic response of the shell. It is concluded from the present study that the HDQ-FD methodolgy is a simple, efficient, and accurate method for the nonlinear analysis of doubly curved shallow shells resting on two-parameter elastic foundation
DEFF Research Database (Denmark)
Yoon, Daeung; Zhdanov, Michael; Mattsson, Johan
2016-01-01
One of the major problems in the modeling and inversion of marine controlled-source electromagnetic (CSEM) data is related to the need for accurate representation of very complex geoelectrical models typical for marine environment. At the same time, the corresponding forward-modeling algorithms...... should be powerful and fast enough to be suitable for repeated use in hundreds of iterations of the inversion and for multiple transmitter/receiver positions. To this end, we have developed a novel 3D modeling and inversion approach, which combines the advantages of the finite-difference (FD......) and integral-equation (IE) methods. In the framework of this approach, we have solved Maxwell’s equations for anomalous electric fields using the FD approximation on a staggered grid. Once the unknown electric fields in the computation domain of the FD method are computed, the electric and magnetic fields...
Advanced finite element method in structural engineering
Long, Yu-Qiu; Long, Zhi-Fei
2009-01-01
This book systematically introduces the research work on the Finite Element Method completed over the past 25 years. Original theoretical achievements and their applications in the fields of structural engineering and computational mechanics are discussed.
Review on Finite Element Method * ERHUNMWUN, ID ...
African Journals Online (AJOL)
ADOWIE PERE
ABSTRACT: In this work, we have discussed what Finite Element Method (FEM) is, its historical development, advantages and ... residual procedures, are examples of the direct approach ... The paper centred on the "stiffness and deflection of ...
Tay, Wei Choon; Tan, Eng Leong
2014-07-01
In this paper, we have proposed a pentadiagonal alternating-direction-implicit (Penta-ADI) finite-difference time-domain (FDTD) method for the two-dimensional Schrödinger equation. Through the separation of complex wave function into real and imaginary parts, a pentadiagonal system of equations for the ADI method is obtained, which results in our Penta-ADI method. The Penta-ADI method is further simplified into pentadiagonal fundamental ADI (Penta-FADI) method, which has matrix-operator-free right-hand-sides (RHS), leading to the simplest and most concise update equations. As the Penta-FADI method involves five stencils in the left-hand-sides (LHS) of the pentadiagonal update equations, special treatments that are required for the implementation of the Dirichlet's boundary conditions will be discussed. Using the Penta-FADI method, a significantly higher efficiency gain can be achieved over the conventional Tri-ADI method, which involves a tridiagonal system of equations.
The finite element method in electromagnetics
Jin, Jianming
2014-01-01
A new edition of the leading textbook on the finite element method, incorporating major advancements and further applications in the field of electromagnetics The finite element method (FEM) is a powerful simulation technique used to solve boundary-value problems in a variety of engineering circumstances. It has been widely used for analysis of electromagnetic fields in antennas, radar scattering, RF and microwave engineering, high-speed/high-frequency circuits, wireless communication, electromagnetic compatibility, photonics, remote sensing, biomedical engineering, and space exploration. The
International Nuclear Information System (INIS)
Su Xiaoxing; Ma Tianxue; Wang Yuesheng
2011-01-01
If the band structure of a three-dimensional (3D) phononic crystal (PNC) is calculated by using the finite difference time domain (FDTD) method combined with the fast Fourier transform (FFT)-based postprocessing method, good results can only be ensured by a sufficiently large number of FDTD iterations. On a common computer platform, the total computation time will be very long. To overcome this difficulty, an excellent harmonic inversion algorithm called the filter diagonalization method (FDM) can be used in the postprocessing to reduce the number of FDTD iterations. However, the low efficiency of the FDM, which occurs when a relatively long time series is given, does not necessarily ensure an effective reduction of the total computation time. In this paper, a postprocessing method based on the FDM is proposed. The main procedure of the method is designed considering the aim to make the time spent on the method itself far less than the corresponding time spent on the FDTD iterations. To this end, the FDTD time series is preprocessed to be shortened significantly before the FDM frequency extraction. The preprocessing procedure is performed with the filter and decimation operations, which are widely used in narrow-band signal processing. Numerical results for a typical 3D solid PNC system show that the proposed postprocessing method can be used to effectively reduce the total computation time of the FDTD calculation of 3D phononic band structures.
Energy Technology Data Exchange (ETDEWEB)
Su Xiaoxing [School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing 100044 (China); Ma Tianxue; Wang Yuesheng, E-mail: xxsu@bjtu.edu.cn [Institute of Engineering Mechanics, Beijing Jiaotong University, Beijing 100044 (China)
2011-10-15
If the band structure of a three-dimensional (3D) phononic crystal (PNC) is calculated by using the finite difference time domain (FDTD) method combined with the fast Fourier transform (FFT)-based postprocessing method, good results can only be ensured by a sufficiently large number of FDTD iterations. On a common computer platform, the total computation time will be very long. To overcome this difficulty, an excellent harmonic inversion algorithm called the filter diagonalization method (FDM) can be used in the postprocessing to reduce the number of FDTD iterations. However, the low efficiency of the FDM, which occurs when a relatively long time series is given, does not necessarily ensure an effective reduction of the total computation time. In this paper, a postprocessing method based on the FDM is proposed. The main procedure of the method is designed considering the aim to make the time spent on the method itself far less than the corresponding time spent on the FDTD iterations. To this end, the FDTD time series is preprocessed to be shortened significantly before the FDM frequency extraction. The preprocessing procedure is performed with the filter and decimation operations, which are widely used in narrow-band signal processing. Numerical results for a typical 3D solid PNC system show that the proposed postprocessing method can be used to effectively reduce the total computation time of the FDTD calculation of 3D phononic band structures.
Finite difference techniques for nonlinear hyperbolic conservation laws
International Nuclear Information System (INIS)
Sanders, R.
1985-01-01
The present study is concerned with numerical approximations to the initial value problem for nonlinear systems of conservative laws. Attention is given to the development of a class of conservation form finite difference schemes which are based on the finite volume method (i.e., the method of averages). These schemes do not fit into the classical framework of conservation form schemes discussed by Lax and Wendroff (1960). The finite volume schemes are specifically intended to approximate solutions of multidimensional problems in the absence of rectangular geometries. In addition, the development is reported of different schemes which utilize the finite volume approach for time discretization. Particular attention is given to local time discretization and moving spatial grids. 17 references
Energy Technology Data Exchange (ETDEWEB)
Dias, Gleide A.N.; Silva, Jadir C.; Rocha, Paula F.; Costa, Jorge L. [Universidade Federal, Rio de Janeiro, RJ (Brazil). Dept. de Geologia]. E-mail: gleidalencar@hotmail.com.br; jadir@geologia.ufrj.br; ferrucio@acd.ufrj.br; jotalc@yahoo.com.br
2003-07-01
Presently the oil industry has shown the importance of defining the structural framework of reservoirs. This study intends to contribute for the solution of this problem, using synthetic models in order to evaluate the electromagnetic signal due to a certain target. Use was made of an algorithm, which is based in the Finite Difference Time Domain Methods (FDTD). The simulated results of this survey found the best parameters for the chosen frequencies. In the present study there were simulated polarization, geometry and constitutive parameters (dielectric permittivity and electric conductivity). The results, using frequencies of 50 and 100 MHz, show clearly the effects of the electromagnetic waves attenuation and their problems related with signal resolution of targets in depth. (author)
Energy Technology Data Exchange (ETDEWEB)
Bourke, J.D. [School of Physics, University of Melbourne, Parkville, Vic 3010 (Australia); Chantler, C.T., E-mail: chantler@physics.unimelb.edu.a [School of Physics, University of Melbourne, Parkville, Vic 3010 (Australia)
2010-07-21
X-ray Absorption Fine Structure (XAFS) is calculated for copper using the cluster based Finite Difference Method for Near-Edge Structure (FDMNES). This approach is conventionally used to produce high accuracy XAFS theory in the near edge region, however, we demonstrate that it can be readily extended to encompass an energy range of more than 1.5 keV (k{approx}20A{sup -1}) from the K absorption edge. Such calculations require extensions to FDMNES to account for thermal effects, in addition to broadening effects due to inelastic processes. Extended calculations beyond the range of near-edge structure also require consideration of technical constraints such as cluster sizes and densities. We find that with our approach, we are able to produce accurate theory ranging from the absorption edge to the smooth atom-like region at high energies, with a single consistent model that is free from any fitting parameters.
International Nuclear Information System (INIS)
Bourke, J.D.; Chantler, C.T.
2010-01-01
X-ray Absorption Fine Structure (XAFS) is calculated for copper using the cluster based Finite Difference Method for Near-Edge Structure (FDMNES). This approach is conventionally used to produce high accuracy XAFS theory in the near edge region, however, we demonstrate that it can be readily extended to encompass an energy range of more than 1.5 keV (k∼20A -1 ) from the K absorption edge. Such calculations require extensions to FDMNES to account for thermal effects, in addition to broadening effects due to inelastic processes. Extended calculations beyond the range of near-edge structure also require consideration of technical constraints such as cluster sizes and densities. We find that with our approach, we are able to produce accurate theory ranging from the absorption edge to the smooth atom-like region at high energies, with a single consistent model that is free from any fitting parameters.
Yang, Lei; Yan, Hongyong; Liu, Hong
2017-03-01
Implicit staggered-grid finite-difference (ISFD) scheme is competitive for its great accuracy and stability, whereas its coefficients are conventionally determined by the Taylor-series expansion (TE) method, leading to a loss in numerical precision. In this paper, we modify the TE method using the minimax approximation (MA), and propose a new optimal ISFD scheme based on the modified TE (MTE) with MA method. The new ISFD scheme takes the advantage of the TE method that guarantees great accuracy at small wavenumbers, and keeps the property of the MA method that keeps the numerical errors within a limited bound at the same time. Thus, it leads to great accuracy for numerical solution of the wave equations. We derive the optimal ISFD coefficients by applying the new method to the construction of the objective function, and using a Remez algorithm to minimize its maximum. Numerical analysis is made in comparison with the conventional TE-based ISFD scheme, indicating that the MTE-based ISFD scheme with appropriate parameters can widen the wavenumber range with high accuracy, and achieve greater precision than the conventional ISFD scheme. The numerical modeling results also demonstrate that the MTE-based ISFD scheme performs well in elastic wave simulation, and is more efficient than the conventional ISFD scheme for elastic modeling.
Finite element method - theory and applications
International Nuclear Information System (INIS)
Baset, S.
1992-01-01
This paper summarizes the mathematical basis of the finite element method. Attention is drawn to the natural development of the method from an engineering analysis tool into a general numerical analysis tool. A particular application to the stress analysis of rubber materials is presented. Special advantages and issues associated with the method are mentioned. (author). 4 refs., 3 figs
Elementary introduction to finite difference equations
International Nuclear Information System (INIS)
White, J.W.
1976-01-01
An elementary description is given of the basic vocabulary and concepts associated with finite difference modeling. The material discussed is biased toward the types of large computer programs used at the Lawrence Livermore Laboratory. Particular attention is focused on truncation error and how it can be affected by zoning patterns. The principle of convergence is discussed, and convergence as a tool for improving calculational accuracy and efficiency is emphasized
Institute of Scientific and Technical Information of China (English)
Yirang YUAN; Qing YANG; Changfeng LI; Tongjun SUN
2017-01-01
Transient behavior of three-dimensional semiconductor device with heat conduction is described by a coupled mathematical system of four quasi-linear partial differential equations with initial-boundary value conditions.The electric potential is defined by an elliptic equation and it appears in the following three equations via the electric field intensity.The electron concentration and the hole concentration are determined by convection-dominated diffusion equations and the temperature is interpreted by a heat conduction equation.A mixed finite volume element approximation,keeping physical conservation law,is used to get numerical values of the electric potential and the accuracy is improved one order.Two concentrations and the heat conduction are computed by a fractional step method combined with second-order upwind differences.This method can overcome numerical oscillation,dispersion and decreases computational complexity.Then a three-dimensional problem is solved by computing three successive one-dimensional problems where the method of speedup is used and the computational work is greatly shortened.An optimal second-order error estimate in L2 norm is derived by using prior estimate theory and other special techniques of partial differential equations.This type of mass-conservative parallel method is important and is most valuable in numerical analysis and application of semiconductor device.
Finite element method for solving neutron transport problems
International Nuclear Information System (INIS)
Ferguson, J.M.; Greenbaum, A.
1984-01-01
A finite element method is introduced for solving the neutron transport equations. Our method falls into the category of Petrov-Galerkin solution, since the trial space differs from the test space. The close relationship between this method and the discrete ordinate method is discussed, and the methods are compared for simple test problems
Finite difference computing with PDEs a modern software approach
Langtangen, Hans Petter
2017-01-01
This book is open access under a CC BY 4.0 license. This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods. Unlike many of the traditional academic works on the topic, this book was written for practitioners. Accordingly, it especially addresses: the construction of finite difference schemes, formulation and implementation of algorithms, verification of implementations, analyses of physical behavior as implied by the numerical solutions, and how to apply the methods and software to solve problems in the fields of physics and biology.
The finite element response matrix method
International Nuclear Information System (INIS)
Nakata, H.; Martin, W.R.
1983-02-01
A new technique is developed with an alternative formulation of the response matrix method implemented with the finite element scheme. Two types of response matrices are generated from the Galerkin solution to the weak form of the diffusion equation subject to an arbitrary current and source. The piecewise polynomials are defined in two levels, the first for the local (assembly) calculations and the second for the global (core) response matrix calculations. This finite element response matrix technique was tested in two 2-dimensional test problems, 2D-IAEA benchmark problem and Biblis benchmark problem, with satisfatory results. The computational time, whereas the current code is not extensively optimized, is of the same order of the well estabilished coarse mesh codes. Furthermore, the application of the finite element technique in an alternative formulation of response matrix method permits the method to easily incorporate additional capabilities such as treatment of spatially dependent cross-sections, arbitrary geometrical configurations, and high heterogeneous assemblies. (Author) [pt
Evaluation of finite difference and FFT-based solutions of the transport of intensity equation.
Zhang, Hongbo; Zhou, Wen-Jing; Liu, Ying; Leber, Donald; Banerjee, Partha; Basunia, Mahmudunnabi; Poon, Ting-Chung
2018-01-01
A finite difference method is proposed for solving the transport of intensity equation. Simulation results show that although slower than fast Fourier transform (FFT)-based methods, finite difference methods are able to reconstruct the phase with better accuracy due to relaxed assumptions for solving the transport of intensity equation relative to FFT methods. Finite difference methods are also more flexible than FFT methods in dealing with different boundary conditions.
International Nuclear Information System (INIS)
Shen, W.
2012-01-01
Recent assessment results indicate that the coarse-mesh finite-difference method (FDM) gives consistently smaller percent differences in channel powers than the fine-mesh FDM when compared to the reference MCNP solution for CANDU-type reactors. However, there is an impression that the fine-mesh FDM should always give more accurate results than the coarse-mesh FDM in theory. To answer the question if the better performance of the coarse-mesh FDM for CANDU-type reactors was just a coincidence (cancellation of errors) or caused by the use of heavy water or the use of lattice-homogenized cross sections for the cluster fuel geometry in the diffusion calculation, three benchmark problems were set up with three different fuel lattices: CANDU, HWR and PWR. These benchmark problems were then used to analyze the root cause of the better performance of the coarse-mesh FDM for CANDU-type reactors. The analyses confirm that the better performance of the coarse-mesh FDM for CANDU-type reactors is mainly caused by the use of lattice-homogenized cross sections for the sub-meshes of the cluster fuel geometry in the diffusion calculation. Based on the analyses, it is recommended to use 2 x 2 coarse-mesh FDM to analyze CANDU-type reactors when lattice-homogenized cross sections are used in the core analysis. (authors)
Energy Technology Data Exchange (ETDEWEB)
Shen, W. [Candu Energy Inc., 2285 Speakman Dr., Mississauga, ON L5B 1K (Canada)
2012-07-01
Recent assessment results indicate that the coarse-mesh finite-difference method (FDM) gives consistently smaller percent differences in channel powers than the fine-mesh FDM when compared to the reference MCNP solution for CANDU-type reactors. However, there is an impression that the fine-mesh FDM should always give more accurate results than the coarse-mesh FDM in theory. To answer the question if the better performance of the coarse-mesh FDM for CANDU-type reactors was just a coincidence (cancellation of errors) or caused by the use of heavy water or the use of lattice-homogenized cross sections for the cluster fuel geometry in the diffusion calculation, three benchmark problems were set up with three different fuel lattices: CANDU, HWR and PWR. These benchmark problems were then used to analyze the root cause of the better performance of the coarse-mesh FDM for CANDU-type reactors. The analyses confirm that the better performance of the coarse-mesh FDM for CANDU-type reactors is mainly caused by the use of lattice-homogenized cross sections for the sub-meshes of the cluster fuel geometry in the diffusion calculation. Based on the analyses, it is recommended to use 2 x 2 coarse-mesh FDM to analyze CANDU-type reactors when lattice-homogenized cross sections are used in the core analysis. (authors)
International Nuclear Information System (INIS)
Kinefuchi, K.; Funaki, I.; Shimada, T.; Abe, T.
2012-01-01
Under certain conditions during rocket flights, ionized exhaust plumes from solid rocket motors may interfere with radio frequency transmissions. To understand the relevant physical processes involved in this phenomenon and establish a prediction process for in-flight attenuation levels, we attempted to measure microwave attenuation caused by rocket exhaust plumes in a sea-level static firing test for a full-scale solid propellant rocket motor. The microwave attenuation level was calculated by a coupling simulation of the inviscid-frozen-flow computational fluid dynamics of an exhaust plume and detailed analysis of microwave transmissions by applying a frequency-dependent finite-difference time-domain method with the Drude dispersion model. The calculated microwave attenuation level agreed well with the experimental results, except in the case of interference downstream the Mach disk in the exhaust plume. It was concluded that the coupling estimation method based on the physics of the frozen plasma flow with Drude dispersion would be suitable for actual flight conditions, although the mixing and afterburning in the plume should be considered depending on the flow condition.
Directory of Open Access Journals (Sweden)
Roberto Rojas
2013-03-01
Full Text Available The applicability of the immersed boundary-finite difference lattice Boltzmann method (IB-FDLBM to high Reynolds number flows about a circular cylinder is examined. Two-dimensional simulations of flows past a stationary circular cylinder are carried out for a wide range of the Reynolds number, Re, i.e., 1 ≤ Re ≤ 1×105. An immersed boundary-lattice Boltzmann method (IB-LBM is also used for comparison. Then free-falling circular cylinders are simulated to demonstrate the feasibility of predicting moving particles at high Reynolds numbers. The main conclusions obtained are as follows: (1 steady and unsteady flows about a stationary cylinder are well predicted with IB-LBM and IB-FDLBM, provided that the spatial resolution is high enough to satisfy the conditions of numerical stability, (2 high spatial resolution is required for stable IB-LBM simulation of high Reynolds number flows, (3 IB-FDLBM can stably simulate flows at very high Reynolds numbers without increasing the spatial resolution, (4 IB-FDLBM gives reasonable predictions of the drag coefficient for 1 ≤ Re ≤ 1×105, and (5 IB-FDLBM gives accurate predictions for the motion of free-falling cylinders at intermediate Reynolds numbers.
Energy Technology Data Exchange (ETDEWEB)
Kinefuchi, K. [Department of Aeronautics and Astronautics, University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo 113-8656 (Japan); Funaki, I.; Shimada, T.; Abe, T. [Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, 3-1-1, Yoshinodai, Chuo-ku, Sagamihara, Kanagawa 252-5210 (Japan)
2012-10-15
Under certain conditions during rocket flights, ionized exhaust plumes from solid rocket motors may interfere with radio frequency transmissions. To understand the relevant physical processes involved in this phenomenon and establish a prediction process for in-flight attenuation levels, we attempted to measure microwave attenuation caused by rocket exhaust plumes in a sea-level static firing test for a full-scale solid propellant rocket motor. The microwave attenuation level was calculated by a coupling simulation of the inviscid-frozen-flow computational fluid dynamics of an exhaust plume and detailed analysis of microwave transmissions by applying a frequency-dependent finite-difference time-domain method with the Drude dispersion model. The calculated microwave attenuation level agreed well with the experimental results, except in the case of interference downstream the Mach disk in the exhaust plume. It was concluded that the coupling estimation method based on the physics of the frozen plasma flow with Drude dispersion would be suitable for actual flight conditions, although the mixing and afterburning in the plume should be considered depending on the flow condition.
Generalized multiscale finite element method. Symmetric interior penalty coupling
Efendiev, Yalchin R.; Galvis, Juan; Lazarov, Raytcho D.; Moon, M.; Sarkis, Marcus V.
2013-01-01
Motivated by applications to numerical simulations of flows in highly heterogeneous porous media, we develop multiscale finite element methods for second order elliptic equations. We discuss a multiscale model reduction technique in the framework of the discontinuous Galerkin finite element method. We propose two different finite element spaces on the coarse mesh. The first space is based on a local eigenvalue problem that uses an interior weighted L2-norm and a boundary weighted L2-norm for computing the "mass" matrix. The second choice is based on generation of a snapshot space and subsequent selection of a subspace of a reduced dimension. The approximation with these multiscale spaces is based on the discontinuous Galerkin finite element method framework. We investigate the stability and derive error estimates for the methods and further experimentally study their performance on a representative number of numerical examples. © 2013 Elsevier Inc.
Generalized multiscale finite element method. Symmetric interior penalty coupling
Efendiev, Yalchin R.
2013-12-01
Motivated by applications to numerical simulations of flows in highly heterogeneous porous media, we develop multiscale finite element methods for second order elliptic equations. We discuss a multiscale model reduction technique in the framework of the discontinuous Galerkin finite element method. We propose two different finite element spaces on the coarse mesh. The first space is based on a local eigenvalue problem that uses an interior weighted L2-norm and a boundary weighted L2-norm for computing the "mass" matrix. The second choice is based on generation of a snapshot space and subsequent selection of a subspace of a reduced dimension. The approximation with these multiscale spaces is based on the discontinuous Galerkin finite element method framework. We investigate the stability and derive error estimates for the methods and further experimentally study their performance on a representative number of numerical examples. © 2013 Elsevier Inc.
The finite-difference and finite-element modeling of seismic wave propagation and earthquake motion
International Nuclear Information System (INIS)
Moczo, P.; Kristek, J.; Pazak, P.; Balazovjech, M.; Moczo, P.; Kristek, J.; Galis, M.
2007-01-01
Numerical modeling of seismic wave propagation and earthquake motion is an irreplaceable tool in investigation of the Earth's structure, processes in the Earth, and particularly earthquake phenomena. Among various numerical methods, the finite-difference method is the dominant method in the modeling of earthquake motion. Moreover, it is becoming more important in the seismic exploration and structural modeling. At the same time we are convinced that the best time of the finite-difference method in seismology is in the future. This monograph provides tutorial and detailed introduction to the application of the finite difference (FD), finite-element (FE), and hybrid FD-FE methods to the modeling of seismic wave propagation and earthquake motion. The text does not cover all topics and aspects of the methods. We focus on those to which we have contributed. We present alternative formulations of equation of motion for a smooth elastic continuum. We then develop alternative formulations for a canonical problem with a welded material interface and free surface. We continue with a model of an earthquake source. We complete the general theoretical introduction by a chapter on the constitutive laws for elastic and viscoelastic media, and brief review of strong formulations of the equation of motion. What follows is a block of chapters on the finite-difference and finite-element methods. We develop FD targets for the free surface and welded material interface. We then present various FD schemes for a smooth continuum, free surface, and welded interface. We focus on the staggered-grid and mainly optimally-accurate FD schemes. We also present alternative formulations of the FE method. We include the FD and FE implementations of the traction-at-split-nodes method for simulation of dynamic rupture propagation. The FD modeling is applied to the model of the deep sedimentary Grenoble basin, France. The FD and FE methods are combined in the hybrid FD-FE method. The hybrid
Integral and finite difference inequalities and applications
Pachpatte, B G
2006-01-01
The monograph is written with a view to provide basic tools for researchers working in Mathematical Analysis and Applications, concentrating on differential, integral and finite difference equations. It contains many inequalities which have only recently appeared in the literature and which can be used as powerful tools and will be a valuable source for a long time to come. It is self-contained and thus should be useful for those who are interested in learning or applying the inequalities with explicit estimates in their studies.- Contains a variety of inequalities discovered which find numero
An implicit finite-difference operator for the Helmholtz equation
Chu, Chunlei; Stoffa, Paul L.
2012-01-01
We have developed an implicit finite-difference operator for the Laplacian and applied it to solving the Helmholtz equation for computing the seismic responses in the frequency domain. This implicit operator can greatly improve the accuracy of the simulation results without adding significant extra computational cost, compared with the corresponding conventional explicit finite-difference scheme. We achieved this by taking advantage of the inherently implicit nature of the Helmholtz equation and merging together the two linear systems: one from the implicit finite-difference discretization of the Laplacian and the other from the discretization of the Helmholtz equation itself. The end result of this simple yet important merging manipulation is a single linear system, similar to the one resulting from the conventional explicit finite-difference discretizations, without involving any differentiation matrix inversions. We analyzed grid dispersions of the discrete Helmholtz equation to show the accuracy of this implicit finite-difference operator and used two numerical examples to demonstrate its efficiency. Our method can be extended to solve other frequency domain wave simulation problems straightforwardly. © 2012 Society of Exploration Geophysicists.
An implicit finite-difference operator for the Helmholtz equation
Chu, Chunlei
2012-07-01
We have developed an implicit finite-difference operator for the Laplacian and applied it to solving the Helmholtz equation for computing the seismic responses in the frequency domain. This implicit operator can greatly improve the accuracy of the simulation results without adding significant extra computational cost, compared with the corresponding conventional explicit finite-difference scheme. We achieved this by taking advantage of the inherently implicit nature of the Helmholtz equation and merging together the two linear systems: one from the implicit finite-difference discretization of the Laplacian and the other from the discretization of the Helmholtz equation itself. The end result of this simple yet important merging manipulation is a single linear system, similar to the one resulting from the conventional explicit finite-difference discretizations, without involving any differentiation matrix inversions. We analyzed grid dispersions of the discrete Helmholtz equation to show the accuracy of this implicit finite-difference operator and used two numerical examples to demonstrate its efficiency. Our method can be extended to solve other frequency domain wave simulation problems straightforwardly. © 2012 Society of Exploration Geophysicists.
Image segmentation with a finite element method
DEFF Research Database (Denmark)
Bourdin, Blaise
1999-01-01
regularization results, make possible to imagine a finite element resolution method.In a first time, the Mumford-Shah functional is introduced and some existing results are quoted. Then, a discrete formulation for the Mumford-Shah problem is proposed and its $\\Gamma$-convergence is proved. Finally, some...
Different radiation impedance models for finite porous materials
DEFF Research Database (Denmark)
Nolan, Melanie; Jeong, Cheol-Ho; Brunskog, Jonas
2015-01-01
The Sabine absorption coefficients of finite absorbers are measured in a reverberation chamber according to the international standard ISO 354. They vary with the specimen size essentially due to diffraction at the specimen edges, which can be seen as the radiation impedance differing from...... the infinite case. Thus, in order to predict the Sabine absorption coefficients of finite porous samples, one can incorporate models of the radiation impedance. In this study, different radiation impedance models are compared with two experimental examples. Thomasson’s model is compared to Rhazi’s method when...
Finite Element Methods and Their Applications
Chen, Zhangxin
2005-01-01
This book serves as a text for one- or two-semester courses for upper-level undergraduates and beginning graduate students and as a professional reference for people who want to solve partial differential equations (PDEs) using finite element methods. The author has attempted to introduce every concept in the simplest possible setting and maintain a level of treatment that is as rigorous as possible without being unnecessarily abstract. Quite a lot of attention is given to discontinuous finite elements, characteristic finite elements, and to the applications in fluid and solid mechanics including applications to porous media flow, and applications to semiconductor modeling. An extensive set of exercises and references in each chapter are provided.
A finite element method for neutron transport
International Nuclear Information System (INIS)
Ackroyd, R.T.
1983-01-01
A completely boundary-free maximum principle for the first-order Boltzmann equation is derived from the completely boundary-free maximum principle for the mixed-parity Boltzmann equation. When continuity is imposed on the trial function for directions crossing interfaces the completely boundary-free principle for the first-order Boltzmann equation reduces to a maximum principle previously established directly from first principles and indirectly by the Euler-Lagrange method. Present finite element methods for the first-order Boltzmann equation are based on a weighted-residual method which permits the use of discontinuous trial functions. The new principle for the first-order equation can be used as a basis for finite-element methods with the same freedom from boundary conditions as those based on the weighted-residual method. The extremum principle as the parent of the variationally-derived weighted-residual equations ensures their good behaviour. (author)
Finite difference time domain modelling of particle accelerators
International Nuclear Information System (INIS)
Jurgens, T.G.; Harfoush, F.A.
1989-03-01
Finite Difference Time Domain (FDTD) modelling has been successfully applied to a wide variety of electromagnetic scattering and interaction problems for many years. Here the method is extended to incorporate the modelling of wake fields in particle accelerators. Algorithmic comparisons are made to existing wake field codes, such as MAFIA T3. 9 refs., 7 figs
Directory of Open Access Journals (Sweden)
Sebastián Otero G
2008-06-01
representa su capacidad de incorporar en el análisis el valor de la flexibilidad operativa del proyecto.In the past few years, real options, an extension of financial derivatives, have arisen as an alternative to traditional valuation methods, such as net present value (NPV. The key attribute of real options is that they take into consideration the uncertainty and flexibility involved in investment valuation. This article provides an overview of the finite difference method, by presenting an application to the real options valuation. The empirical section of the article, which makes use of the implicit finite difference method (IFD, analyzes the options of waiting, abandoning, contracting, expanding and switching, by valuing all the options involved and their possible combinations. The results are compared with those of the NPV method and the binomial tree with a logarithmic transformation (BTLT. Both methods (IFD and BTLT yield similar results, being both greater than those provided by the NPV. This difference comes to no surprise as it represents the value of the flexibility associated to an investment opportunity.
El Harouny, El Hassan; Nakra Mohajer, Soukaina; Ibral, Asmaa; El Khamkhami, Jamal; Assaid, El Mahdi
2018-05-01
Eigenvalues equation of hydrogen-like off-center single donor impurity confined in polarized homogeneous hemispherical quantum dot deposited on a wetting layer, capped by insulated matrix and submitted to external uniform electric field is solved in the framework of the effective mass approximation. An infinitely deep potential is used to describe effects of quantum confinement due to conduction band offsets at surfaces where quantum dot and surrounding materials meet. Single donor ground state total and binding energies in presence of electric field are determined via two-dimensional finite difference approach and Ritz-Hassé variation principle. For the latter method, attractive coulomb correlation between electron and ionized single donor is taken into account in the expression of trial wave function. It appears that off-center single dopant binding energy, spatial extension and radial probability density are strongly dependent on hemisphere radius and single dopant position inside quantum dot. Influence of a uniform electric field is also investigated. It shows that Stark effect appears even for very small size dots and that single dopant energy shift is more significant when the single donor is near hemispherical surface.
Mathematical aspects of finite element methods for incompressible viscous flows
Gunzburger, M. D.
1986-01-01
Mathematical aspects of finite element methods are surveyed for incompressible viscous flows, concentrating on the steady primitive variable formulation. The discretization of a weak formulation of the Navier-Stokes equations are addressed, then the stability condition is considered, the satisfaction of which insures the stability of the approximation. Specific choices of finite element spaces for the velocity and pressure are then discussed. Finally, the connection between different weak formulations and a variety of boundary conditions is explored.
Finite element methods for incompressible flow problems
John, Volker
2016-01-01
This book explores finite element methods for incompressible flow problems: Stokes equations, stationary Navier-Stokes equations, and time-dependent Navier-Stokes equations. It focuses on numerical analysis, but also discusses the practical use of these methods and includes numerical illustrations. It also provides a comprehensive overview of analytical results for turbulence models. The proofs are presented step by step, allowing readers to more easily understand the analytical techniques.
International Nuclear Information System (INIS)
Priimak, Dmitri
2014-01-01
We present a finite difference numerical algorithm for solving two dimensional spatially homogeneous Boltzmann transport equation which describes electron transport in a semiconductor superlattice subject to crossed time dependent electric and constant magnetic fields. The algorithm is implemented both in C language targeted to CPU and in CUDA C language targeted to commodity NVidia GPU. We compare performances and merits of one implementation versus another and discuss various software optimisation techniques
Energy Technology Data Exchange (ETDEWEB)
Priimak, Dmitri
2014-12-01
We present a finite difference numerical algorithm for solving two dimensional spatially homogeneous Boltzmann transport equation which describes electron transport in a semiconductor superlattice subject to crossed time dependent electric and constant magnetic fields. The algorithm is implemented both in C language targeted to CPU and in CUDA C language targeted to commodity NVidia GPU. We compare performances and merits of one implementation versus another and discuss various software optimisation techniques.
Finite Element Method in Machining Processes
Markopoulos, Angelos P
2013-01-01
Finite Element Method in Machining Processes provides a concise study on the way the Finite Element Method (FEM) is used in the case of manufacturing processes, primarily in machining. The basics of this kind of modeling are detailed to create a reference that will provide guidelines for those who start to study this method now, but also for scientists already involved in FEM and want to expand their research. A discussion on FEM, formulations and techniques currently in use is followed up by machining case studies. Orthogonal cutting, oblique cutting, 3D simulations for turning and milling, grinding, and state-of-the-art topics such as high speed machining and micromachining are explained with relevant examples. This is all supported by a literature review and a reference list for further study. As FEM is a key method for researchers in the manufacturing and especially in the machining sector, Finite Element Method in Machining Processes is a key reference for students studying manufacturing processes but al...
New mixed finite-element methods
International Nuclear Information System (INIS)
Franca, L.P.
1987-01-01
New finite-element methods are proposed for mixed variational formulations. The methods are constructed by adding to the classical Galerkin method various least-squares like terms. The additional terms involve integrals over element interiors, and include mesh-parameter dependent coefficients. The methods are designed to enhance stability. Consistency is achieved in the sense that exact solutions identically satisfy the variational equations.Applied to several problems, simple finite-element interpolations are rendered convergent, including convenient equal-order interpolations generally unstable within the Galerkin approach. The methods are subdivided into two classes according to the manner in which stability is attained: (1) circumventing Babuska-Brezzi condition methods; (2) satisfying Babuska-Brezzi condition methods. Convergence is established for each class of methods. Applications of the first class of methods to Stokes flow and compressible linear elasticity are presented. The second class of methods is applied to the Poisson, Timoshenko beam and incompressible elasticity problems. Numerical results demonstrate the good stability and accuracy of the methods, and confirm the error estimates
Development and analysis of finite volume methods
International Nuclear Information System (INIS)
Omnes, P.
2010-05-01
This document is a synthesis of a set of works concerning the development and the analysis of finite volume methods used for the numerical approximation of partial differential equations (PDEs) stemming from physics. In the first part, the document deals with co-localized Godunov type schemes for the Maxwell and wave equations, with a study on the loss of precision of this scheme at low Mach number. In the second part, discrete differential operators are built on fairly general, in particular very distorted or nonconforming, bidimensional meshes. These operators are used to approach the solutions of PDEs modelling diffusion, electro and magneto-statics and electromagnetism by the discrete duality finite volume method (DDFV) on staggered meshes. The third part presents the numerical analysis and some a priori as well as a posteriori error estimations for the discretization of the Laplace equation by the DDFV scheme. The last part is devoted to the order of convergence in the L2 norm of the finite volume approximation of the solution of the Laplace equation in one dimension and on meshes with orthogonality properties in two dimensions. Necessary and sufficient conditions, relatively to the mesh geometry and to the regularity of the data, are provided that ensure the second-order convergence of the method. (author)
The finite element response Matrix method
International Nuclear Information System (INIS)
Nakata, H.; Martin, W.R.
1983-01-01
A new method for global reactor core calculations is described. This method is based on a unique formulation of the response matrix method, implemented with a higher order finite element method. The unique aspects of this approach are twofold. First, there are two levels to the overall calculational scheme: the local or assembly level and the global or core level. Second, the response matrix scheme, which is formulated at both levels, consists of two separate response matrices rather than one response matrix as is generally the case. These separate response matrices are seen to be quite beneficial for the criticality eigenvalue calculation, because they are independent of k /SUB eff/. The response matrices are generated from a Galerkin finite element solution to the weak form of the diffusion equation, subject to an arbitrary incoming current and an arbitrary distributed source. Calculational results are reported for two test problems, the two-dimensional International Atomic Energy Agency benchmark problem and a two-dimensional pressurized water reactor test problem (Biblis reactor), and they compare well with standard coarse mesh methods with respect to accuracy and efficiency. Moreover, the accuracy (and capability) is comparable to fine mesh for a fraction of the computational cost. Extension of the method to treat heterogeneous assemblies and spatial depletion effects is discussed
A finite element method for neutron transport
International Nuclear Information System (INIS)
Ackroyd, R.T.
1978-01-01
A variational treatment of the finite element method for neutron transport is given based on a version of the even-parity Boltzmann equation which does not assume that the differential scattering cross-section has a spherical harmonic expansion. The theory of minimum and maximum principles is based on the Cauchy-Schwartz equality and the properties of a leakage operator G and a removal operator C. For systems with extraneous sources, two maximum and one minimum principles are given in boundary free form, to ease finite element computations. The global error of an approximate variational solution is given, the relationship of one the maximum principles to the method of least squares is shown, and the way in which approximate solutions converge locally to the exact solution is established. A method for constructing local error bounds is given, based on the connection between the variational method and the method of the hypercircle. The source iteration technique and a maximum principle for a system with extraneous sources suggests a functional for a variational principle for a self-sustaining system. The principle gives, as a consequence of the properties of G and C, an upper bound to the lowest eigenvalue. A related functional can be used to determine both upper and lower bounds for the lowest eigenvalue from an inspection of any approximate solution for the lowest eigenfunction. The basis for the finite element is presented in a general form so that two modes of exploitation can be undertaken readily. The model can be in phase space, with positional and directional co-ordinates defining points of the model, or it can be restricted to the positional co-ordinates and an expansion in orthogonal functions used for the directional co-ordinates. Suitable sets of functions are spherical harmonics and Walsh functions. The latter set is appropriate if a discrete direction representation of the angular flux is required. (author)
Finite Mathematics and Discrete Mathematics: Is There a Difference?
Johnson, Marvin L.
Discrete mathematics and finite mathematics differ in a number of ways. First, finite mathematics has a longer history and is therefore more stable in terms of course content. Finite mathematics courses emphasize certain particular mathematical tools which are useful in solving the problems of business and the social sciences. Discrete mathematics…
Integral equations with difference kernels on finite intervals
Sakhnovich, Lev A
2015-01-01
This book focuses on solving integral equations with difference kernels on finite intervals. The corresponding problem on the semiaxis was previously solved by N. Wiener–E. Hopf and by M.G. Krein. The problem on finite intervals, though significantly more difficult, may be solved using our method of operator identities. This method is also actively employed in inverse spectral problems, operator factorization and nonlinear integral equations. Applications of the obtained results to optimal synthesis, light scattering, diffraction, and hydrodynamics problems are discussed in this book, which also describes how the theory of operators with difference kernels is applied to stable processes and used to solve the famous M. Kac problems on stable processes. In this second edition these results are extensively generalized and include the case of all Levy processes. We present the convolution expression for the well-known Ito formula of the generator operator, a convolution expression that has proven to be fruitful...
Linear finite element method for one-dimensional diffusion problems
Energy Technology Data Exchange (ETDEWEB)
Brandao, Michele A.; Dominguez, Dany S.; Iglesias, Susana M., E-mail: micheleabrandao@gmail.com, E-mail: dany@labbi.uesc.br, E-mail: smiglesias@uesc.br [Universidade Estadual de Santa Cruz (LCC/DCET/UESC), Ilheus, BA (Brazil). Departamento de Ciencias Exatas e Tecnologicas. Laboratorio de Computacao Cientifica
2011-07-01
We describe in this paper the fundamentals of Linear Finite Element Method (LFEM) applied to one-speed diffusion problems in slab geometry. We present the mathematical formulation to solve eigenvalue and fixed source problems. First, we discretized a calculus domain using a finite set of elements. At this point, we obtain the spatial balance equations for zero order and first order spatial moments inside each element. Then, we introduce the linear auxiliary equations to approximate neutron flux and current inside the element and architect a numerical scheme to obtain the solution. We offer numerical results for fixed source typical model problems to illustrate the method's accuracy for coarse-mesh calculations in homogeneous and heterogeneous domains. Also, we compare the accuracy and computational performance of LFEM formulation with conventional Finite Difference Method (FDM). (author)
Non Standard Finite Difference Scheme for Mutualistic Interaction Description
Gabbriellini, Gianluca
2012-01-01
One of the more interesting themes of the mathematical ecology is the description of the mutualistic interaction between two interacting species. Based on continuous-time model developed by Holland and DeAngelis 2009 for consumer-resource mutualism description, this work deals with the application of the Mickens Non Standard Finite Difference method to transform the continuous-time scheme into a discrete-time one. It has been proved that the Mickens scheme is dynamically consistent with the o...
Application of finite-element-methods in food processing
DEFF Research Database (Denmark)
Risum, Jørgen
2004-01-01
Presentation of the possible use of finite-element-methods in food processing. Examples from diffusion studies are given.......Presentation of the possible use of finite-element-methods in food processing. Examples from diffusion studies are given....
The Laguerre finite difference one-way equation solver
Terekhov, Andrew V.
2017-05-01
This paper presents a new finite difference algorithm for solving the 2D one-way wave equation with a preliminary approximation of a pseudo-differential operator by a system of partial differential equations. As opposed to the existing approaches, the integral Laguerre transform instead of Fourier transform is used. After carrying out the approximation of spatial variables it is possible to obtain systems of linear algebraic equations with better computing properties and to reduce computer costs for their solution. High accuracy of calculations is attained at the expense of employing finite difference approximations of higher accuracy order that are based on the dispersion-relationship-preserving method and the Richardson extrapolation in the downward continuation direction. The numerical experiments have verified that as compared to the spectral difference method based on Fourier transform, the new algorithm allows one to calculate wave fields with a higher degree of accuracy and a lower level of numerical noise and artifacts including those for non-smooth velocity models. In the context of solving the geophysical problem the post-stack migration for velocity models of the types Syncline and Sigsbee2A has been carried out. It is shown that the images obtained contain lesser noise and are considerably better focused as compared to those obtained by the known Fourier Finite Difference and Phase-Shift Plus Interpolation methods. There is an opinion that purely finite difference approaches do not allow carrying out the seismic migration procedure with sufficient accuracy, however the results obtained disprove this statement. For the supercomputer implementation it is proposed to use the parallel dichotomy algorithm when solving systems of linear algebraic equations with block-tridiagonal matrices.
Introduction to finite and spectral element methods using Matlab
Pozrikidis, Constantine
2014-01-01
The Finite Element Method in One Dimension. Further Applications in One Dimension. High-Order and Spectral Elements in One Dimension. The Finite Element Method in Two Dimensions. Quadratic and Spectral Elements in Two Dimensions. Applications in Mechanics. Viscous Flow. Finite and Spectral Element Methods in Three Dimensions. Appendices. References. Index.
Finite Volume Method for Unstructured Grid
International Nuclear Information System (INIS)
Casmara; Kardana, N.D.
1997-01-01
The success of a computational method depends on the solution algorithm and mesh generation techniques. cell distributions are needed, which allow the solution to be calculated over the entire body surface with sufficient accuracy. to handle the mesh generation for multi-connected region such as multi-element bodies, the unstructured finite volume method will be applied. the advantages of the unstructured meshes are it provides a great deal more flexibility for generating meshes about complex geometries and provides a natural setting for the use of adaptive meshing. the governing equations to be discretized are inviscid and rotational euler equations. Applications of the method will be evaluated on flow around single and multi-component bodies
Adaptive finite element methods for differential equations
Bangerth, Wolfgang
2003-01-01
These Lecture Notes discuss concepts of `self-adaptivity' in the numerical solution of differential equations, with emphasis on Galerkin finite element methods. The key issues are a posteriori error estimation and it automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual method for goal-oriented error estimation, is discussed in detail. This method aims at economical computation of arbitrary quantities of physical interest by properly adapting the computational mesh. This is typically required in the design cycles of technical applications. For example, the drag coefficient of a body immersed in a viscous flow is computed, then it is minimized by varying certain control parameters, and finally the stability of the resulting flow is investigated by solving an eigenvalue problem. `Goal-oriented' adaptivity is designed to achieve these tasks with minimal cost. At the end of each chapter some exercises are posed in order ...
Experimental Methods for Implementing Graphene Contacts to Finite Bandgap Semiconductors
DEFF Research Database (Denmark)
Meyer-Holdt, Jakob
Present Ph.D. thesis describes my work on implanting graphene as electrical contact to finite bandgap semiconductors. Different transistor architectures, types of graphene and finite bandgap semiconductors have been employed. The device planned from the beginning of my Ph.D. fellowship...... contacts to semiconductor nanowires, more specifically, epitaxially grown InAs nanowires. First, we tried a top down method where CVD graphene was deposited on substrate supported InAs nanowires followed by selective graphene ashing to define graphene electrodes. While electrical contact between...
Adaptive finite element method for shape optimization
Morin, Pedro; Nochetto, Ricardo H.; Pauletti, Miguel S.; Verani, Marco
2012-01-01
We examine shape optimization problems in the context of inexact sequential quadratic programming. Inexactness is a consequence of using adaptive finite element methods (AFEM) to approximate the state and adjoint equations (via the dual weighted residual method), update the boundary, and compute the geometric functional. We present a novel algorithm that equidistributes the errors due to shape optimization and discretization, thereby leading to coarse resolution in the early stages and fine resolution upon convergence, and thus optimizing the computational effort. We discuss the ability of the algorithm to detect whether or not geometric singularities such as corners are genuine to the problem or simply due to lack of resolution - a new paradigm in adaptivity. © EDP Sciences, SMAI, 2012.
Adaptive finite element method for shape optimization
Morin, Pedro
2012-01-16
We examine shape optimization problems in the context of inexact sequential quadratic programming. Inexactness is a consequence of using adaptive finite element methods (AFEM) to approximate the state and adjoint equations (via the dual weighted residual method), update the boundary, and compute the geometric functional. We present a novel algorithm that equidistributes the errors due to shape optimization and discretization, thereby leading to coarse resolution in the early stages and fine resolution upon convergence, and thus optimizing the computational effort. We discuss the ability of the algorithm to detect whether or not geometric singularities such as corners are genuine to the problem or simply due to lack of resolution - a new paradigm in adaptivity. © EDP Sciences, SMAI, 2012.
Kurtz, L. A.; Smith, R. E.; Parks, C. L.; Boney, L. R.
1978-01-01
Steady state solutions to two time dependent partial differential systems have been obtained by the Method of Lines (MOL) and compared to those obtained by efficient standard finite difference methods: (1) Burger's equation over a finite space domain by a forward time central space explicit method, and (2) the stream function - vorticity form of viscous incompressible fluid flow in a square cavity by an alternating direction implicit (ADI) method. The standard techniques were far more computationally efficient when applicable. In the second example, converged solutions at very high Reynolds numbers were obtained by MOL, whereas solution by ADI was either unattainable or impractical. With regard to 'set up' time, solution by MOL is an attractive alternative to techniques with complicated algorithms, as much of the programming difficulty is eliminated.
The finite element method in engineering, 2nd edition
International Nuclear Information System (INIS)
Rao, S.S.
1986-01-01
This work provides a systematic introduction to the various aspects of the finite element method as applied to engineering problems. Contents include: introduction to finite element method; solution of finite element equations; solid and structural mechanics; static analysis; dynamic analysis; heat transfer; fluid mechanics and additional applications
A multiscale mortar multipoint flux mixed finite element method
Wheeler, Mary Fanett; Xue, Guangri; Yotov, Ivan
2012-01-01
In this paper, we develop a multiscale mortar multipoint flux mixed finite element method for second order elliptic problems. The equations in the coarse elements (or subdomains) are discretized on a fine grid scale by a multipoint flux mixed finite
A particle finite element method for machining simulations
Sabel, Matthias; Sator, Christian; Müller, Ralf
2014-07-01
The particle finite element method (PFEM) appears to be a convenient technique for machining simulations, since the geometry and topology of the problem can undergo severe changes. In this work, a short outline of the PFEM-algorithm is given, which is followed by a detailed description of the involved operations. The -shape method, which is used to track the topology, is explained and tested by a simple example. Also the kinematics and a suitable finite element formulation are introduced. To validate the method simple settings without topological changes are considered and compared to the standard finite element method for large deformations. To examine the performance of the method, when dealing with separating material, a tensile loading is applied to a notched plate. This investigation includes a numerical analysis of the different meshing parameters, and the numerical convergence is studied. With regard to the cutting simulation it is found that only a sufficiently large number of particles (and thus a rather fine finite element discretisation) leads to converged results of process parameters, such as the cutting force.
Finite element and discontinuous Galerkin methods for transient wave equations
Cohen, Gary
2017-01-01
This monograph presents numerical methods for solving transient wave equations (i.e. in time domain). More precisely, it provides an overview of continuous and discontinuous finite element methods for these equations, including their implementation in physical models, an extensive description of 2D and 3D elements with different shapes, such as prisms or pyramids, an analysis of the accuracy of the methods and the study of the Maxwell’s system and the important problem of its spurious free approximations. After recalling the classical models, i.e. acoustics, linear elastodynamics and electromagnetism and their variational formulations, the authors present a wide variety of finite elements of different shapes useful for the numerical resolution of wave equations. Then, they focus on the construction of efficient continuous and discontinuous Galerkin methods and study their accuracy by plane wave techniques and a priori error estimates. A chapter is devoted to the Maxwell’s system and the important problem ...
Flow Applications of the Least Squares Finite Element Method
Jiang, Bo-Nan
1998-01-01
The main thrust of the effort has been towards the development, analysis and implementation of the least-squares finite element method (LSFEM) for fluid dynamics and electromagnetics applications. In the past year, there were four major accomplishments: 1) special treatments in computational fluid dynamics and computational electromagnetics, such as upwinding, numerical dissipation, staggered grid, non-equal order elements, operator splitting and preconditioning, edge elements, and vector potential are unnecessary; 2) the analysis of the LSFEM for most partial differential equations can be based on the bounded inverse theorem; 3) the finite difference and finite volume algorithms solve only two Maxwell equations and ignore the divergence equations; and 4) the first numerical simulation of three-dimensional Marangoni-Benard convection was performed using the LSFEM.
Mimetic Finite Differences for Flow in Fractures from Microseismic Data
Al-Hinai, Omar; Srinivasan, Sanjay; Wheeler, Mary F.
2015-01-01
We present a method for porous media flow in the presence of complex fracture networks. The approach uses the Mimetic Finite Difference method (MFD) and takes advantage of MFD's ability to solve over a general set of polyhedral cells. This flexibility is used to mesh fracture intersections in two and three-dimensional settings without creating small cells at the intersection point. We also demonstrate how to use general polyhedra for embedding fracture boundaries in the reservoir domain. The target application is representing fracture networks inferred from microseismic analysis.
Mimetic Finite Differences for Flow in Fractures from Microseismic Data
Al-Hinai, Omar
2015-01-01
We present a method for porous media flow in the presence of complex fracture networks. The approach uses the Mimetic Finite Difference method (MFD) and takes advantage of MFD\\'s ability to solve over a general set of polyhedral cells. This flexibility is used to mesh fracture intersections in two and three-dimensional settings without creating small cells at the intersection point. We also demonstrate how to use general polyhedra for embedding fracture boundaries in the reservoir domain. The target application is representing fracture networks inferred from microseismic analysis.
A Novel Polygonal Finite Element Method: Virtual Node Method
Tang, X. H.; Zheng, C.; Zhang, J. H.
2010-05-01
Polygonal finite element method (PFEM), which can construct shape functions on polygonal elements, provides greater flexibility in mesh generation. However, the non-polynomial form of traditional PFEM, such as Wachspress method and Mean Value method, leads to inexact numerical integration. Since the integration technique for non-polynomial functions is immature. To overcome this shortcoming, a great number of integration points have to be used to obtain sufficiently exact results, which increases computational cost. In this paper, a novel polygonal finite element method is proposed and called as virtual node method (VNM). The features of present method can be list as: (1) It is a PFEM with polynomial form. Thereby, Hammer integral and Gauss integral can be naturally used to obtain exact numerical integration; (2) Shape functions of VNM satisfy all the requirements of finite element method. To test the performance of VNM, intensive numerical tests are carried out. It found that, in standard patch test, VNM can achieve significantly better results than Wachspress method and Mean Value method. Moreover, it is observed that VNM can achieve better results than triangular 3-node elements in the accuracy test.
Commutative algebra constructive methods finite projective modules
Lombardi, Henri
2015-01-01
Translated from the popular French edition, this book offers a detailed introduction to various basic concepts, methods, principles, and results of commutative algebra. It takes a constructive viewpoint in commutative algebra and studies algorithmic approaches alongside several abstract classical theories. Indeed, it revisits these traditional topics with a new and simplifying manner, making the subject both accessible and innovative. The algorithmic aspects of such naturally abstract topics as Galois theory, Dedekind rings, Prüfer rings, finitely generated projective modules, dimension theory of commutative rings, and others in the current treatise, are all analysed in the spirit of the great developers of constructive algebra in the nineteenth century. This updated and revised edition contains over 350 well-arranged exercises, together with their helpful hints for solution. A basic knowledge of linear algebra, group theory, elementary number theory as well as the fundamentals of ring and module theory is r...
Exact Finite Differences. The Derivative on Non Uniformly Spaced Partitions
Directory of Open Access Journals (Sweden)
Armando Martínez-Pérez
2017-10-01
Full Text Available We define a finite-differences derivative operation, on a non uniformly spaced partition, which has the exponential function as an exact eigenvector. We discuss some properties of this operator and we propose a definition for the components of a finite-differences momentum operator. This allows us to perform exact discrete calculations.
Steam generator tube rupture simulation using extended finite element method
Energy Technology Data Exchange (ETDEWEB)
Mohanty, Subhasish, E-mail: smohanty@anl.gov; Majumdar, Saurin; Natesan, Ken
2016-08-15
Highlights: • Extended finite element method used for modeling the steam generator tube rupture. • Crack propagation is modeled in an arbitrary solution dependent path. • The FE model is used for estimating the rupture pressure of steam generator tubes. • Crack coalescence modeling is also demonstrated. • The method can be used for crack modeling of tubes under severe accident condition. - Abstract: A steam generator (SG) is an important component of any pressurized water reactor. Steam generator tubes represent a primary pressure boundary whose integrity is vital to the safe operation of the reactor. SG tubes may rupture due to propagation of a crack created by mechanisms such as stress corrosion cracking, fatigue, etc. It is thus important to estimate the rupture pressures of cracked tubes for structural integrity evaluation of SGs. The objective of the present paper is to demonstrate the use of extended finite element method capability of commercially available ABAQUS software, to model SG tubes with preexisting flaws and to estimate their rupture pressures. For the purpose, elastic–plastic finite element models were developed for different SG tubes made from Alloy 600 material. The simulation results were compared with experimental results available from the steam generator tube integrity program (SGTIP) sponsored by the United States Nuclear Regulatory Commission (NRC) and conducted at Argonne National Laboratory (ANL). A reasonable correlation was found between extended finite element model results and experimental results.
Steam generator tube rupture simulation using extended finite element method
International Nuclear Information System (INIS)
Mohanty, Subhasish; Majumdar, Saurin; Natesan, Ken
2016-01-01
Highlights: • Extended finite element method used for modeling the steam generator tube rupture. • Crack propagation is modeled in an arbitrary solution dependent path. • The FE model is used for estimating the rupture pressure of steam generator tubes. • Crack coalescence modeling is also demonstrated. • The method can be used for crack modeling of tubes under severe accident condition. - Abstract: A steam generator (SG) is an important component of any pressurized water reactor. Steam generator tubes represent a primary pressure boundary whose integrity is vital to the safe operation of the reactor. SG tubes may rupture due to propagation of a crack created by mechanisms such as stress corrosion cracking, fatigue, etc. It is thus important to estimate the rupture pressures of cracked tubes for structural integrity evaluation of SGs. The objective of the present paper is to demonstrate the use of extended finite element method capability of commercially available ABAQUS software, to model SG tubes with preexisting flaws and to estimate their rupture pressures. For the purpose, elastic–plastic finite element models were developed for different SG tubes made from Alloy 600 material. The simulation results were compared with experimental results available from the steam generator tube integrity program (SGTIP) sponsored by the United States Nuclear Regulatory Commission (NRC) and conducted at Argonne National Laboratory (ANL). A reasonable correlation was found between extended finite element model results and experimental results.
A multiscale mortar multipoint flux mixed finite element method
Wheeler, Mary Fanett
2012-02-03
In this paper, we develop a multiscale mortar multipoint flux mixed finite element method for second order elliptic problems. The equations in the coarse elements (or subdomains) are discretized on a fine grid scale by a multipoint flux mixed finite element method that reduces to cell-centered finite differences on irregular grids. The subdomain grids do not have to match across the interfaces. Continuity of flux between coarse elements is imposed via a mortar finite element space on a coarse grid scale. With an appropriate choice of polynomial degree of the mortar space, we derive optimal order convergence on the fine scale for both the multiscale pressure and velocity, as well as the coarse scale mortar pressure. Some superconvergence results are also derived. The algebraic system is reduced via a non-overlapping domain decomposition to a coarse scale mortar interface problem that is solved using a multiscale flux basis. Numerical experiments are presented to confirm the theory and illustrate the efficiency and flexibility of the method. © EDP Sciences, SMAI, 2012.
A finite difference, multipoint flux numerical approach to flow in porous media: Numerical examples
Osman, Hossam Omar; Salama, Amgad; Sun, Shuyu; Bao, Kai
2012-01-01
It is clear that none of the current available numerical schemes which may be adopted to solve transport phenomena in porous media fulfill all the required robustness conditions. That is while the finite difference methods are the simplest of all, they face several difficulties in complex geometries and anisotropic media. On the other hand, while finite element methods are well suited to complex geometries and can deal with anisotropic media, they are more involved in coding and usually require more execution time. Therefore, in this work we try to combine some features of the finite element technique, namely its ability to work with anisotropic media with the finite difference approach. We reduce the multipoint flux, mixed finite element technique through some quadrature rules to an equivalent cell-centered finite difference approximation. We show examples on using this technique to single-phase flow in anisotropic porous media.
A finite difference, multipoint flux numerical approach to flow in porous media: Numerical examples
Osman, Hossam Omar
2012-06-17
It is clear that none of the current available numerical schemes which may be adopted to solve transport phenomena in porous media fulfill all the required robustness conditions. That is while the finite difference methods are the simplest of all, they face several difficulties in complex geometries and anisotropic media. On the other hand, while finite element methods are well suited to complex geometries and can deal with anisotropic media, they are more involved in coding and usually require more execution time. Therefore, in this work we try to combine some features of the finite element technique, namely its ability to work with anisotropic media with the finite difference approach. We reduce the multipoint flux, mixed finite element technique through some quadrature rules to an equivalent cell-centered finite difference approximation. We show examples on using this technique to single-phase flow in anisotropic porous media.
Finite difference time domain modeling of spiral antennas
Penney, Christopher W.; Beggs, John H.; Luebbers, Raymond J.
1992-01-01
The objectives outlined in the original proposal for this project were to create a well-documented computer analysis model based on the finite-difference, time-domain (FDTD) method that would be capable of computing antenna impedance, far-zone radiation patterns, and radar cross-section (RCS). The ability to model a variety of penetrable materials in addition to conductors is also desired. The spiral antennas under study by this project meet these requirements since they are constructed of slots cut into conducting surfaces which are backed by dielectric materials.
Chabory, A.; Hon, de B.P.; Schilders, W.H.A.; Tijhuis, A.G.
2008-01-01
Finite-difference techniques are very popular and versatile numerical tools in computational electromagnetics. In this paper, we propose a preconditioned finite-difference frequency-domain method (FDFD) to model periodic structures in 2D and 3D. The preconditioner follows from a modal decoupling
Chabory, A.; Hon, de B.P.; Schilders, W.H.A.; Tijhuis, A.G.
2008-01-01
Finite-difference techniques are very popular and versatile numerical tools in computational electromagnetics. In this paper, we propose a preconditioned finite-difference frequency-domain method (FDFD) to model periodic structures in 2D and 3D. The preconditioner follows from a modal decoupling
[Application of Finite Element Method in Thoracolumbar Spine Traumatology].
Zhang, Min; Qiu, Yong-gui; Shao, Yu; Gu, Xiao-feng; Zeng, Ming-wei
2015-04-01
The finite element method (FEM) is a mathematical technique using modern computer technology for stress analysis, and has been gradually used in simulating human body structures in the biomechanical field, especially more widely used in the research of thoracolumbar spine traumatology. This paper reviews the establishment of the thoracolumbar spine FEM, the verification of the FEM, and the thoracolumbar spine FEM research status in different fields, and discusses its prospects and values in forensic thoracolumbar traumatology.
Two-dimensional isostatic meshes in the finite element method
Martínez Marín, Rubén; Samartín, Avelino
2002-01-01
In a Finite Element (FE) analysis of elastic solids several items are usually considered, namely, type and shape of the elements, number of nodes per element, node positions, FE mesh, total number of degrees of freedom (dot) among others. In this paper a method to improve a given FE mesh used for a particular analysis is described. For the improvement criterion different objective functions have been chosen (Total potential energy and Average quadratic error) and the number of nodes and dof's...
Finite-difference schemes for anisotropic diffusion
Energy Technology Data Exchange (ETDEWEB)
Es, Bram van, E-mail: es@cwi.nl [Centrum Wiskunde and Informatica, P.O. Box 94079, 1090GB Amsterdam (Netherlands); FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, Association EURATOM-FOM (Netherlands); Koren, Barry [Eindhoven University of Technology (Netherlands); Blank, Hugo J. de [FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, Association EURATOM-FOM (Netherlands)
2014-09-01
In fusion plasmas diffusion tensors are extremely anisotropic due to the high temperature and large magnetic field strength. This causes diffusion, heat conduction, and viscous momentum loss, to effectively be aligned with the magnetic field lines. This alignment leads to different values for the respective diffusive coefficients in the magnetic field direction and in the perpendicular direction, to the extent that heat diffusion coefficients can be up to 10{sup 12} times larger in the parallel direction than in the perpendicular direction. This anisotropy puts stringent requirements on the numerical methods used to approximate the MHD-equations since any misalignment of the grid may cause the perpendicular diffusion to be polluted by the numerical error in approximating the parallel diffusion. Currently the common approach is to apply magnetic field-aligned coordinates, an approach that automatically takes care of the directionality of the diffusive coefficients. This approach runs into problems at x-points and at points where there is magnetic re-connection, since this causes local non-alignment. It is therefore useful to consider numerical schemes that are tolerant to the misalignment of the grid with the magnetic field lines, both to improve existing methods and to help open the possibility of applying regular non-aligned grids. To investigate this, in this paper several discretization schemes are developed and applied to the anisotropic heat diffusion equation on a non-aligned grid.
The finite element method its basis and fundamentals
Zienkiewicz, Olek C; Zhu, JZ
2013-01-01
The Finite Element Method: Its Basis and Fundamentals offers a complete introduction to the basis of the finite element method, covering fundamental theory and worked examples in the detail required for readers to apply the knowledge to their own engineering problems and understand more advanced applications. This edition sees a significant rearrangement of the book's content to enable clearer development of the finite element method, with major new chapters and sections added to cover: Weak forms Variational forms Multi-dimensional field prob
A finite element solution method for quadrics parallel computer
International Nuclear Information System (INIS)
Zucchini, A.
1996-08-01
A distributed preconditioned conjugate gradient method for finite element analysis has been developed and implemented on a parallel SIMD Quadrics computer. The main characteristic of the method is that it does not require any actual assembling of all element equations in a global system. The physical domain of the problem is partitioned in cells of n p finite elements and each cell element is assigned to a different node of an n p -processors machine. Element stiffness matrices are stored in the data memory of the assigned processing node and the solution process is completely executed in parallel at element level. Inter-element and therefore inter-processor communications are required once per iteration to perform local sums of vector quantities between neighbouring elements. A prototype implementation has been tested on an 8-nodes Quadrics machine in a simple 2D benchmark problem
Finite element analysis of thermal stress distribution in different ...
African Journals Online (AJOL)
Nigerian Journal of Clinical Practice. Journal Home ... Von Mises and thermal stress distributions were evaluated. Results: In all ... distribution. Key words: Amalgam, finite element method, glass ionomer cement, resin composite, thermal stress ...
A simple finite element method for linear hyperbolic problems
International Nuclear Information System (INIS)
Mu, Lin; Ye, Xiu
2017-01-01
Here, we introduce a simple finite element method for solving first order hyperbolic equations with easy implementation and analysis. Our new method, with a symmetric, positive definite system, is designed to use discontinuous approximations on finite element partitions consisting of arbitrary shape of polygons/polyhedra. Error estimate is established. Extensive numerical examples are tested that demonstrate the robustness and flexibility of the method.
Directory of Open Access Journals (Sweden)
W.R. Azzam
2015-08-01
Full Text Available This paper reports the application of using a skirted foundation system to study the behavior of foundations with structural skirts adjacent to a sand slope and subjected to earthquake loading. The effect of the adopted skirts to safeguard foundation and slope from collapse is studied. The skirts effect on controlling horizontal soil movement and decreasing pore water pressure beneath foundations and beside the slopes during earthquake is investigated. This technique is investigated numerically using finite element analysis. A four story reinforced concrete building that rests on a raft foundation is idealized as a two-dimensional model with and without skirts. A two dimensional plain strain program PLAXIS, (dynamic version is adopted. A series of models for the problem under investigation were run under different skirt depths and lactation from the slope crest. The effect of subgrade relative density and skirts thickness is also discussed. Nodal displacement and element strains were analyzed for the foundation with and without skirts and at different studied parameters. The research results showed a great effectiveness in increasing the overall stability of the slope and foundation. The confined soil footing system by such skirts reduced the foundation acceleration therefore it can be tended to damping element and relieved the transmitted disturbance to the adjacent slope. This technique can be considered as a good method to control the slope deformation and decrease the slope acceleration during earthquakes.
International Nuclear Information System (INIS)
Xi Li-Ying; Chen Huan-Ming; Zheng Fu; Gao Hua; Tong Yang; Ma Zhi
2015-01-01
Three-dimensional simulations of ferroelectric hysteresis and butterfly loops are carried out based on solving the time dependent Ginzburg–Landau equations using a finite volume method. The influence of externally mechanical loadings with a tensile strain and a compressive strain on the hysteresis and butterfly loops is studied numerically. Different from the traditional finite element and finite difference methods, the finite volume method is applicable to simulate the ferroelectric phase transitions and properties of ferroelectric materials even for more realistic and physical problems. (paper)
A multigrid solution method for mixed hybrid finite elements
Energy Technology Data Exchange (ETDEWEB)
Schmid, W. [Universitaet Augsburg (Germany)
1996-12-31
We consider the multigrid solution of linear equations arising within the discretization of elliptic second order boundary value problems of the form by mixed hybrid finite elements. Using the equivalence of mixed hybrid finite elements and non-conforming nodal finite elements, we construct a multigrid scheme for the corresponding non-conforming finite elements, and, by this equivalence, for the mixed hybrid finite elements, following guidelines from Arbogast/Chen. For a rectangular triangulation of the computational domain, this non-conforming schemes are the so-called nodal finite elements. We explicitly construct prolongation and restriction operators for this type of non-conforming finite elements. We discuss the use of plain multigrid and the multilevel-preconditioned cg-method and compare their efficiency in numerical tests.
A hybrid finite-volume and finite difference scheme for depth-integrated non-hydrostatic model
Yin, Jing; Sun, Jia-wen; Wang, Xing-gang; Yu, Yong-hai; Sun, Zhao-chen
2017-06-01
A depth-integrated, non-hydrostatic model with hybrid finite difference and finite volume numerical algorithm is proposed in this paper. By utilizing a fraction step method, the governing equations are decomposed into hydrostatic and non-hydrostatic parts. The first part is solved by using the finite volume conservative discretization method, whilst the latter is considered by solving discretized Poisson-type equations with the finite difference method. The second-order accuracy, both in time and space, of the finite volume scheme is achieved by using an explicit predictor-correction step and linear construction of variable state in cells. The fluxes across the cell faces are computed in a Godunov-based manner by using MUSTA scheme. Slope and flux limiting technique is used to equip the algorithm with total variation dimensioning property for shock capturing purpose. Wave breaking is treated as a shock by switching off the non-hydrostatic pressure in the steep wave front locally. The model deals with moving wet/dry front in a simple way. Numerical experiments are conducted to verify the proposed model.
A parallel adaptive finite difference algorithm for petroleum reservoir simulation
Energy Technology Data Exchange (ETDEWEB)
Hoang, Hai Minh
2005-07-01
Adaptive finite differential for problems arising in simulation of flow in porous medium applications are considered. Such methods have been proven useful for overcoming limitations of computational resources and improving the resolution of the numerical solutions to a wide range of problems. By local refinement of the computational mesh where it is needed to improve the accuracy of solutions, yields better solution resolution representing more efficient use of computational resources than is possible with traditional fixed-grid approaches. In this thesis, we propose a parallel adaptive cell-centered finite difference (PAFD) method for black-oil reservoir simulation models. This is an extension of the adaptive mesh refinement (AMR) methodology first developed by Berger and Oliger (1984) for the hyperbolic problem. Our algorithm is fully adaptive in time and space through the use of subcycling, in which finer grids are advanced at smaller time steps than the coarser ones. When coarse and fine grids reach the same advanced time level, they are synchronized to ensure that the global solution is conservative and satisfy the divergence constraint across all levels of refinement. The material in this thesis is subdivided in to three overall parts. First we explain the methodology and intricacies of AFD scheme. Then we extend a finite differential cell-centered approximation discretization to a multilevel hierarchy of refined grids, and finally we are employing the algorithm on parallel computer. The results in this work show that the approach presented is robust, and stable, thus demonstrating the increased solution accuracy due to local refinement and reduced computing resource consumption. (Author)
Finite element method for neutron diffusion problems in hexagonal geometry
International Nuclear Information System (INIS)
Wei, T.Y.C.; Hansen, K.F.
1975-06-01
The use of the finite element method for solving two-dimensional static neutron diffusion problems in hexagonal reactor configurations is considered. It is investigated as a possible alternative to the low-order finite difference method. Various piecewise polynomial spaces are examined for their use in hexagonal problems. The central questions which arise in the design of these spaces are the degree of incompleteness permissible and the advantages of using a low-order space fine-mesh approach over that of a high-order space coarse-mesh one. There is also the question of the degree of smoothness required. Two schemes for the construction of spaces are described and a number of specific spaces, constructed with the questions outlined above in mind, are presented. They range from a complete non-Lagrangian, non-Hermite quadratic space to an incomplete ninth order space. Results are presented for two-dimensional problems typical of a small high temperature gas-cooled reactor. From the results it is concluded that the space used should at least include the complete linear one. Complete spaces are to be preferred to totally incomplete ones. Once function continuity is imposed any additional degree of smoothness is of secondary importance. For flux shapes typical of the small high temperature gas-cooled reactor the linear space fine-mesh alternative is to be preferred to the perturbation quadratic space coarse-mesh one and the low-order finite difference method is to be preferred over both finite element schemes
DEFF Research Database (Denmark)
Bieniasz, Leslaw K.; Østerby, Ole; Britz, Dieter
1995-01-01
The stepwise numerical stability of the classic explicit, fully implicit and Crank-Nicolson finite difference discretizations of example diffusional initial boundary value problems from electrochemical kinetics has been investigated using the matrix method of stability analysis. Special attention...... has been paid to the effect of the discretization of the mixed, linear boundary condition with time-dependent coefficients on stability, assuming the two-point forward-difference approximations for the gradient at the left boundary (electrode). Under accepted assumptions one obtains the usual...... stability criteria for the classic explicit and fully implicit methods. The Crank-Nicolson method turns out to be only conditionally stable in contrast to the current thought regarding this method....
International Nuclear Information System (INIS)
Wang Shumin; Duyn, Jeff H
2008-01-01
A hybrid method that combines the finite-difference time-domain (FDTD) method and the finite-element time-domain (FETD) method is presented for simulating radio-frequency (RF) coils in magnetic resonance imaging. This method applies a high-fidelity FETD method to RF coils, while the human body is modeled with a low-cost FDTD method. Since the FDTD and the FETD methods are applied simultaneously, the dynamic interaction between RF coils and the human body is fully accounted for. In order to simplify the treatment of the highly irregular FDTD/FETD interface, composite elements are proposed. Two examples are provided to demonstrate the validity and effectiveness of the hybrid method in high-field receive-and-transmit coil design. This approach is also applicable to general bio-electromagnetic simulations
Patra, Asim
2018-03-01
This paper displays the approach of the time-splitting Fourier spectral (TSFS) technique for the linear Riesz fractional Schrödinger equation (RFSE) in the semi-classical regime. The splitting technique is shown to be unconditionally stable. Further a suitable implicit finite difference discretization of second order has been manifested for the RFSE where the Riesz derivative has been discretized via an approach of fractional centered difference. Moreover the stability analysis for the implicit scheme has also been presented here via von Neumann analysis. The L2-norm and L^{∞}-norm errors are calculated for \\vert u(x,t)\\vert2, Re(u(x,t)) and Im(u(x,t)) for various cases. The results obtained by the methods are further tabulated for the absolute errors for \\vert u(x,t)\\vert2. Furthermore the graphs are depicted showing comparison of \\vert u(x,t)\\vert2 by both techniques. The derivatives are taken here in the context of the Riesz fractional sense. Apart from that, the comparative study put forth in the following section via tables and graphs between the implicit second-order finite difference method (IFDM) and the TSFS method is for the purpose of investigating the efficiency of the results obtained. Moreover the stability analysis of the presented techniques manifesting their unconditional stability makes the proposed approach more competing and accurate.
Symbolic generation of finite difference formulas
International Nuclear Information System (INIS)
Keller, H.; Pereyra, V.
1978-01-01
Tables of coefficients for high order accurate, compact approximations to the first ten derivatives on and at the midpoints of uniform nets are presented. The exact rational weights are generated and tested by means of symbolic manipulation implemented through MACSYMA. These weights are required in the application of deferred corrections to new methods for solving higher order two point boundary value problems
Energy Technology Data Exchange (ETDEWEB)
Sanada, Y; Ashida, Y; Sassa, K [Kyoto University, Kyoto (Japan)
1996-10-01
3-D numerical modeling by FDTD method was studied for ground penetrating radar. Radar radiates electromagnetic wave, and determines the existence and distance of objects by reflection wave. Ground penetrating radar uses the above functions for underground surveys, however, its resolution and velocity analysis accuracy are problems. In particular, propagation characteristics of electromagnetic wave in media such as heterogeneous and anisotropic soil and rock are essential. The behavior of electromagnetic wave in the ground could be precisely reproduced by 3-D numerical modeling using FDTD method. FDTD method makes precise analysis in time domain and electric and magnetic fields possible by sequentially calculating the difference equation of Maxwell`s equation. Because of the high calculation efficiency of FDTD method, more precise complicated analysis can be expected by using the latest advanced computers. The numerical model and calculation example are illustrated for surface type electromagnetic pulse ground penetrating radar assuming the survey of steel pipes of 1m deep. 4 refs., 3 figs., 1 tab.
Coupled Finite Volume and Finite Element Method Analysis of a Complex Large-Span Roof Structure
Szafran, J.; Juszczyk, K.; Kamiński, M.
2017-12-01
The main goal of this paper is to present coupled Computational Fluid Dynamics and structural analysis for the precise determination of wind impact on internal forces and deformations of structural elements of a longspan roof structure. The Finite Volume Method (FVM) serves for a solution of the fluid flow problem to model the air flow around the structure, whose results are applied in turn as the boundary tractions in the Finite Element Method problem structural solution for the linear elastostatics with small deformations. The first part is carried out with the use of ANSYS 15.0 computer system, whereas the FEM system Robot supports stress analysis in particular roof members. A comparison of the wind pressure distribution throughout the roof surface shows some differences with respect to that available in the engineering designing codes like Eurocode, which deserves separate further numerical studies. Coupling of these two separate numerical techniques appears to be promising in view of future computational models of stochastic nature in large scale structural systems due to the stochastic perturbation method.
Finite difference computing with exponential decay models
Langtangen, Hans Petter
2016-01-01
This text provides a very simple, initial introduction to the complete scientific computing pipeline: models, discretization, algorithms, programming, verification, and visualization. The pedagogical strategy is to use one case study – an ordinary differential equation describing exponential decay processes – to illustrate fundamental concepts in mathematics and computer science. The book is easy to read and only requires a command of one-variable calculus and some very basic knowledge about computer programming. Contrary to similar texts on numerical methods and programming, this text has a much stronger focus on implementation and teaches testing and software engineering in particular. .
Çelik Köycü, Berrak; İmirzalıoğlu, Pervin
2017-07-01
Daily consumption of food and drink creates rapid temperature changes in the oral cavity. Heat transfer and thermal stress caused by temperature changes in restored teeth may damage the hard and soft tissue components, resulting in restoration failure. This study evaluates the temperature distribution and related thermal stress on mandibular molar teeth restored via three indirect restorations using three-dimensional (3D) finite element analysis (FEA). A 3D finite element model was constructed of a mandibular first molar and included enamel, dentin, pulp, surrounding bone, and indirect class 2 restorations of type 2 dental gold alloy, ceramic, and composite resin. A transient thermal FEA was performed to investigate the temperature distribution and the resulting thermal stress after simulated temperature changes from 36°C to 4 or 60°C for a 2-second time period. The restoration models had similar temperature distributions at 2 seconds in both the thermal conditions. Compared with 60°C exposure, the 4°C condition resulted in thermal stress values of higher magnitudes. At 4ºC, the highest stress value observed was tensile stress (56 to 57 MPa), whereas at 60°C, the highest stress value observed was compressive stress (42 to 43 MPa). These stresses appeared at the cervical region of the lingual enamel. The thermal stress at the restoration surface and resin cement showed decreasing order of magnitude as follows: composite > gold > ceramic, in both thermal conditions. The properties of the restorative materials do not affect temperature distribution at 2 seconds in restored teeth. The pulpal temperature is below the threshold for vital pulp tissue (42ºC). Temperature changes generate maximum thermal stress at the cervical region of the enamel. With the highest thermal expansion coefficient, composite resin restorations exhibit higher stress patterns than ceramic and gold restorations. © 2015 by the American College of Prosthodontists.
Moving magnets in a micromagnetic finite-difference framework
Rissanen, Ilari; Laurson, Lasse
2018-05-01
We present a method and an implementation for smooth linear motion in a finite-difference-based micromagnetic simulation code, to be used in simulating magnetic friction and other phenomena involving moving microscale magnets. Our aim is to accurately simulate the magnetization dynamics and relative motion of magnets while retaining high computational speed. To this end, we combine techniques for fast scalar potential calculation and cubic b-spline interpolation, parallelizing them on a graphics processing unit (GPU). The implementation also includes the possibility of explicitly simulating eddy currents in the case of conducting magnets. We test our implementation by providing numerical examples of stick-slip motion of thin films pulled by a spring and the effect of eddy currents on the switching time of magnetic nanocubes.
Mixed isogeometric finite cell methods for the stokes problem
Hoang, T.; Verhoosel, C.V.; Auricchio, F.; van Brummelen, E.H.; Reali, A.
2017-01-01
We study the application of the Isogeometric Finite Cell Method (IGA-FCM) to mixed formulations in the context of the Stokes problem. We investigate the performance of the IGA-FCM when utilizing some isogeometric mixed finite elements, namely: Taylor-Hood, Sub-grid, Raviart-Thomas, and Nédélec
A Note on Symplectic, Multisymplectic Scheme in Finite Element Method
Institute of Scientific and Technical Information of China (English)
GUO Han-Ying; JI Xiao-Mei; LI Yu-Qi; WU Ke
2001-01-01
We find that with uniform mesh, the numerical schemes derived from finite element method can keep a preserved symplectic structure in one-dimensional case and a preserved multisymplectic structure in two-dimensional case respectively. These results are in fact the intrinsic reason why the numerical experiments show that such finite element algorithms are accurate in practice.``
THE PRACTICAL ANALYSIS OF FINITE ELEMENTS METHOD ERRORS
Directory of Open Access Journals (Sweden)
Natalia Bakhova
2011-03-01
Full Text Available Abstract. The most important in the practical plan questions of reliable estimations of finite elementsmethod errors are considered. Definition rules of necessary calculations accuracy are developed. Methodsand ways of the calculations allowing receiving at economical expenditures of computing work the best finalresults are offered.Keywords: error, given the accuracy, finite element method, lagrangian and hermitian elements.
Meshfree simulation of avalanches with the Finite Pointset Method (FPM)
Michel, Isabel; Kuhnert, Jörg; Kolymbas, Dimitrios
2017-04-01
Meshfree methods are the numerical method of choice in case of applications which are characterized by strong deformations in conjunction with free surfaces or phase boundaries. In the past the meshfree Finite Pointset Method (FPM) developed by Fraunhofer ITWM (Kaiserslautern, Germany) has been successfully applied to problems in computational fluid dynamics such as water crossing of cars, water turbines, and hydraulic valves. Most recently the simulation of granular flows, e.g. soil interaction with cars (rollover), has also been tackled. This advancement is the basis for the simulation of avalanches. Due to the generalized finite difference formulation in FPM, the implementation of different material models is quite simple. We will demonstrate 3D simulations of avalanches based on the Drucker-Prager yield criterion as well as the nonlinear barodesy model. The barodesy model (Division of Geotechnical and Tunnel Engineering, University of Innsbruck, Austria) describes the mechanical behavior of soil by an evolution equation for the stress tensor. The key feature of successful and realistic simulations of avalanches - apart from the numerical approximation of the occurring differential operators - is the choice of the boundary conditions (slip, no-slip, friction) between the different phases of the flow as well as the geometry. We will discuss their influences for simplified one- and two-phase flow examples. This research is funded by the German Research Foundation (DFG) and the FWF Austrian Science Fund.
Piezoelectric Analysis of Saw Sensor Using Finite Element Method
Directory of Open Access Journals (Sweden)
Vladimír KUTIŠ
2013-06-01
Full Text Available In this contribution modeling and simulation of surface acoustic waves (SAW sensor using finite element method will be presented. SAW sensor is made from piezoelectric GaN layer and SiC substrate. Two different analysis types are investigated - modal and transient. Both analyses are only 2D. The goal of modal analysis, is to determine the eigenfrequency of SAW, which is used in following transient analysis. In transient analysis, wave propagation in SAW sensor is investigated. Both analyses were performed using FEM code ANSYS.
Scientific use of the finite element method in Orthodontics
Knop, Luegya; Gandini, Luiz Gonzaga; Shintcovsk, Ricardo Lima; Gandini, Marcia Regina Elisa Aparecida Schiavon
2015-01-01
INTRODUCTION: The finite element method (FEM) is an engineering resource applied to calculate the stress and deformation of complex structures, and has been widely used in orthodontic research. With the advantage of being a non-invasive and accurate method that provides quantitative and detailed data on the physiological reactions possible to occur in tissues, applying the FEM can anticipate the visualization of these tissue responses through the observation of areas of stress created from applied orthodontic mechanics. OBJECTIVE: This article aims at reviewing and discussing the stages of the finite element method application and its applicability in Orthodontics. RESULTS: FEM is able to evaluate the stress distribution at the interface between periodontal ligament and alveolar bone, and the shifting trend in various types of tooth movement when using different types of orthodontic devices. Therefore, it is necessary to know specific software for this purpose. CONCLUSIONS: FEM is an important experimental method to answer questions about tooth movement, overcoming the disadvantages of other experimental methods. PMID:25992996
Factorization method for simulating QCD at finite density
International Nuclear Information System (INIS)
Nishimura, Jun
2003-01-01
We propose a new method for simulating QCD at finite density. The method is based on a general factorization property of distribution functions of observables, and it is therefore applicable to any system with a complex action. The so-called overlap problem is completely eliminated by the use of constrained simulations. We test this method in a Random Matrix Theory for finite density QCD, where we are able to reproduce the exact results for the quark number density. (author)
Topology optimization using the finite volume method
DEFF Research Database (Denmark)
Gersborg-Hansen, Allan; Bendsøe, Martin P.; Sigmund, Ole
2005-01-01
in this presentation is focused on a prototype model for topology optimization of steady heat diffusion. This allows for a study of the basic ingredients in working with FVM methods when dealing with topology optimization problems. The FVM and FEM based formulations differ both in how one computes the design...... derivative of the system matrix $\\mathbf K$ and in how one computes the discretized version of certain objective functions. Thus for a cost function for minimum dissipated energy (like minimum compliance for an elastic structure) one obtains an expression $ c = \\mathbf u^\\T \\tilde{\\mathbf K} \\mathbf u...... the arithmetic and harmonic average with the latter being the well known Reuss lower bound. [1] Bendsøe, MP and Sigmund, O 2004: Topology Optimization - Theory, Methods, and Applications. Berlin Heidelberg: Springer Verlag [2] Versteeg, HK and Malalasekera, W 1995: An introduction to Computational Fluid Dynamics...
On the spectral properties of random finite difference operators
International Nuclear Information System (INIS)
Kunz, H.; Souillard, B.
1980-01-01
We study a class of random finite difference operators, a typical example of which is the finite difference Schroedinger operator with a random potential which arises in solid state physics in the tight binding approximation. We obtain with probability one, in various situations, the exact location of the spectrum, and criterions for a given part in the spectrum to be pure point or purely continuous, or for the static electric conductivity to vanish. A general formalism is developped which transforms the study of these random operators into that of the asymptotics of a multiple integral constructed from a given recipe. Finally we apply our criterions and formalism to prove that, with probability one, the one-dimensional finite difference Schroedinger operator with a random potential has pure point spectrum and developps no static conductivity. (orig.)
Numerical experiment on finite element method for matching data
International Nuclear Information System (INIS)
Tokuda, Shinji; Kumakura, Toshimasa; Yoshimura, Koichi.
1993-03-01
Numerical experiments are presented on the finite element method by Pletzer-Dewar for matching data of an ordinary differential equation with regular singular points by using model equation. Matching data play an important role in nonideal MHD stability analysis of a magnetically confined plasma. In the Pletzer-Dewar method, the Frobenius series for the 'big solution', the fundamental solution which is not square-integrable at the regular singular point, is prescribed. The experiments include studies of the convergence rate of the matching data obtained by the finite element method and of the effect on the results of computation by truncating the Frobenius series at finite terms. It is shown from the present study that the finite element method is an effective method for obtaining the matching data with high accuracy. (author)
The Mixed Finite Element Multigrid Method for Stokes Equations
Muzhinji, K.; Shateyi, S.; Motsa, S. S.
2015-01-01
The stable finite element discretization of the Stokes problem produces a symmetric indefinite system of linear algebraic equations. A variety of iterative solvers have been proposed for such systems in an attempt to construct efficient, fast, and robust solution techniques. This paper investigates one of such iterative solvers, the geometric multigrid solver, to find the approximate solution of the indefinite systems. The main ingredient of the multigrid method is the choice of an appropriate smoothing strategy. This study considers the application of different smoothers and compares their effects in the overall performance of the multigrid solver. We study the multigrid method with the following smoothers: distributed Gauss Seidel, inexact Uzawa, preconditioned MINRES, and Braess-Sarazin type smoothers. A comparative study of the smoothers shows that the Braess-Sarazin smoothers enhance good performance of the multigrid method. We study the problem in a two-dimensional domain using stable Hood-Taylor Q 2-Q 1 pair of finite rectangular elements. We also give the main theoretical convergence results. We present the numerical results to demonstrate the efficiency and robustness of the multigrid method and confirm the theoretical results. PMID:25945361
3-D spherical harmonics code FFT3 by the finite Fourier transformation method
International Nuclear Information System (INIS)
Kobayashi, K.
1997-01-01
In the odd order spherical harmonics method, the rigorous boundary condition at the material interfaces is that the even moments of the angular flux and the normal components of the even order moments of current vectors must be continuous. However, it is difficult to derive spatial discretized equations by the finite difference or finite element methods, which satisfy this material interface condition. It is shown that using the finite Fourier transformation method, space discretized equations which satisfy this interface condition can be easily derived. The discrepancies of the flux distribution near void region between spherical harmonics method codes may be due to the difference of application of the material interface condition. (author)
International Nuclear Information System (INIS)
Al-Akhrass, Dina
2014-01-01
Simulations in solid mechanics exhibit several difficulties, as dealing with incompressibility, with nonlinearities due to finite strains, contact laws, or constitutive laws. The basic motivation of our work is to propose efficient finite element methods capable of dealing with incompressibility in finite strain context, and using elements of low order. During the three last decades, many approaches have been proposed in the literature to overcome the incompressibility problem. Among them, mixed formulations offer an interesting theoretical framework. In this work, a three-field mixed formulation (displacement, pressure, volumetric strain) is investigated. In some cases, this formulation can be condensed in a two-field (displacement - pressure) mixed formulation. However, it is well-known that the discrete problem given by the Galerkin finite element technique, does not inherit the 'inf-sup' stability condition from the continuous problem. Hence, the interpolation orders in displacement and pressure have to be chosen in a way to satisfy the Brezzi-Babuska stability conditions when using Galerkin approaches. Interpolation orders must be chosen so as to satisfy this condition. Two possibilities are considered: to use stable finite element satisfying this requirement, or to use finite element that does not satisfy this condition, and to add terms stabilizing the FE Galerkin formulation. The latter approach allows the use of equal order interpolation. In this work, stable finite element P2/P1 and P2/P1/P1 are used as reference, and compared to P1/P1 and P1/P1/P1 formulations stabilized with a bubble function or with a VMS method (Variational Multi-Scale) based on a sub-grid-space orthogonal to the FE space. A finite strain model based on logarithmic strain is selected. This approach is extended to three and two field mixed formulations with stable or stabilized elements. These approaches are validated on academic cases and used on industrial cases. (author)
田中, 英一; TANAKA, Eiichi; 山本, 創太; YAMAMOTO, Sota; 坂本, 誠二; SAKAMOTO, Seiji; 中西, 孝文; NAKANISHI, Takafumi; 原田, 敦; HARADA, Atsushi; 水野, 雅士; MIZUNO, Masashi
2004-01-01
This paper is concerned with an individual finite element modeling system for femur and biomechanical evaluations of the influences of loading conditions, bone shape and bone density on risks of hip fracture. Firstly, a method to construct an individual finite element model by morphological parameters that represent femoral shapes was developed. Using the models with different shapes constructed by this method, the effects of fall direction, posture of upper body, femur shape and bone density...
Review of Tomographic Imaging using Finite Element Method
Directory of Open Access Journals (Sweden)
Mohd Fua’ad RAHMAT
2011-12-01
Full Text Available Many types of techniques for process tomography were proposed and developed during the past 20 years. This paper review the techniques and the current state of knowledge and experience on the subject, aimed at highlighting the problems associated with the non finite element methods, such as the ill posed, ill conditioned which relates to the accuracy and sensitivity of measurements. In this paper, considerations for choice of sensors and its applications were outlined and descriptions of non finite element tomography systems were presented. The finite element method tomography system as obtained from recent works, suitable for process control and measurement were also presented.
Generalization of mixed multiscale finite element methods with applications
Energy Technology Data Exchange (ETDEWEB)
Lee, C S [Texas A & M Univ., College Station, TX (United States)
2016-08-01
Many science and engineering problems exhibit scale disparity and high contrast. The small scale features cannot be omitted in the physical models because they can affect the macroscopic behavior of the problems. However, resolving all the scales in these problems can be prohibitively expensive. As a consequence, some types of model reduction techniques are required to design efficient solution algorithms. For practical purpose, we are interested in mixed finite element problems as they produce solutions with certain conservative properties. Existing multiscale methods for such problems include the mixed multiscale finite element methods. We show that for complicated problems, the mixed multiscale finite element methods may not be able to produce reliable approximations. This motivates the need of enrichment for coarse spaces. Two enrichment approaches are proposed, one is based on generalized multiscale finte element metthods (GMsFEM), while the other is based on spectral element-based algebraic multigrid (rAMGe). The former one, which is called mixed GMsFEM, is developed for both Darcy’s flow and linear elasticity. Application of the algorithm in two-phase flow simulations are demonstrated. For linear elasticity, the algorithm is subtly modified due to the symmetry requirement of the stress tensor. The latter enrichment approach is based on rAMGe. The algorithm differs from GMsFEM in that both of the velocity and pressure spaces are coarsened. Due the multigrid nature of the algorithm, recursive application is available, which results in an efficient multilevel construction of the coarse spaces. Stability, convergence analysis, and exhaustive numerical experiments are carried out to validate the proposed enrichment approaches. iii
A multipoint flux mixed finite element method on distorted quadrilaterals and hexahedra
Wheeler, Mary; Xue, Guangri; Yotov, Ivan
2011-01-01
In this paper, we develop a new mixed finite element method for elliptic problems on general quadrilateral and hexahedral grids that reduces to a cell-centered finite difference scheme. A special non-symmetric quadrature rule is employed that yields
A Finite Segment Method for Skewed Box Girder Analysis
Directory of Open Access Journals (Sweden)
Xingwei Xue
2018-01-01
Full Text Available A finite segment method is presented to analyze the mechanical behavior of skewed box girders. By modeling the top and bottom plates of the segments with skew plate beam element under an inclined coordinate system and the webs with normal plate beam element, a spatial elastic displacement model for skewed box girder is constructed, which can satisfy the compatibility condition at the corners of the cross section for box girders. The formulation of the finite segment is developed based on the variational principle. The major advantage of the proposed approach, in comparison with the finite element method, is that it can simplify a three-dimensional structure into a one-dimensional structure for structural analysis, which results in significant saving in computational times. At last, the accuracy and efficiency of the proposed finite segment method are verified by a model test.
Finite element formulation for a digital image correlation method
International Nuclear Information System (INIS)
Sun Yaofeng; Pang, John H. L.; Wong, Chee Khuen; Su Fei
2005-01-01
A finite element formulation for a digital image correlation method is presented that will determine directly the complete, two-dimensional displacement field during the image correlation process on digital images. The entire interested image area is discretized into finite elements that are involved in the common image correlation process by use of our algorithms. This image correlation method with finite element formulation has an advantage over subset-based image correlation methods because it satisfies the requirements of displacement continuity and derivative continuity among elements on images. Numerical studies and a real experiment are used to verify the proposed formulation. Results have shown that the image correlation with the finite element formulation is computationally efficient, accurate, and robust
Finite Difference Schemes as Algebraic Correspondences between Layers
Malykh, Mikhail; Sevastianov, Leonid
2018-02-01
For some differential equations, especially for Riccati equation, new finite difference schemes are suggested. These schemes define protective correspondences between the layers. Calculation using these schemes can be extended to the area beyond movable singularities of exact solution without any error accumulation.
Huang, Lianjie
2013-10-29
Methods for enhancing ultrasonic reflection imaging are taught utilizing a split-step Fourier propagator in which the reconstruction is based on recursive inward continuation of ultrasonic wavefields in the frequency-space and frequency-wave number domains. The inward continuation within each extrapolation interval consists of two steps. In the first step, a phase-shift term is applied to the data in the frequency-wave number domain for propagation in a reference medium. The second step consists of applying another phase-shift term to data in the frequency-space domain to approximately compensate for ultrasonic scattering effects of heterogeneities within the tissue being imaged (e.g., breast tissue). Results from various data input to the method indicate significant improvements are provided in both image quality and resolution.
A finite element conjugate gradient FFT method for scattering
Collins, Jeffery D.; Ross, Dan; Jin, J.-M.; Chatterjee, A.; Volakis, John L.
1991-01-01
Validated results are presented for the new 3D body of revolution finite element boundary integral code. A Fourier series expansion of the vector electric and mangnetic fields is employed to reduce the dimensionality of the system, and the exact boundary condition is employed to terminate the finite element mesh. The mesh termination boundary is chosen such that is leads to convolutional boundary operatores of low O(n) memory demand. Improvements of this code are discussed along with the proposed formulation for a full 3D implementation of the finite element boundary integral method in conjunction with a conjugate gradiant fast Fourier transformation (CGFFT) solution.
Directory of Open Access Journals (Sweden)
Peng Jiang
2013-01-01
Full Text Available The authors attempt to construct the exact finite-difference schemes for linear stochastic differential equations with constant coefficients. The explicit solutions to Itô and Stratonovich linear stochastic differential equations with constant coefficients are adopted with the view of providing exact finite-difference schemes to solve them. In particular, the authors utilize the exact finite-difference schemes of Stratonovich type linear stochastic differential equations to solve the Kubo oscillator that is widely used in physics. Further, the authors prove that the exact finite-difference schemes can preserve the symplectic structure and first integral of the Kubo oscillator. The authors also use numerical examples to prove the validity of the numerical methods proposed in this paper.
Chu, Chunlei
2009-01-01
We analyze the dispersion properties and stability conditions of the high‐order convolutional finite difference operators and compare them with the conventional finite difference schemes. We observe that the convolutional finite difference method has better dispersion properties and becomes more efficient than the conventional finite difference method with the increasing order of accuracy. This makes the high‐order convolutional operator a good choice for anisotropic elastic wave simulations on rotated staggered grids since its enhanced dispersion properties can help to suppress the numerical dispersion error that is inherent in the rotated staggered grid structure and its efficiency can help us tackle 3D problems cost‐effectively.
Numerical solution of multi group-Two dimensional- Adjoint equation with finite element method
International Nuclear Information System (INIS)
Poursalehi, N.; Khalafi, H.; Shahriari, M.; Minoochehr
2008-01-01
Adjoint equation is used for perturbation theory in nuclear reactor design. For numerical solution of adjoint equation, usually two methods are applied. These are Finite Element and Finite Difference procedures. Usually Finite Element Procedure is chosen for solving of adjoint equation, because it is more use able in variety of geometries. In this article, Galerkin Finite Element method is discussed. This method is applied for numerical solving multi group, multi region and two dimensional (X, Y) adjoint equation. Typical reactor geometry is partitioned with triangular meshes and boundary condition for adjoint flux is considered zero. Finally, for a case of defined parameters, Finite Element Code was applied and results were compared with Citation Code
Finite differences versus finite elements in slab geometry, even-parity transport theory
International Nuclear Information System (INIS)
Miller, W.F. Jr.; Noh, T.
1993-01-01
There continues to be considerable interest in the application of the even-parity transport equation to problems of radiation transfer and neutron transport. The motivation for this interest arises from several potential advantages of this equation when compared with the more traditional first-order form of the equation. First, assuming that the scalar flux is of primary interest, the angular domain under consideration is one-half of that required for the first-order equation. Thus, for the same degree of accuracy, one would hopefully require substantiably fewer unknown values of the dependent variable to be determined. Secondly, the elliptic-like nature of the set of even-parity equations should allow certain parallel computer architectures to be used more readily. In a recent paper, it was shown that for neutron transport applications in slab geometry, finite differencing the even-parity equation on the cell edges yields algebraic equations with numerical properties that are superior to the traditional diamond difference approach. Specifically, a positive, second-order method with a rapidly convergent iteration approach emerged from cell-edge differencing. Additionally, for radiation transfer problems that are optically thick, it was shown that cell-edge differencing demonstrates better behavior than does diamond-differencing. However, some problems in accuracy could occur due to vacuum boundaries as well as at interfaces between very different types of material regions. These problems emerge from a boundary-layer analysis of the so called open-quotes thickclose quotes diffusion limit. For neutronics calculations, which are the subject of this paper, however, the open-quotes thickclose quotes diffusion limit analysis has little applicability, and the cell-edge differencing derived previously seems to have considerable promise. 13 refs., 2 figs., 3 tabs
Galerkin finite element methods for wave problems
Indian Academy of Sciences (India)
basis functions (called G1FEM here) and quadratic basis functions (called G2FEM) ... mulation of Brookes & Hughes (1982) that implicitly incorporates numerical ..... functions and (c) SUPG method in the (kh − ω t)-plane for explicit Euler.
Hermitian Mindlin Plate Wavelet Finite Element Method for Load Identification
Directory of Open Access Journals (Sweden)
Xiaofeng Xue
2016-01-01
Full Text Available A new Hermitian Mindlin plate wavelet element is proposed. The two-dimensional Hermitian cubic spline interpolation wavelet is substituted into finite element functions to construct frequency response function (FRF. It uses a system’s FRF and response spectrums to calculate load spectrums and then derives loads in the time domain via the inverse fast Fourier transform. By simulating different excitation cases, Hermitian cubic spline wavelets on the interval (HCSWI finite elements are used to reverse load identification in the Mindlin plate. The singular value decomposition (SVD method is adopted to solve the ill-posed inverse problem. Compared with ANSYS results, HCSWI Mindlin plate element can accurately identify the applied load. Numerical results show that the algorithm of HCSWI Mindlin plate element is effective. The accuracy of HCSWI can be verified by comparing the FRF of HCSWI and ANSYS elements with the experiment data. The experiment proves that the load identification of HCSWI Mindlin plate is effective and precise by using the FRF and response spectrums to calculate the loads.
Finite-element method modeling of hyper-frequency structures
International Nuclear Information System (INIS)
Zhang, Min
1990-01-01
The modelization of microwave propagation problems, including Eigen-value problem and scattering problem, is accomplished by the finite element method with vector functional and scalar functional. For Eigen-value problem, propagation modes in waveguides and resonant modes in cavities can be calculated in a arbitrarily-shaped structure with inhomogeneous material. Several microwave structures are resolved in order to verify the program. One drawback associated with the vector functional is the appearance of spurious or non-physical solutions. A penalty function method has been introduced to reduce spurious' solutions. The adaptive charge method is originally proposed in this thesis to resolve waveguide scattering problem. This method, similar to VSWR measuring technique, is more efficient to obtain the reflection coefficient than the matrix method. Two waveguide discontinuity structures are calculated by the two methods and their results are compared. The adaptive charge method is also applied to a microwave plasma excitor. It allows us to understand the role of different physical parameters of excitor in the coupling of microwave energy to plasma mode and the mode without plasma. (author) [fr
Precise magnetostatic field using the finite element method
International Nuclear Information System (INIS)
Nascimento, Francisco Rogerio Teixeira do
2013-01-01
The main objective of this work is to simulate electromagnetic fields using the Finite Element Method. Even in the easiest case of electrostatic and magnetostatic numerical simulation some problems appear when the nodal finite element is used. It is difficult to model vector fields with scalar functions mainly in non-homogeneous materials. With the aim to solve these problems two types of techniques are tried: the adaptive remeshing using nodal elements and the edge finite element that ensure the continuity of tangential components. Some numerical analysis of simple electromagnetic problems with homogeneous and non-homogeneous materials are performed using first, the adaptive remeshing based in various error indicators and second, the numerical solution of waveguides using edge finite element. (author)
Complex finite element sensitivity method for creep analysis
International Nuclear Information System (INIS)
Gomez-Farias, Armando; Montoya, Arturo; Millwater, Harry
2015-01-01
The complex finite element method (ZFEM) has been extended to perform sensitivity analysis for mechanical and structural systems undergoing creep deformation. ZFEM uses a complex finite element formulation to provide shape, material, and loading derivatives of the system response, providing an insight into the essential factors which control the behavior of the system as a function of time. A complex variable-based quadrilateral user element (UEL) subroutine implementing the power law creep constitutive formulation was incorporated within the Abaqus commercial finite element software. The results of the complex finite element computations were verified by comparing them to the reference solution for the steady-state creep problem of a thick-walled cylinder in the power law creep range. A practical application of the ZFEM implementation to creep deformation analysis is the calculation of the skeletal point of a notched bar test from a single ZFEM run. In contrast, the standard finite element procedure requires multiple runs. The value of the skeletal point is that it identifies the location where the stress state is accurate, regardless of the certainty of the creep material properties. - Highlights: • A novel finite element sensitivity method (ZFEM) for creep was introduced. • ZFEM has the capability to calculate accurate partial derivatives. • ZFEM can be used for identification of the skeletal point of creep structures. • ZFEM can be easily implemented in a commercial software, e.g. Abaqus. • ZFEM results were shown to be in excellent agreement with analytical solutions
A fast finite-difference algorithm for topology optimization of permanent magnets
Abert, Claas; Huber, Christian; Bruckner, Florian; Vogler, Christoph; Wautischer, Gregor; Suess, Dieter
2017-09-01
We present a finite-difference method for the topology optimization of permanent magnets that is based on the fast-Fourier-transform (FFT) accelerated computation of the stray-field. The presented method employs the density approach for topology optimization and uses an adjoint method for the gradient computation. Comparison to various state-of-the-art finite-element implementations shows a superior performance and accuracy. Moreover, the presented method is very flexible and easy to implement due to various preexisting FFT stray-field implementations that can be used.
Optimized Finite-Difference Coefficients for Hydroacoustic Modeling
Preston, L. A.
2014-12-01
Responsible utilization of marine renewable energy sources through the use of current energy converter (CEC) and wave energy converter (WEC) devices requires an understanding of the noise generation and propagation from these systems in the marine environment. Acoustic noise produced by rotating turbines, for example, could adversely affect marine animals and human-related marine activities if not properly understood and mitigated. We are utilizing a 3-D finite-difference acoustic simulation code developed at Sandia that can accurately propagate noise in the complex bathymetry in the near-shore to open ocean environment. As part of our efforts to improve computation efficiency in the large, high-resolution domains required in this project, we investigate the effects of using optimized finite-difference coefficients on the accuracy of the simulations. We compare accuracy and runtime of various finite-difference coefficients optimized via criteria such as maximum numerical phase speed error, maximum numerical group speed error, and L-1 and L-2 norms of weighted numerical group and phase speed errors over a given spectral bandwidth. We find that those coefficients optimized for L-1 and L-2 norms are superior in accuracy to those based on maximal error and can produce runtimes of 10% of the baseline case, which uses Taylor Series finite-difference coefficients at the Courant time step limit. We will present comparisons of the results for the various cases evaluated as well as recommendations for utilization of the cases studied. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
Nonlinear nonstationary analysis with the finite element method
International Nuclear Information System (INIS)
Vaz, L.E.
1981-01-01
In this paper, after some introductory remarks on numerical methods for the integration of initial value problems, the applicability of the finite element method for transient diffusion analysis as well as dynamic and inelastic analysis is discussed, and some examples are presented. (RW) [de
The future of the finite element method in geotechnics
Brinkgreve, R.B.J.
2012-01-01
In this presentation a vision is given on tlie fiiture of the finite element method (FEM) for geotechnical engineering and design. In the past 20 years the FEM has proven to be a powerful method for estimating deformation, stability and groundwater flow in geoteclmical stmctures. Much has been
Discontinuous Galerkin finite element methods for hyperbolic differential equations
van der Vegt, Jacobus J.W.; van der Ven, H.; Boelens, O.J.; Boelens, O.J.; Toro, E.F.
2002-01-01
In this paper a suryey is given of the important steps in the development of discontinuous Galerkin finite element methods for hyperbolic partial differential equations. Special attention is paid to the application of the discontinuous Galerkin method to the solution of the Euler equations of gas
Finite-difference time-domain analysis of time-resolved terahertz spectroscopy experiments
DEFF Research Database (Denmark)
Larsen, Casper; Cooke, David G.; Jepsen, Peter Uhd
2011-01-01
In this paper we report on the numerical analysis of a time-resolved terahertz (THz) spectroscopy experiment using a modified finite-difference time-domain method. Using this method, we show that ultrafast carrier dynamics can be extracted with a time resolution smaller than the duration of the T...
A coupled boundary element-finite difference solution of the elliptic modified mild slope equation
DEFF Research Database (Denmark)
Naserizadeh, R.; Bingham, Harry B.; Noorzad, A.
2011-01-01
The modified mild slope equation of [5] is solved using a combination of the boundary element method (BEM) and the finite difference method (FDM). The exterior domain of constant depth and infinite horizontal extent is solved by a BEM using linear or quadratic elements. The interior domain...
Matlab and C programming for Trefftz finite element methods
Qin, Qing-Hua
2008-01-01
Although the Trefftz finite element method (FEM) has become a powerful computational tool in the analysis of plane elasticity, thin and thick plate bending, Poisson's equation, heat conduction, and piezoelectric materials, there are few books that offer a comprehensive computer programming treatment of the subject. Collecting results scattered in the literature, MATLAB® and C Programming for Trefftz Finite Element Methods provides the detailed MATLAB® and C programming processes in applications of the Trefftz FEM to potential and elastic problems. The book begins with an introduction to th
The finite section method and problems in frame theory
DEFF Research Database (Denmark)
Christensen, Ole; Strohmer, T.
2005-01-01
solves related computational problems in frame theory. In the case of a frame which is localized w.r.t. an orthonormal basis we are able to estimate the rate of approximation. The results are applied to the reproducing kernel frame appearing in the theory for shift-invariant spaces generated by a Riesz......The finite section method is a convenient tool for approximation of the inverse of certain operators using finite-dimensional matrix techniques. In this paper we demonstrate that the method is very useful in frame theory: it leads to an efficient approximation of the inverse frame operator and also...
Comparison of finite-difference and variational solutions to advection-diffusion problems
International Nuclear Information System (INIS)
Lee, C.E.; Washington, K.E.
1984-01-01
Two numerical solution methods are developed for 1-D time-dependent advection-diffusion problems on infinite and finite domains. Numerical solutions are compared with analytical results for constant coefficients and various boundary conditions. A finite-difference spectrum method is solved exactly in time for periodic boundary conditions by a matrix operator method and exhibits excellent accuracy compared with other methods, especially at late times, where it is also computationally more efficient. Finite-system solutions are determined from a conservational variational principle with cubic spatial trial functions and solved in time by a matrix operator method. Comparisons of problems with few nodes show excellent agreement with analytical solutions and exhibit the necessity of implementing Lagrangian conservational constraints for physically-correct solutions. (author)
Finite difference program for calculating hydride bed wall temperature profiles
International Nuclear Information System (INIS)
Klein, J.E.
1992-01-01
A QuickBASIC finite difference program was written for calculating one dimensional temperature profiles in up to two media with flat, cylindrical, or spherical geometries. The development of the program was motivated by the need to calculate maximum temperature differences across the walls of the Tritium metal hydrides beds for thermal fatigue analysis. The purpose of this report is to document the equations and the computer program used to calculate transient wall temperatures in stainless steel hydride vessels. The development of the computer code was motivated by the need to calculate maximum temperature differences across the walls of the hydrides beds in the Tritium Facility for thermal fatigue analysis
Engineering computation of structures the finite element method
Neto, Maria Augusta; Roseiro, Luis; Cirne, José; Leal, Rogério
2015-01-01
This book presents theories and the main useful techniques of the Finite Element Method (FEM), with an introduction to FEM and many case studies of its use in engineering practice. It supports engineers and students to solve primarily linear problems in mechanical engineering, with a main focus on static and dynamic structural problems. Readers of this text are encouraged to discover the proper relationship between theory and practice, within the finite element method: Practice without theory is blind, but theory without practice is sterile. Beginning with elasticity basic concepts and the classical theories of stressed materials, the work goes on to apply the relationship between forces, displacements, stresses and strains on the process of modeling, simulating and designing engineered technical systems. Chapters discuss the finite element equations for static, eigenvalue analysis, as well as transient analyses. Students and practitioners using commercial FEM software will find this book very helpful. It us...
Energy flow in plate assembles by hierarchical version of finite element method
DEFF Research Database (Denmark)
Wachulec, Marcin; Kirkegaard, Poul Henning
method has been proposed. In this paper a modified hierarchical version of finite element method is used for modelling of energy flow in plate assembles. The formulation includes description of in-plane forces so that planes lying in different planes can be modelled. Two examples considered are: L......The dynamic analysis of structures in medium and high frequencies are usually focused on frequency and spatial averages of energy of components, and not the displacement/velocity fields. This is especially true for structure-borne noise modelling. For the analysis of complicated structures...... the finite element method has been used to study the energy flow. The finite element method proved its usefulness despite the computational expense. Therefore studies have been conducted in order to simplify and reduce the computations required. Among others, the use of hierarchical version of finite element...
Coupling of smooth particle hydrodynamics with the finite element method
International Nuclear Information System (INIS)
Attaway, S.W.; Heinstein, M.W.; Swegle, J.W.
1994-01-01
A gridless technique called smooth particle hydrodynamics (SPH) has been coupled with the transient dynamics finite element code ppercase[pronto]. In this paper, a new weighted residual derivation for the SPH method will be presented, and the methods used to embed SPH within ppercase[pronto] will be outlined. Example SPH ppercase[pronto] calculations will also be presented. One major difficulty associated with the Lagrangian finite element method is modeling materials with no shear strength; for example, gases, fluids and explosive biproducts. Typically, these materials can be modeled for only a short time with a Lagrangian finite element code. Large distortions cause tangling of the mesh, which will eventually lead to numerical difficulties, such as negative element area or ''bow tie'' elements. Remeshing will allow the problem to continue for a short while, but the large distortions can prevent a complete analysis. SPH is a gridless Lagrangian technique. Requiring no mesh, SPH has the potential to model material fracture, large shear flows and penetration. SPH computes the strain rate and the stress divergence based on the nearest neighbors of a particle, which are determined using an efficient particle-sorting technique. Embedding the SPH method within ppercase[pronto] allows part of the problem to be modeled with quadrilateral finite elements, while other parts are modeled with the gridless SPH method. SPH elements are coupled to the quadrilateral elements through a contact-like algorithm. ((orig.))
Modeling seismic wave propagation using staggered-grid mimetic finite differences
Directory of Open Access Journals (Sweden)
Freysimar Solano-Feo
2017-04-01
Full Text Available Mimetic finite difference (MFD approximations of continuous gradient and divergence operators satisfy a discrete version of the Gauss-Divergence theorem on staggered grids. On the mimetic approximation of this integral conservation principle, an unique boundary flux operator is introduced that also intervenes on the discretization of a given boundary value problem (BVP. In this work, we present a second-order MFD scheme for seismic wave propagation on staggered grids that discretized free surface and absorbing boundary conditions (ABC with same accuracy order. This scheme is time explicit after coupling a central three-level finite difference (FD stencil for numerical integration. Here, we briefly discuss the convergence properties of this scheme and show its higher accuracy on a challenging test when compared to a traditional FD method. Preliminary applications to 2-D seismic scenarios are also presented and show the potential of the mimetic finite difference method.
Energy Technology Data Exchange (ETDEWEB)
Nascimento, E.O.; Oliveira, L.N., E-mail: lucas@ifg.edu.br [Instituto Federal de Educacao, Ciencia e Tecnologia de Goias (IFG), Goiania, GO (Brazil)
2014-11-01
Partial Differential Equations (PDE) can model natural phenomena, such as related to physics, chemistry and engineering. For these classes of equations, analytical solutions are difficult to be obtained, so a computational approach is indicted. In this context, the Finite Difference Method (FDM) can provide useful tools for the field of Medical Physics. In this study, is described the implementation of a computational mesh, in order to be used in determining the Diffusion Coefficient (DC) of the Fricke Xylenol Gel dosimeter (FXG). The initial and boundary conditions both referred by experimental factors are modelled in FDM, thus making a semi-empirical study in determining the DC. Together, the method of Reflection and Superposition (SRM) and the analysis of experimental data, served as first validation for the simulation. Such methodologies interface generated concordant results for a range of error of 3% in concentration lines for small times when compared to the analytical solution. The result for the DC was 0.43 mm{sup 2} /h. This value is in concordance with measures parameters range found in polymer gels dosimeters: 0.3-2.0 mm{sup 2} /h. Therefore, the application of computer simulation methodology supported by the FDM may be used in determining the diffusion coefficient in FXG dosimeter. (author)
Thermal buckling comparative analysis using Different FE (Finite Element) tools
Energy Technology Data Exchange (ETDEWEB)
Banasiak, Waldemar; Labouriau, Pedro [INTECSEA do Brasil, Rio de Janeiro, RJ (Brazil); Burnett, Christopher [INTECSEA UK, Surrey (United Kingdom); Falepin, Hendrik [Fugro Engineers SA/NV, Brussels (Belgium)
2009-12-19
High operational temperature and pressure in offshore pipelines may lead to unexpected lateral movements, sometimes call lateral buckling, which can have serious consequences for the integrity of the pipeline. The phenomenon of lateral buckling in offshore pipelines needs to be analysed in the design phase using FEM. The analysis should take into account many parameters, including operational temperature and pressure, fluid characteristic, seabed profile, soil parameters, coatings of the pipe, free spans etc. The buckling initiation force is sensitive to small changes of any initial geometric out-of-straightness, thus the modeling of the as-laid state of the pipeline is an important part of the design process. Recently some dedicated finite elements programs have been created making modeling of the offshore environment more convenient that has been the case with the use of general purpose finite element software. The present paper aims to compare thermal buckling analysis of sub sea pipeline performed using different finite elements tools, i.e. general purpose programs (ANSYS, ABAQUS) and dedicated software (SAGE Profile 3D) for a single pipeline resting on an the seabed. The analyses considered the pipeline resting on a flat seabed with a small levels of out-of straightness initiating the lateral buckling. The results show the quite good agreement of results of buckling in elastic range and in the conclusions next comparative analyses with sensitivity cases are recommended. (author)
Czech Academy of Sciences Publication Activity Database
Berezovski, A.; Kolman, Radek; Blažek, Jiří; Kopačka, Ján; Gabriel, Dušan; Plešek, Jiří
2014-01-01
Roč. 19, č. 12 (2014) ISSN 1435-4934. [European Conference on Non-Destructive Testing (ECNDT 2014) /11./. Praha, 06.10.2014-10.10.2014] R&D Projects: GA ČR(CZ) GAP101/11/0288; GA ČR(CZ) GAP101/12/2315 Institutional support: RVO:61388998 Keywords : elastic wave propagation * finite element method * isogeometric analysis * finite volume method * stress discontinuities * spurious oscillations Subject RIV: JR - Other Machinery http://www.ndt.net/events/ECNDT2014/app/content/Paper/25_Berezovski_Rev1.pdf
A finite element method for SSI time history calculation
International Nuclear Information System (INIS)
Ni, X.; Gantenbein, F.; Petit, M.
1989-01-01
The method which is proposed is based on a finite element modelization for the soil and the structure and a time history calculation. It has been developed for plane and axisymmetric geometries. The principle of this method is presented, then applications are given, first to a linear calculation for which results will be compared to those obtained by standard methods. Then results for a non linear behavior are described
Thermohydraulic analysis in pipelines using the finite element method
International Nuclear Information System (INIS)
Costa, L.E.; Idelsohn, S.R.
1984-01-01
The Finite Element Method (FEM) is employed for the numerical solution of fluid flow problems with combined heat transfer mechanisms. Boussinesq approximations are used for the solution of the governing equations. The application of the FEM leads to a set of simultaneous nonlinear equations. The development of the method, for the solution of bidimensional and axisymmetric problems, is presented. Examples of fluid flow in pipes, including natural and forced convection, are solved with the proposed method and discussed in the paper. (Author) [pt
A finite element method for SSI time history calculations
International Nuclear Information System (INIS)
Ni, X.M.; Gantenbein, F.; Petit, M.
1989-01-01
The method which is proposed is based on a finite element modelisation for the soil and the structure and a time history calculation. It has been developed for plane and axisymmetric geometries. The principle of this method will be presented, then applications will be given, first to a linear calculation for which results will be compared to those obtained by standard methods. Then results for a non linear behavior will be described
Piezoelectric Accelerometers Modification Based on the Finite Element Method
DEFF Research Database (Denmark)
Liu, Bin; Kriegbaum, B.
2000-01-01
The paper describes the modification of piezoelectric accelerometers using a Finite Element (FE) method. Brüel & Kjær Accelerometer Type 8325 is chosen as an example to illustrate the advanced accelerometer development procedure. The deviation between the measurement and FE simulation results...
A mixed finite element method for particle simulation in lasertron
International Nuclear Information System (INIS)
Le Meur, G.
1987-03-01
A particle simulation code is being developed with the aim to treat the motion of charged particles in electromagnetic devices, such as Lasertron. The paper describes the use of mixed finite element methods in computing the field components, without derivating them from scalar or vector potentials. Graphical results are shown
Possibilities of Particle Finite Element Methods in Industrial Forming Processes
Oliver, J.; Cante, J. C.; Weyler, R.; Hernandez, J.
2007-04-01
The work investigates the possibilities offered by the particle finite element method (PFEM) in the simulation of forming problems involving large deformations, multiple contacts, and new boundaries generation. The description of the most distinguishing aspects of the PFEM, and its application to simulation of representative forming processes, illustrate the proposed methodology.
Computations of finite temperature QCD with the pseudofermion method
International Nuclear Information System (INIS)
Fucito, F.; Solomon, S.
1985-01-01
The authors discuss the phase diagram of finite temperature QCD as it is obtained including the effects of dynamical quarks by the pseudofermion method. They compare their results with the results obtained by other groups and comment on the actual state of the art for these kind of computations
A mixed finite element method for particle simulation in Lasertron
International Nuclear Information System (INIS)
Le Meur, G.
1987-01-01
A particle simulation code is being developed with the aim to treat the motion of charged particles in electromagnetic devices, such as Lasertron. The paper describes the use of mixed finite element methods in computing the field components, without derivating them from scalar or vector potentials. Graphical results are shown
Deflation in preconditioned conjugate gradient methods for Finite Element Problems
Vermolen, F.J.; Vuik, C.; Segal, A.
2002-01-01
We investigate the influence of the value of deflation vectors at interfaces on the rate of convergence of preconditioned conjugate gradient methods applied to a Finite Element discretization for an elliptic equation. Our set-up is a Poisson problem in two dimensions with continuous or discontinuous
Spectral Analysis of Large Finite Element Problems by Optimization Methods
Directory of Open Access Journals (Sweden)
Luca Bergamaschi
1994-01-01
Full Text Available Recently an efficient method for the solution of the partial symmetric eigenproblem (DACG, deflated-accelerated conjugate gradient was developed, based on the conjugate gradient (CG minimization of successive Rayleigh quotients over deflated subspaces of decreasing size. In this article four different choices of the coefficient βk required at each DACG iteration for the computation of the new search direction Pk are discussed. The “optimal” choice is the one that yields the same asymptotic convergence rate as the CG scheme applied to the solution of linear systems. Numerical results point out that the optimal βk leads to a very cost effective algorithm in terms of CPU time in all the sample problems presented. Various preconditioners are also analyzed. It is found that DACG using the optimal βk and (LLT−1 as a preconditioner, L being the incomplete Cholesky factor of A, proves a very promising method for the partial eigensolution. It appears to be superior to the Lanczos method in the evaluation of the 40 leftmost eigenpairs of five finite element problems, and particularly for the largest problem, with size equal to 4560, for which the speed gain turns out to fall between 2.5 and 6.0, depending on the eigenpair level.
Zhebel, E.; Minisini, S.; Kononov, A.; Mulder, W.A.
2013-01-01
With the rapid developments in parallel compute architectures, algorithms for seismic modeling and imaging need to be reconsidered in terms of parallelization. The aim of this paper is to compare scalability of seismic modeling algorithms: finite differences, continuous mass-lumped finite elements
Finite difference evolution equations and quantum dynamical semigroups
International Nuclear Information System (INIS)
Ghirardi, G.C.; Weber, T.
1983-12-01
We consider the recently proposed [Bonifacio, Lett. Nuovo Cimento, 37, 481 (1983)] coarse grained description of time evolution for the density operator rho(t) through a finite difference equation with steps tau, and we prove that there exists a generator of the quantum dynamical semigroup type yielding an equation giving a continuous evolution coinciding at all time steps with the one induced by the coarse grained description. The map rho(0)→rho(t) derived in this way takes the standard form originally proposed by Lindblad [Comm. Math. Phys., 48, 119 (1976)], even when the map itself (and, therefore, the corresponding generator) is not bounded. (author)
Guessing lexicon entries using finite-state methods
Koskenniemi, Kimmo Matti
2018-01-01
A practical method for interactive guessing of LEXC lexicon entries is presented. The method is based on describing groups of similarly inflected words using regular expressions. The patterns are compiled into a finite-state transducer (FST) which maps any word form into the possible LEXC lexicon entries which could generate it. The same FST can be used (1) for converting conventional headword lists into LEXC entries, (2) for interactive guessing of entries, (3) for corpus-assisted interactiv...
Convergence of a residual based artificial viscosity finite element method
Nazarov, Murtazo
2013-02-01
We present a residual based artificial viscosity finite element method to solve conservation laws. The Galerkin approximation is stabilized by only residual based artificial viscosity, without any least-squares, SUPG, or streamline diffusion terms. We prove convergence of the method, applied to a scalar conservation law in two space dimensions, toward an unique entropy solution for implicit time stepping schemes. © 2012 Elsevier B.V. All rights reserved.
A code for obtaining temperature distribution by finite element method
International Nuclear Information System (INIS)
Bloch, M.
1984-01-01
The ELEFIB Fortran language computer code using finite element method for calculating temperature distribution of linear and two dimensional problems, in permanent region or in the transient phase of heat transfer, is presented. The formulation of equations uses the Galerkin method. Some examples are shown and the results are compared with other papers. The comparative evaluation shows that the elaborated code gives good values. (M.C.K.) [pt
Formulation of coarse mesh finite difference to calculate mathematical adjoint flux
International Nuclear Information System (INIS)
Pereira, Valmir; Martinez, Aquilino Senra; Silva, Fernando Carvalho da
2002-01-01
The objective of this work is the obtention of the mathematical adjoint flux, having as its support the nodal expansion method (NEM) for coarse mesh problems. Since there are difficulties to evaluate this flux by using NEM. directly, a coarse mesh finite difference program was developed to obtain this adjoint flux. The coarse mesh finite difference formulation (DFMG) adopted uses results of the direct calculation (node average flux and node face averaged currents) obtained by NEM. These quantities (flux and currents) are used to obtain the correction factors which modify the classical finite differences formulation . Since the DFMG formulation is also capable of calculating the direct flux it was also tested to obtain this flux and it was verified that it was able to reproduce with good accuracy both the flux and the currents obtained via NEM. In this way, only matrix transposition is needed to calculate the mathematical adjoint flux. (author)
International Nuclear Information System (INIS)
Hong, Ser Gi; Lee, Young Ouk; Song, Jae Seung
2009-01-01
This paper analyzes the convergence of the rebalance iteration methods for the discrete ordinates transport equation in the multiplying finite slab problem. The finite slab is assumed to be homogeneous and it has the periodic boundary conditions. A general formulation is used to include three well-known rebalance methods of the linearized form in a unified way. The rebalance iteration methods considered in this paper are the CMR (Coarse-Mesh Rebalance), the CMFD (Coarse-Mesh Finite Difference), and p-CMFD (Partial Current-Based Coarse Mesh Finite Difference) methods which have been popularly used in the reactor physics. The convergence analysis is performed with the well-known Fourier analysis through a linearization. The analyses are applied for one-group problems. The theoretical analysis shows that there are one fundamental mode and N-1 Eigen-modes which determine the convergence if the finite slab is divided into N uniform meshes. The numerical tests show that the Fourier convergence analysis provides the reasonable estimate of the numerical spectral radii for the model problems and the spectral radius for the finite slab approaches the one for the infinite slab as the thickness of the slab increases. (author)
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.
Numerical simulation for cracks detection using the finite elements method
Directory of Open Access Journals (Sweden)
S Bennoud
2016-09-01
Full Text Available The means of detection must ensure controls either during initial construction, or at the time of exploitation of all parts. The Non destructive testing (NDT gathers the most widespread methods for detecting defects of a part or review the integrity of a structure. In the areas of advanced industry (aeronautics, aerospace, nuclear …, assessing the damage of materials is a key point to control durability and reliability of parts and materials in service. In this context, it is necessary to quantify the damage and identify the different mechanisms responsible for the progress of this damage. It is therefore essential to characterize materials and identify the most sensitive indicators attached to damage to prevent their destruction and use them optimally. In this work, simulation by finite elements method is realized with aim to calculate the electromagnetic energy of interaction: probe and piece (with/without defect. From calculated energy, we deduce the real and imaginary components of the impedance which enables to determine the characteristic parameters of a crack in various metallic parts.
Development op finite volume methods for fluid dynamics
International Nuclear Information System (INIS)
Delcourte, S.
2007-09-01
We aim to develop a finite volume method which applies to a greater class of meshes than other finite volume methods, restricted by orthogonality constraints. We build discrete differential operators over the three staggered tessellations needed for the construction of the method. These operators verify some analogous properties to those of the continuous operators. At first, the method is applied to the Div-Curl problem, which can be viewed as a building block of the Stokes problem. Then, the Stokes problem is dealt with with various boundary conditions. It is well known that when the computational domain is polygonal and non-convex, the order of convergence of numerical methods is deteriorated. Consequently, we have studied how an appropriate local refinement is able to restore the optimal order of convergence for the Laplacian problem. At last, we have discretized the non-linear Navier-Stokes problem, using the rotational formulation of the convection term, associated to the Bernoulli pressure. With an iterative algorithm, we are led to solve a saddle-point problem at each iteration. We give a particular interest to this linear problem by testing some pre-conditioners issued from finite elements, which we adapt to our method. Each problem is illustrated by numerical results on arbitrary meshes, such as strongly non-conforming meshes. (author)
Detailed balance principle and finite-difference stochastic equation in a field theory
International Nuclear Information System (INIS)
Kozhamkulov, T.A.
1986-01-01
A finite-difference equation, which is a generalization of the Langevin equation in field theory, has been obtained basing upon the principle of detailed balance for the Markov chain. Advantages of the present approach as compared with the conventional Parisi-Wu method are shown for examples of an exactly solvable problem of zero-dimensional quantum theory and a simple numerical simulation
Principle of detailed balance and the finite-difference stochastic equation in field theory
International Nuclear Information System (INIS)
Kozhamkulov, T.A.
1986-01-01
The principle of detailed balance for the Markov chain is used to obtain a finite-difference equation which generalizes the Langevin equation in field theory. The advantages of using this approach compared to the conventional Parisi-Wu method are demonstrated for the examples of an exactly solvable problem in zero-dimensional quantum theory and a simple numerical simulation
Finite cover method with mortar elements for elastoplasticity problems
Kurumatani, M.; Terada, K.
2005-06-01
Finite cover method (FCM) is extended to elastoplasticity problems. The FCM, which was originally developed under the name of manifold method, has recently been recognized as one of the generalized versions of finite element methods (FEM). Since the mesh for the FCM can be regular and squared regardless of the geometry of structures to be analyzed, structural analysts are released from a burdensome task of generating meshes conforming to physical boundaries. Numerical experiments are carried out to assess the performance of the FCM with such discretization in elastoplasticity problems. Particularly to achieve this accurately, the so-called mortar elements are introduced to impose displacement boundary conditions on the essential boundaries, and displacement compatibility conditions on material interfaces of two-phase materials or on joint surfaces between mutually incompatible meshes. The validity of the mortar approximation is also demonstrated in the elastic-plastic FCM.
Stability Analysis of Anchored Soil Slope Based on Finite Element Limit Equilibrium Method
Directory of Open Access Journals (Sweden)
Rui Zhang
2016-01-01
Full Text Available Under the condition of the plane strain, finite element limit equilibrium method is used to study some key problems of stability analysis for anchored slope. The definition of safe factor in slices method is generalized into FEM. The “true” stress field in the whole structure can be obtained by elastic-plastic finite element analysis. Then, the optimal search for the most dangerous sliding surface with Hooke-Jeeves optimized searching method is introduced. Three cases of stability analysis of natural slope, anchored slope with seepage, and excavation anchored slope are conducted. The differences in safety factor quantity, shape and location of slip surface, anchoring effect among slices method, finite element strength reduction method (SRM, and finite element limit equilibrium method are comparatively analyzed. The results show that the safety factor given by the FEM is greater and the unfavorable slip surface is deeper than that by the slice method. The finite element limit equilibrium method has high calculation accuracy, and to some extent the slice method underestimates the effect of anchor, and the effect of anchor is overrated in the SRM.
International Nuclear Information System (INIS)
Ishikawa, H.; Nakano, S.; Yuuki, R.; Chung, N.Y.
1991-01-01
In the virtual crack extension method, the stress intensity factor, K, is obtained from the converged value of the energy release rate by the difference of the finite element stiffness matrix when some crack extension are taken. Instead of the numerical difference of the finite element stiffness, a new method to use a direct dirivative of the finite element stiffness matrix with respect to crack length is proposed. By the present method, the results of some example problems, such as uniform tension problems of a square plate with a center crack and a rectangular plate with an internal slant crack, are obtained with high accuracy and good efficiency. Comparing with analytical results, the present values of the stress intensity factors of the problems are obtained with the error that is less than 0.6%. This shows the numerical assurance of the usefulness of the present method. A personal computer program for the analysis is developed
Hybrid finite volume/ finite element method for radiative heat transfer in graded index media
Zhang, L.; Zhao, J. M.; Liu, L. H.; Wang, S. Y.
2012-09-01
The rays propagate along curved path determined by the Fermat principle in the graded index medium. The radiative transfer equation in graded index medium (GRTE) contains two specific redistribution terms (with partial derivatives to the angular coordinates) accounting for the effect of the curved ray path. In this paper, the hybrid finite volume with finite element method (hybrid FVM/FEM) (P.J. Coelho, J. Quant. Spectrosc. Radiat. Transf., vol. 93, pp. 89-101, 2005) is extended to solve the radiative heat transfer in two-dimensional absorbing-emitting-scattering graded index media, in which the spatial discretization is carried out using a FVM, while the angular discretization is by a FEM. The FEM angular discretization is demonstrated to be preferable in dealing with the redistribution terms in the GRTE. Two stiff matrix assembly schemes of the angular FEM discretization, namely, the traditional assembly approach and a new spherical assembly approach (assembly on the unit sphere of the solid angular space), are discussed. The spherical assembly scheme is demonstrated to give better results than the traditional assembly approach. The predicted heat flux distributions and temperature distributions in radiative equilibrium are determined by the proposed method and compared with the results available in other references. The proposed hybrid FVM/FEM method can predict the radiative heat transfer in absorbing-emitting-scattering graded index medium with good accuracy.
Hybrid finite volume/ finite element method for radiative heat transfer in graded index media
International Nuclear Information System (INIS)
Zhang, L.; Zhao, J.M.; Liu, L.H.; Wang, S.Y.
2012-01-01
The rays propagate along curved path determined by the Fermat principle in the graded index medium. The radiative transfer equation in graded index medium (GRTE) contains two specific redistribution terms (with partial derivatives to the angular coordinates) accounting for the effect of the curved ray path. In this paper, the hybrid finite volume with finite element method (hybrid FVM/FEM) (P.J. Coelho, J. Quant. Spectrosc. Radiat. Transf., vol. 93, pp. 89-101, 2005) is extended to solve the radiative heat transfer in two-dimensional absorbing-emitting-scattering graded index media, in which the spatial discretization is carried out using a FVM, while the angular discretization is by a FEM. The FEM angular discretization is demonstrated to be preferable in dealing with the redistribution terms in the GRTE. Two stiff matrix assembly schemes of the angular FEM discretization, namely, the traditional assembly approach and a new spherical assembly approach (assembly on the unit sphere of the solid angular space), are discussed. The spherical assembly scheme is demonstrated to give better results than the traditional assembly approach. The predicted heat flux distributions and temperature distributions in radiative equilibrium are determined by the proposed method and compared with the results available in other references. The proposed hybrid FVM/FEM method can predict the radiative heat transfer in absorbing-emitting-scattering graded index medium with good accuracy.
The finite element method and applications in engineering using ANSYS
Madenci, Erdogan
2015-01-01
This textbook offers theoretical and practical knowledge of the finite element method. The book equips readers with the skills required to analyze engineering problems using ANSYS®, a commercially available FEA program. Revised and updated, this new edition presents the most current ANSYS® commands and ANSYS® screen shots, as well as modeling steps for each example problem. This self-contained, introductory text minimizes the need for additional reference material by covering both the fundamental topics in finite element methods and advanced topics concerning modeling and analysis. It focuses on the use of ANSYS® through both the Graphics User Interface (GUI) and the ANSYS® Parametric Design Language (APDL). Extensive examples from a range of engineering disciplines are presented in a straightforward, step-by-step fashion. Key topics include: • An introduction to FEM • Fundamentals and analysis capabilities of ANSYS® • Fundamentals of discretization and approximation functions • Modeling techniq...
Numerical renormalization group method for entanglement negativity at finite temperature
Shim, Jeongmin; Sim, H.-S.; Lee, Seung-Sup B.
2018-04-01
We develop a numerical method to compute the negativity, an entanglement measure for mixed states, between the impurity and the bath in quantum impurity systems at finite temperature. We construct a thermal density matrix by using the numerical renormalization group (NRG), and evaluate the negativity by implementing the NRG approximation that reduces computational cost exponentially. We apply the method to the single-impurity Kondo model and the single-impurity Anderson model. In the Kondo model, the negativity exhibits a power-law scaling at temperature much lower than the Kondo temperature and a sudden death at high temperature. In the Anderson model, the charge fluctuation of the impurity contributes to the negativity even at zero temperature when the on-site Coulomb repulsion of the impurity is finite, while at low temperature the negativity between the impurity spin and the bath exhibits the same power-law scaling behavior as in the Kondo model.
Introduction to assembly of finite element methods on graphics processors
International Nuclear Information System (INIS)
Cecka, Cristopher; Lew, Adrian; Darve, Eric
2010-01-01
Recently, graphics processing units (GPUs) have had great success in accelerating numerical computations. We present their application to computations on unstructured meshes such as those in finite element methods. Multiple approaches in assembling and solving sparse linear systems with NVIDIA GPUs and the Compute Unified Device Architecture (CUDA) are presented and discussed. Multiple strategies for efficient use of global, shared, and local memory, methods to achieve memory coalescing, and optimal choice of parameters are introduced. We find that with appropriate preprocessing and arrangement of support data, the GPU coprocessor achieves speedups of 30x or more in comparison to a well optimized serial implementation on the CPU. We also find that the optimal assembly strategy depends on the order of polynomials used in the finite-element discretization.
Assembly of finite element methods on graphics processors
Cecka, Cris
2010-08-23
Recently, graphics processing units (GPUs) have had great success in accelerating many numerical computations. We present their application to computations on unstructured meshes such as those in finite element methods. Multiple approaches in assembling and solving sparse linear systems with NVIDIA GPUs and the Compute Unified Device Architecture (CUDA) are created and analyzed. Multiple strategies for efficient use of global, shared, and local memory, methods to achieve memory coalescing, and optimal choice of parameters are introduced. We find that with appropriate preprocessing and arrangement of support data, the GPU coprocessor using single-precision arithmetic achieves speedups of 30 or more in comparison to a well optimized double-precision single core implementation. We also find that the optimal assembly strategy depends on the order of polynomials used in the finite element discretization. © 2010 John Wiley & Sons, Ltd.
Finite Element Method for Analysis of Material Properties
DEFF Research Database (Denmark)
Rauhe, Jens Christian
and the finite element method. The material microstructure of the heterogeneous material is non-destructively determined using X-ray microtomography. A software program has been generated which uses the X-ray tomographic data as an input for the mesh generation of the material microstructure. To obtain a proper...... which are used for the determination of the effective properties of the heterogeneous material. Generally, the properties determined using the finite element method coupled with X-ray microtomography are in good agreement with both experimentally determined properties and properties determined using......The use of cellular and composite materials have in recent years become more and more common in all kinds of structural components and accurate knowledge of the effective properties is therefore essential. In this wok the effective properties are determined using the real material microstructure...
Free vibration of finite cylindrical shells by the variational method
International Nuclear Information System (INIS)
Campen, D.H. van; Huetink, J.
1975-01-01
The calculation of the free vibrations of circular cylindrical shells of finite length has been of engineer's interest for a long time. The motive for the present calculations originates from a particular type of construction at the inlet of a sodium heated superheater with helix heating bundle for SNR-Kalkar. The variational analysis is based on a modified energy functional for cylindrical shells, proposed by Koiter and resulting in Morley's equilibrium equations. As usual, the dispacement amplitude is assumed to be distributed harmonically in the circumferential direction of the shell. Following the method of Gontkevich, the dependence between the displacements of the shell middle surface and the axial shell co-ordinate is expressed approximately by a set of eigenfunctions of a free vibrating beam satisfying the desired boundary conditions. Substitution of this displacement expression into the virtual work equation for the complete shell leads to a characteristic equation determining the natural frequencies. The calculations are carried out for a clamped-clamped and a clamped-free cylinder. A comparison is given between the above numerical results and experimental and theoretical results from literature. In addition, the influence of surrounding fluid mass on the above frequencies is analysed for a clamped-clamped shell. The solution for the velocity potential used in this case differs from the solutions used in literature until now in that not only travelling waves in the axial direction are considered. (Auth.)
A finite element method for flow problems in blast loading
International Nuclear Information System (INIS)
Forestier, A.; Lepareux, M.
1984-06-01
This paper presents a numerical method which describes fast dynamic problems in flow transient situations as in nuclear plants. A finite element formulation has been chosen; it is described by a preprocessor in CASTEM system: GIBI code. For these typical flow problems, an A.L.E. formulation for physical equations is used. So, some applications are presented: the well known problem of shock tube, the same one in 2D case and a last application to hydrogen detonation
Analysis of Piezoelectric Solids using Finite Element Method
Aslam, Mohammed; Nagarajan, Praveen; Remanan, Mini
2018-03-01
Piezoelectric materials are extensively used in smart structures as sensors and actuators. In this paper, static analysis of three piezoelectric solids is done using general-purpose finite element software, Abaqus. The simulation results from Abaqus are compared with the results obtained using numerical methods like Boundary Element Method (BEM) and meshless point collocation method (PCM). The BEM and PCM are cumbersome for complex shape and complicated boundary conditions. This paper shows that the software Abaqus can be used to solve the governing equations of piezoelectric solids in a much simpler and faster way than the BEM and PCM.
Finite element method for time-space-fractional Schrodinger equation
Directory of Open Access Journals (Sweden)
Xiaogang Zhu
2017-07-01
Full Text Available In this article, we develop a fully discrete finite element method for the nonlinear Schrodinger equation (NLS with time- and space-fractional derivatives. The time-fractional derivative is described in Caputo's sense and the space-fractional derivative in Riesz's sense. Its stability is well derived; the convergent estimate is discussed by an orthogonal operator. We also extend the method to the two-dimensional time-space-fractional NLS and to avoid the iterative solvers at each time step, a linearized scheme is further conducted. Several numerical examples are implemented finally, which confirm the theoretical results as well as illustrate the accuracy of our methods.
Navier-Stokes equations by the finite element method
International Nuclear Information System (INIS)
Portella, P.E.
1984-01-01
A computer program to solve the Navier-Stokes equations by using the Finite Element Method is implemented. The solutions variables investigated are stream-function/vorticity in the steady case and velocity/pressure in the steady state and transient cases. For steady state flow the equations are solved simultaneously by the Newton-Raphson method. For the time dependent formulation, a fractional step method is employed to discretize in time and artificial viscosity is used to preclude spurious oscilations in the solution. The element used is the three node triangle. Some numerical examples are presented and comparisons are made with applications already existent. (Author) [pt
A Review on the Modified Finite Point Method
Directory of Open Access Journals (Sweden)
Nan-Jing Wu
2014-01-01
Full Text Available The objective of this paper is to make a review on recent advancements of the modified finite point method, named MFPM hereafter. This MFPM method is developed for solving general partial differential equations. Benchmark examples of employing this method to solve Laplace, Poisson, convection-diffusion, Helmholtz, mild-slope, and extended mild-slope equations are verified and then illustrated in fluid flow problems. Application of MFPM to numerical generation of orthogonal grids, which is governed by Laplace equation, is also demonstrated.
Eddy current analysis by the finite element circuit method
International Nuclear Information System (INIS)
Kameari, A.; Suzuki, Y.
1977-01-01
The analysis of the transient eddy current in the conductors by ''Finite Element Circuit Method'' is developed. This method can be easily applied to various geometrical shapes of thin conductors. The eddy currents on the vacuum vessel and the upper and lower support plates of JT-60 machine (which is now being constructed by Japan Atomic Energy Research Institute) are calculated by this method. The magnetic field induced by the eddy current is estimated in the domain occupied by the plasma. And the force exerted to the vacuum vessel is also estimated
Acoustic, finite-difference, time-domain technique development
International Nuclear Information System (INIS)
Kunz, K.
1994-01-01
A close analog exists between the behavior of sound waves in an ideal gas and the radiated waves of electromagnetics. This analog has been exploited to obtain an acoustic, finite-difference, time-domain (AFDTD) technique capable of treating small signal vibrations in elastic media, such as air, water, and metal, with the important feature of bending motion included in the behavior of the metal. This bending motion is particularly important when the metal is formed into sheets or plates. Bending motion does not have an analog in electromagnetics, but can be readily appended to the acoustic treatment since it appears as a single additional term in the force equation for plate motion, which is otherwise analogous to the electromagnetic wave equation. The AFDTD technique has been implemented in a code architecture that duplicates the electromagnetic, finite-difference, time-domain technique code. The main difference in the implementation is the form of the first-order coupled differential equations obtained from the wave equation. The gradient of pressure and divergence of velocity appear in these equations in the place of curls of the electric and magnetic fields. Other small changes exist as well, but the codes are essentially interchangeable. The pre- and post-processing for model construction and response-data evaluation of the electromagnetic code, in the form of the TSAR code at Lawrence Livermore National Laboratory, can be used for the acoustic version. A variety of applications is possible, pending validation of the bending phenomenon. The applications include acoustic-radiation-pattern predictions for a submerged object; mine detection analysis; structural noise analysis for cars; acoustic barrier analysis; and symphonic hall/auditorium predictions and speaker enclosure modeling
Coupled convective and conductive heat transfer by up-wind finite element method
International Nuclear Information System (INIS)
Kushwaha, H.S.
1981-01-01
Some of concepts relating to finite element formulation of the Navier-Stoke's equations using mixed formulation and Penality formulation have been discussed. The two different approaches for solution of nonlinear differential equations for two different types of formulation have been described. Incremental Newton Raphson method can also be applied to mixed formulation. (author)
Hybrid finite element and Brownian dynamics method for charged particles
Energy Technology Data Exchange (ETDEWEB)
Huber, Gary A., E-mail: ghuber@ucsd.edu; Miao, Yinglong [Howard Hughes Medical Institute, University of California San Diego, La Jolla, California 92093-0365 (United States); Zhou, Shenggao [Department of Mathematics and Mathematical Center for Interdiscipline Research, Soochow University, 1 Shizi Street, Suzhou, 215006 Jiangsu (China); Li, Bo [Department of Mathematics and Quantitative Biology Graduate Program, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0112 (United States); McCammon, J. Andrew [Howard Hughes Medical Institute, University of California San Diego, La Jolla, California 92093 (United States); Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093-0365 (United States); Department of Pharmacology, University of California San Diego, La Jolla, California 92093-0636 (United States)
2016-04-28
Diffusion is often the rate-determining step in many biological processes. Currently, the two main computational methods for studying diffusion are stochastic methods, such as Brownian dynamics, and continuum methods, such as the finite element method. A previous study introduced a new hybrid diffusion method that couples the strengths of each of these two methods, but was limited by the lack of interactions among the particles; the force on each particle had to be from an external field. This study further develops the method to allow charged particles. The method is derived for a general multidimensional system and is presented using a basic test case for a one-dimensional linear system with one charged species and a radially symmetric system with three charged species.
HEATING-7, Multidimensional Finite-Difference Heat Conduction Analysis
International Nuclear Information System (INIS)
2000-01-01
problems, surface fluxes may be plotted with H7TECPLOT which requires the proprietary software TECPLOT. HEATING 7.3 runs under Windows95 and WindowsNT on PC's. No future modifications are planned for HEATING7. See README.1ST for more information. 2 - Method of solution: Three steady-state solution techniques are available: point-successive over-relaxation iterative method with extrapolation, direct-solution (for one-dimensional or two-dimensional problems), and conjugate gradient. Transient problems may be solved using any one of several finite-difference schemes: Crank-Nicolson implicit, Classical Implicit Procedure (CIP), Classical Explicit Procedure (CEP), or Levy explicit method (which for some circumstances allows a time step greater than the CEP stability criterion.) The solution of the system of equations arising from the implicit techniques is accomplished by point-successive over-relaxation iteration and includes procedures to estimate the optimum acceleration parameter. 3 - Restrictions on the complexity of the problem: All surfaces in a model must be parallel to one of the coordinate axes which makes modeling complex geometries difficult. Transient change of phase problems can only be solved with one of the explicit techniques - an implicit change-of-phase capability has not been implemented
Finite-difference modeling of commercial aircraft using TSAR
Energy Technology Data Exchange (ETDEWEB)
Pennock, S.T.; Poggio, A.J.
1994-11-15
Future aircraft may have systems controlled by fiber optic cables, to reduce susceptibility to electromagnetic interference. However, the digital systems associated with the fiber optic network could still experience upset due to powerful radio stations, radars, and other electromagnetic sources, with potentially serious consequences. We are modeling the electromagnetic behavior of commercial transport aircraft in support of the NASA Fly-by-Light/Power-by-Wire program, using the TSAR finite-difference time-domain code initially developed for the military. By comparing results obtained from TSAR with data taken on a Boeing 757 at the Air Force Phillips Lab., we hope to show that FDTD codes can serve as an important tool in the design and certification of U.S. commercial aircraft, helping American companies to produce safe, reliable air transportation.
Visualization of elastic wavefields computed with a finite difference code
Energy Technology Data Exchange (ETDEWEB)
Larsen, S. [Lawrence Livermore National Lab., CA (United States); Harris, D.
1994-11-15
The authors have developed a finite difference elastic propagation model to simulate seismic wave propagation through geophysically complex regions. To facilitate debugging and to assist seismologists in interpreting the seismograms generated by the code, they have developed an X Windows interface that permits viewing of successive temporal snapshots of the (2D) wavefield as they are calculated. The authors present a brief video displaying the generation of seismic waves by an explosive source on a continent, which propagate to the edge of the continent then convert to two types of acoustic waves. This sample calculation was part of an effort to study the potential of offshore hydroacoustic systems to monitor seismic events occurring onshore.
An adaptive finite element method for steady and transient problems
International Nuclear Information System (INIS)
Benner, R.E. Jr.; Davis, H.T.; Scriven, L.E.
1987-01-01
Distributing integral error uniformly over variable subdomains, or finite elements, is an attractive criterion by which to subdivide a domain for the Galerkin/finite element method when localized steep gradients and high curvatures are to be resolved. Examples are fluid interfaces, shock fronts and other internal layers, as well as fluid mechanical and other boundary layers, e.g. thin-film states at solid walls. The uniform distribution criterion is developed into an adaptive technique for one-dimensional problems. Nodal positions can be updated simultaneously with nodal values during Newton iteration, but it is usually better to adopt nearly optimal nodal positions during Newton iteration upon nodal values. Three illustrative problems are solved: steady convection with diffusion, gradient theory of fluid wetting on a solid surface and Buckley-Leverett theory of two phase Darcy flow in porous media
Finite element method for simulation of the semiconductor devices
International Nuclear Information System (INIS)
Zikatanov, L.T.; Kaschiev, M.S.
1991-01-01
An iterative method for solving the system of nonlinear equations of the drift-diffusion representation for the simulation of the semiconductor devices is worked out. The Petrov-Galerkin method is taken for the discretization of these equations using the bilinear finite elements. It is shown that the numerical scheme is a monotonous one and there are no oscillations of the solutions in the region of p-n transition. The numerical calculations of the simulation of one semiconductor device are presented. 13 refs.; 3 figs
Optimal variable-grid finite-difference modeling for porous media
International Nuclear Information System (INIS)
Liu, Xinxin; Yin, Xingyao; Li, Haishan
2014-01-01
Numerical modeling of poroelastic waves by the finite-difference (FD) method is more expensive than that of acoustic or elastic waves. To improve the accuracy and computational efficiency of seismic modeling, variable-grid FD methods have been developed. In this paper, we derived optimal staggered-grid finite difference schemes with variable grid-spacing and time-step for seismic modeling in porous media. FD operators with small grid-spacing and time-step are adopted for low-velocity or small-scale geological bodies, while FD operators with big grid-spacing and time-step are adopted for high-velocity or large-scale regions. The dispersion relations of FD schemes were derived based on the plane wave theory, then the FD coefficients were obtained using the Taylor expansion. Dispersion analysis and modeling results demonstrated that the proposed method has higher accuracy with lower computational cost for poroelastic wave simulation in heterogeneous reservoirs. (paper)
A novel strong tracking finite-difference extended Kalman filter for nonlinear eye tracking
Institute of Scientific and Technical Information of China (English)
ZHANG ZuTao; ZHANG JiaShu
2009-01-01
Non-Intrusive methods for eye tracking are Important for many applications of vision-based human computer interaction. However, due to the high nonlinearity of eye motion, how to ensure the robust-ness of external interference and accuracy of eye tracking poses the primary obstacle to the integration of eye movements into today's interfaces. In this paper, we present a strong tracking finite-difference extended Kalman filter algorithm, aiming to overcome the difficulty In modeling nonlinear eye tracking. In filtering calculation, strong tracking factor is introduced to modify a priori covariance matrix and im-prove the accuracy of the filter. The filter uses finite-difference method to calculate partial derivatives of nonlinear functions for eye tracking. The latest experimental results show the validity of our method for eye tracking under realistic conditions.
International Nuclear Information System (INIS)
Masoud Ziaei-Rad
2010-01-01
In this paper, a two-dimensional numerical scheme is presented for the simulation of turbulent, viscous, transient compressible flows in the simultaneously developing hydraulic and thermal boundary layer region. The numerical procedure is a finite-volume-based finite-element method applied to unstructured grids. This combination together with a new method applied for the boundary conditions allows for accurate computation of the variables in the entrance region and for a wide range of flow fields from subsonic to transonic. The Roe-Riemann solver is used for the convective terms, whereas the standard Galerkin technique is applied for the viscous terms. A modified κ-ε model with a two-layer equation for the near-wall region combined with a compressibility correction is used to predict the turbulent viscosity. Parallel processing is also employed to divide the computational domain among the different processors to reduce the computational time. The method is applied to some test cases in order to verify the numerical accuracy. The results show significant differences between incompressible and compressible flows in the friction coefficient, Nusselt number, shear stress and the ratio of the compressible turbulent viscosity to the molecular viscosity along the developing region. A transient flow generated after an accidental rupture in a pipeline was also studied as a test case. The results show that the present numerical scheme is stable, accurate and efficient enough to solve the problem of transient wall-bounded flow.
High-resolution finite-difference algorithms for conservation laws
International Nuclear Information System (INIS)
Towers, J.D.
1987-01-01
A new class of Total Variation Decreasing (TVD) schemes for 2-dimensional scalar conservation laws is constructed using either flux-limited or slope-limited numerical fluxes. The schemes are proven to have formal second-order accuracy in regions where neither u/sub x/ nor y/sub y/ vanishes. A new class of high-resolution large-time-step TVD schemes is constructed by adding flux-limited correction terms to the first-order accurate large-time-step version of the Engquist-Osher scheme. The use of the transport-collapse operator in place of the exact solution operator for the construction of difference schemes is studied. The production of spurious extrema by difference schemes is studied. A simple condition guaranteeing the nonproduction of spurious extrema is derived. A sufficient class of entropy inequalities for a conservation law with a flux having a single inflection point is presented. Finite-difference schemes satisfying a discrete version of each entropy inequality are only first-order accurate
Comparison between microscopic methods for finite-temperature Bose gases
DEFF Research Database (Denmark)
Cockburn, S.P.; Negretti, Antonio; Proukakis, N.P.
2011-01-01
We analyze the equilibrium properties of a weakly interacting, trapped quasi-one-dimensional Bose gas at finite temperatures and compare different theoretical approaches. We focus in particular on two stochastic theories: a number-conserving Bogoliubov (NCB) approach and a stochastic Gross...... on different thermodynamic ensembles (NCB, canonical; SGPE, grand-canonical), they yield the correct condensate statistics in a large Bose-Einstein condensate (BEC) (strong enough particle interactions). For smaller systems, the SGPE results are prone to anomalously large number fluctuations, well known...
Finite element method for one-dimensional rill erosion simulation on a curved slope
Directory of Open Access Journals (Sweden)
Lijuan Yan
2015-03-01
Full Text Available Rill erosion models are important to hillslope soil erosion prediction and to land use planning. The development of rill erosion models and their use has become increasingly of great concern. The purpose of this research was to develop mathematic models with computer simulation procedures to simulate and predict rill erosion. The finite element method is known as an efficient tool in many other applications than in rill soil erosion. In this study, the hydrodynamic and sediment continuity model equations for a rill erosion system were solved by the Galerkin finite element method and Visual C++ procedures. The simulated results are compared with the data for spatially and temporally measured processes for rill erosion under different conditions. The results indicate that the one-dimensional linear finite element method produced excellent predictions of rill erosion processes. Therefore, this study supplies a tool for further development of a dynamic soil erosion prediction model.
An outgoing energy flux boundary condition for finite difference ICRP antenna models
International Nuclear Information System (INIS)
Batchelor, D.B.; Carter, M.D.
1992-11-01
For antennas at the ion cyclotron range of frequencies (ICRF) modeling in vacuum can now be carried out to a high level of detail such that shaping of the current straps, isolating septa, and discrete Faraday shield structures can be included. An efficient approach would be to solve for the fields in the vacuum region near the antenna in three dimensions by finite methods and to match this solution at the plasma-vacuum interface to a solution obtained in the plasma region in one dimension by Fourier methods. This approach has been difficult to carry out because boundary conditions must be imposed at the edge of the finite difference grid on a point-by-point basis, whereas the condition for outgoing energy flux into the plasma is known only in terms of the Fourier transform of the plasma fields. A technique is presented by which a boundary condition can be imposed on the computational grid of a three-dimensional finite difference, or finite element, code by constraining the discrete Fourier transform of the fields at the boundary points to satisfy an outgoing energy flux condition appropriate for the plasma. The boundary condition at a specific grid point appears as a coupling to other grid points on the boundary, with weighting determined by a kemel calctdated from the plasma surface impedance matrix for the various plasma Fourier modes. This boundary condition has been implemented in a finite difference solution of a simple problem in two dimensions, which can also be solved directly by Fourier transformation. Results are presented, and it is shown that the proposed boundary condition does enforce outgoing energy flux and yields the same solution as is obtained by Fourier methods
Extrusion Process by Finite Volume Method Using OpenFoam Software
International Nuclear Information System (INIS)
Matos Martins, Marcelo; Tonini Button, Sergio; Divo Bressan, Jose; Ivankovic, Alojz
2011-01-01
The computational codes are very important tools to solve engineering problems. In the analysis of metal forming process, such as extrusion, this is not different because the computational codes allow analyzing the process with reduced cost. Traditionally, the Finite Element Method is used to solve solid mechanic problems, however, the Finite Volume Method (FVM) have been gaining force in this field of applications. This paper presents the velocity field and friction coefficient variation results, obtained by numerical simulation using the OpenFoam Software and the FVM to solve an aluminum direct cold extrusion process.
A multipoint flux mixed finite element method on distorted quadrilaterals and hexahedra
Wheeler, Mary
2011-11-06
In this paper, we develop a new mixed finite element method for elliptic problems on general quadrilateral and hexahedral grids that reduces to a cell-centered finite difference scheme. A special non-symmetric quadrature rule is employed that yields a positive definite cell-centered system for the pressure by eliminating local velocities. The method is shown to be accurate on highly distorted rough quadrilateral and hexahedral grids, including hexahedra with non-planar faces. Theoretical and numerical results indicate first-order convergence for the pressure and face fluxes. © 2011 Springer-Verlag.
Prediction of residual stress using explicit finite element method
Directory of Open Access Journals (Sweden)
W.A. Siswanto
2015-12-01
Full Text Available This paper presents the residual stress behaviour under various values of friction coefficients and scratching displacement amplitudes. The investigation is based on numerical solution using explicit finite element method in quasi-static condition. Two different aeroengine materials, i.e. Super CMV (Cr-Mo-V and Titanium alloys (Ti-6Al-4V, are examined. The usage of FEM analysis in plate under normal contact is validated with Hertzian theoretical solution in terms of contact pressure distributions. The residual stress distributions along with normal and shear stresses on elastic and plastic regimes of the materials are studied for a simple cylinder-on-flat contact configuration model subjected to normal loading, scratching and followed by unloading. The investigated friction coefficients are 0.3, 0.6 and 0.9, while scratching displacement amplitudes are 0.05 mm, 0.10 mm and 0.20 mm respectively. It is found that friction coefficient of 0.6 results in higher residual stress for both materials. Meanwhile, the predicted residual stress is proportional to the scratching displacement amplitude, higher displacement amplitude, resulting in higher residual stress. It is found that less residual stress is predicted on Super CMV material compared to Ti-6Al-4V material because of its high yield stress and ultimate strength. Super CMV material with friction coefficient of 0.3 and scratching displacement amplitude of 0.10 mm is recommended to be used in contact engineering applications due to its minimum possibility of fatigue.
Applications of meshless methods for damage computations with finite strains
International Nuclear Information System (INIS)
Pan Xiaofei; Yuan Huang
2009-01-01
Material defects such as cavities have great effects on the damage process in ductile materials. Computations based on finite element methods (FEMs) often suffer from instability due to material failure as well as large distortions. To improve computational efficiency and robustness the element-free Galerkin (EFG) method is applied in the micro-mechanical constitute damage model proposed by Gurson and modified by Tvergaard and Needleman (the GTN damage model). The EFG algorithm is implemented in the general purpose finite element code ABAQUS via the user interface UEL. With the help of the EFG method, damage processes in uniaxial tension specimens and notched specimens are analyzed and verified with experimental data. Computational results reveal that the damage which takes place in the interior of specimens will extend to the exterior and cause fracture of specimens; the damage is a fast procedure relative to the whole tensing process. The EFG method provides more stable and robust numerical solution in comparing with the FEM analysis
Finite-difference analysis of shells impacting rigid barriers
International Nuclear Information System (INIS)
Pirotin, S.D.; Witmer, E.A.
1977-01-01
Nuclear power plants must be protected from the adverse effects of missile impacts. A significant category of missile impact involves deformable structures (pressure vessel components, whipping pipes) striking relatively rigid targets (concrete walls, bumpers) which act as protective devices. The response and interaction of these structures is needed to assess the adequacy of these barriers for protecting vital safety related equipment. The present investigation represents an initial attempt to develop an efficient numerical procedure for predicting the deformations and impact force time-histories of shells which impact upon a rigid target. The general large-deflection equations of motion of the shell are expressed in finite-difference form in space and integrated in time through application of the central-difference temporal operator. The effect of material nonlinearities is treated by a mechanical sublayer material model which handles the strain-hardening, Bauschinger, and strain-rate effects. The general adequacy of this shell treatment has been validated by comparing predictions with the results of various experiments in which structures have been subjected to well-defined transient forcing functions (typically high-explosive impulse loading). The 'new' ingredient addressed in the present study involves an accounting for impact interaction and response of both the target structure and the attacking body. (Auth.)
Seakeeping with the semi-Lagrangian particle finite element method
Nadukandi, Prashanth; Servan-Camas, Borja; Becker, Pablo Agustín; Garcia-Espinosa, Julio
2017-07-01
The application of the semi-Lagrangian particle finite element method (SL-PFEM) for the seakeeping simulation of the wave adaptive modular vehicle under spray generating conditions is presented. The time integration of the Lagrangian advection is done using the explicit integration of the velocity and acceleration along the streamlines (X-IVAS). Despite the suitability of the SL-PFEM for the considered seakeeping application, small time steps were needed in the X-IVAS scheme to control the solution accuracy. A preliminary proposal to overcome this limitation of the X-IVAS scheme for seakeeping simulations is presented.
Stress and Deformation Analysis in Base Isolation Elements Using the Finite Element Method
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Claudiu Iavornic
2011-01-01
Full Text Available In Modern tools as Finite Element Method can be used to study the behavior of elastomeric isolation systems. The simulation results obtained in this way provide a large series of data about the behavior of elastomeric isolation bearings under different types of loads and help in taking right decisions regarding geometrical optimizations needed for improve such kind of devices.
A Finite Element Method for Simulation of Compressible Cavitating Flows
Shams, Ehsan; Yang, Fan; Zhang, Yu; Sahni, Onkar; Shephard, Mark; Oberai, Assad
2016-11-01
This work focuses on a novel approach for finite element simulations of multi-phase flows which involve evolving interface with phase change. Modeling problems, such as cavitation, requires addressing multiple challenges, including compressibility of the vapor phase, interface physics caused by mass, momentum and energy fluxes. We have developed a mathematically consistent and robust computational approach to address these problems. We use stabilized finite element methods on unstructured meshes to solve for the compressible Navier-Stokes equations. Arbitrary Lagrangian-Eulerian formulation is used to handle the interface motions. Our method uses a mesh adaptation strategy to preserve the quality of the volumetric mesh, while the interface mesh moves along with the interface. The interface jump conditions are accurately represented using a discontinuous Galerkin method on the conservation laws. Condensation and evaporation rates at the interface are thermodynamically modeled to determine the interface velocity. We will present initial results on bubble cavitation the behavior of an attached cavitation zone in a separated boundary layer. We acknowledge the support from Army Research Office (ARO) under ARO Grant W911NF-14-1-0301.
Strength Analysis on Ship Ladder Using Finite Element Method
Budianto; Wahyudi, M. T.; Dinata, U.; Ruddianto; Eko P., M. M.
2018-01-01
In designing the ship’s structure, it should refer to the rules in accordance with applicable classification standards. In this case, designing Ladder (Staircase) on a Ferry Ship which is set up, it must be reviewed based on the loads during ship operations, either during sailing or at port operations. The classification rules in ship design refer to the calculation of the structure components described in Classification calculation method and can be analysed using the Finite Element Method. Classification Regulations used in the design of Ferry Ships used BKI (Bureau of Classification Indonesia). So the rules for the provision of material composition in the mechanical properties of the material should refer to the classification of the used vessel. The analysis in this structure used program structure packages based on Finite Element Method. By using structural analysis on Ladder (Ladder), it obtained strength and simulation structure that can withstand load 140 kg both in static condition, dynamic, and impact. Therefore, the result of the analysis included values of safety factors in the ship is to keep the structure safe but the strength of the structure is not excessive.
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Fan Yuxin
2014-12-01
Full Text Available A fluid–structure interaction method combining a nonlinear finite element algorithm with a preconditioning finite volume method is proposed in this paper to simulate parachute transient dynamics. This method uses a three-dimensional membrane–cable fabric model to represent a parachute system at a highly folded configuration. The large shape change during parachute inflation is computed by the nonlinear Newton–Raphson iteration and the linear system equation is solved by the generalized minimal residual (GMRES method. A membrane wrinkling algorithm is also utilized to evaluate the special uniaxial tension state of membrane elements on the parachute canopy. In order to avoid large time expenses during structural nonlinear iteration, the implicit Hilber–Hughes–Taylor (HHT time integration method is employed. For the fluid dynamic simulations, the Roe and HLLC (Harten–Lax–van Leer contact scheme has been modified and extended to compute flow problems at all speeds. The lower–upper symmetric Gauss–Seidel (LU-SGS approximate factorization is applied to accelerate the numerical convergence speed. Finally, the test model of a highly folded C-9 parachute is simulated at a prescribed speed and the results show similar characteristics compared with experimental results and previous literature.
International Nuclear Information System (INIS)
Waligorski, M.P.R.; Urbanczyk, K.M.
1975-01-01
The basic principles of the finite-difference approximation applied to the solution of electrostatic field distributions in gaseous proportional counters are given. Using this method, complicated two-dimensional electrostatic problems may be solved, taking into account any number of anodes, each with its own radius, and any cathode shape. A general formula for introducing the anode radii into the calculations is derived and a method of obtaining extremely accurate (up to 0.1%) solutions is developed. Several examples of potential and absolute field distributions for single rectangular and multiwire proportional counters are calculated and compared with exact results according to Tomitani, in order to discuss in detail errors of the finite-difference approximation. (author)
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Lindemberg Lima Fernandes
2009-03-01
ão recomenda-se a integração de dados de superfície com os de poço, com o objetivo de obter melhor imagem dos alvos abaixo das soleiras de diabásio.This paper discusses the seismic modeling in medium with strong discontinuities in its physical properties. The approach takes in consideration the existences diffractions and multiple reflections in the analyzed medium, which, at that case, is the Amazon Basin. The stability and boundary conditions of modeling were analyzed by the method of the finite differences. Sedimentary rocks deposited since the Ordovician to the present, reaching depth up to 5 Km. The bodies of diabasic between the paleozoic sediments are layers reaching thickness of hundred meters, which add to 90.000 km3, form the geology of the Amazon Basin. The occurrence of these structures is responsible for multiple reflections during the propagation of the seismic waves, which become impossible a better imaging of horizons located bellow the layers. The representation this geological situation was performed an (synthetic acoustic velocity model. The numerical discretization scheme is based in a fourth order approximation of the acoustic wave equation in space and time The understanding of the wave propagation heterogeneous medium has improved for the application of the finite difference method. The method achieves a good resolution in the interpretation of seismic reflection events. The numerical results discusses in this paper have allowed to observed the influence of the multiple reflection in a high velocity layer. It increase a loss of energy and difficult the interpretation of the target. For this reason the integration of surface data with the well data is recommended, with the objective to get one better image of the targets below of the diabasic layer.
Finite-difference numerical simulations of underground explosion cavity decoupling
Aldridge, D. F.; Preston, L. A.; Jensen, R. P.
2012-12-01
Earth models containing a significant portion of ideal fluid (e.g., air and/or water) are of increasing interest in seismic wave propagation simulations. Examples include a marine model with a thick water layer, and a land model with air overlying a rugged topographic surface. The atmospheric infrasound community is currently interested in coupled seismic-acoustic propagation of low-frequency signals over long ranges (~tens to ~hundreds of kilometers). Also, accurate and efficient numerical treatment of models containing underground air-filled voids (caves, caverns, tunnels, subterranean man-made facilities) is essential. In support of the Source Physics Experiment (SPE) conducted at the Nevada National Security Site (NNSS), we are developing a numerical algorithm for simulating coupled seismic and acoustic wave propagation in mixed solid/fluid media. Solution methodology involves explicit, time-domain, finite-differencing of the elastodynamic velocity-stress partial differential system on a three-dimensional staggered spatial grid. Conditional logic is used to avoid shear stress updating within the fluid zones; this approach leads to computational efficiency gains for models containing a significant proportion of ideal fluid. Numerical stability and accuracy are maintained at air/rock interfaces (where the contrast in mass density is on the order of 1 to 2000) via a finite-difference operator "order switching" formalism. The fourth-order spatial FD operator used throughout the bulk of the earth model is reduced to second-order in the immediate vicinity of a high-contrast interface. Current modeling efforts are oriented toward quantifying the amount of atmospheric infrasound energy generated by various underground seismic sources (explosions and earthquakes). Source depth and orientation, and surface topography play obvious roles. The cavity decoupling problem, where an explosion is detonated within an air-filled void, is of special interest. A point explosion
Application of a circulation model in bays, using the finite element method
International Nuclear Information System (INIS)
Soares, R.
1984-01-01
The circulation of water was studied in different areas in 'Baia de Sepetiba', in the State of Rio de Janeiro, Brazil. The method applied on the mathematical studies was Galerkin's method and ths originated a system of equations which described all the water motions. The Finite Element method used, had great sensitivity to modifications of input data. Comparison between computed and measured data was made in order to verify the conclusions. (M.A.C.) [pt
Finite element method for solving Kohn-Sham equations based on self-adaptive tetrahedral mesh
International Nuclear Information System (INIS)
Zhang Dier; Shen Lihua; Zhou Aihui; Gong Xingao
2008-01-01
A finite element (FE) method with self-adaptive mesh-refinement technique is developed for solving the density functional Kohn-Sham equations. The FE method adopts local piecewise polynomials basis functions, which produces sparsely structured matrices of Hamiltonian. The method is well suitable for parallel implementation without using Fourier transform. In addition, the self-adaptive mesh-refinement technique can control the computational accuracy and efficiency with optimal mesh density in different regions
Generalized multiscale finite element methods. nonlinear elliptic equations
Efendiev, Yalchin R.; Galvis, Juan; Li, Guanglian; Presho, Michael
2013-01-01
In this paper we use the Generalized Multiscale Finite Element Method (GMsFEM) framework, introduced in [26], in order to solve nonlinear elliptic equations with high-contrast coefficients. The proposed solution method involves linearizing the equation so that coarse-grid quantities of previous solution iterates can be regarded as auxiliary parameters within the problem formulation. With this convention, we systematically construct respective coarse solution spaces that lend themselves to either continuous Galerkin (CG) or discontinuous Galerkin (DG) global formulations. Here, we use Symmetric Interior Penalty Discontinuous Galerkin approach. Both methods yield a predictable error decline that depends on the respective coarse space dimension, and we illustrate the effectiveness of the CG and DG formulations by offering a variety of numerical examples. © 2014 Global-Science Press.
Mixed Generalized Multiscale Finite Element Methods and Applications
Chung, Eric T.
2015-03-03
In this paper, we present a mixed generalized multiscale finite element method (GMsFEM) for solving flow in heterogeneous media. Our approach constructs multiscale basis functions following a GMsFEM framework and couples these basis functions using a mixed finite element method, which allows us to obtain a mass conservative velocity field. To construct multiscale basis functions for each coarse edge, we design a snapshot space that consists of fine-scale velocity fields supported in a union of two coarse regions that share the common interface. The snapshot vectors have zero Neumann boundary conditions on the outer boundaries, and we prescribe their values on the common interface. We describe several spectral decompositions in the snapshot space motivated by the analysis. In the paper, we also study oversampling approaches that enhance the accuracy of mixed GMsFEM. A main idea of oversampling techniques is to introduce a small dimensional snapshot space. We present numerical results for two-phase flow and transport, without updating basis functions in time. Our numerical results show that one can achieve good accuracy with a few basis functions per coarse edge if one selects appropriate offline spaces. © 2015 Society for Industrial and Applied Mathematics.
Adaptive Finite Element Methods for Elliptic Problems with Discontinuous Coefficients
Bonito, Andrea; DeVore, Ronald A.; Nochetto, Ricardo H.
2013-01-01
Elliptic PDEs with discontinuous diffusion coefficients occur in application domains such as diffusions through porous media, electromagnetic field propagation on heterogeneous media, and diffusion processes on rough surfaces. The standard approach to numerically treating such problems using finite element methods is to assume that the discontinuities lie on the boundaries of the cells in the initial triangulation. However, this does not match applications where discontinuities occur on curves, surfaces, or manifolds, and could even be unknown beforehand. One of the obstacles to treating such discontinuity problems is that the usual perturbation theory for elliptic PDEs assumes bounds for the distortion of the coefficients in the L∞ norm and this in turn requires that the discontinuities are matched exactly when the coefficients are approximated. We present a new approach based on distortion of the coefficients in an Lq norm with q < ∞ which therefore does not require the exact matching of the discontinuities. We then use this new distortion theory to formulate new adaptive finite element methods (AFEMs) for such discontinuity problems. We show that such AFEMs are optimal in the sense of distortion versus number of computations, and report insightful numerical results supporting our analysis. © 2013 Societ y for Industrial and Applied Mathematics.
Heat Conduction Analysis Using Semi Analytical Finite Element Method
International Nuclear Information System (INIS)
Wargadipura, A. H. S.
1997-01-01
Heat conduction problems are very often found in science and engineering fields. It is of accrual importance to determine quantitative descriptions of this important physical phenomena. This paper discusses the development and application of a numerical formulation and computation that can be used to analyze heat conduction problems. The mathematical equation which governs the physical behaviour of heat conduction is in the form of second order partial differential equations. The numerical resolution used in this paper is performed using the finite element method and Fourier series, which is known as semi-analytical finite element methods. The numerical solution results in simultaneous algebraic equations which is solved using the Gauss elimination methodology. The computer implementation is carried out using FORTRAN language. In the final part of the paper, a heat conduction problem in a rectangular plate domain with isothermal boundary conditions in its edge is solved to show the application of the computer program developed and also a comparison with analytical solution is discussed to assess the accuracy of the numerical solution obtained
The intervals method: a new approach to analyse finite element outputs using multivariate statistics
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Jordi Marcé-Nogué
2017-10-01
Full Text Available Background In this paper, we propose a new method, named the intervals’ method, to analyse data from finite element models in a comparative multivariate framework. As a case study, several armadillo mandibles are analysed, showing that the proposed method is useful to distinguish and characterise biomechanical differences related to diet/ecomorphology. Methods The intervals’ method consists of generating a set of variables, each one defined by an interval of stress values. Each variable is expressed as a percentage of the area of the mandible occupied by those stress values. Afterwards these newly generated variables can be analysed using multivariate methods. Results Applying this novel method to the biological case study of whether armadillo mandibles differ according to dietary groups, we show that the intervals’ method is a powerful tool to characterize biomechanical performance and how this relates to different diets. This allows us to positively discriminate between specialist and generalist species. Discussion We show that the proposed approach is a useful methodology not affected by the characteristics of the finite element mesh. Additionally, the positive discriminating results obtained when analysing a difficult case study suggest that the proposed method could be a very useful tool for comparative studies in finite element analysis using multivariate statistical approaches.
The intervals method: a new approach to analyse finite element outputs using multivariate statistics
De Esteban-Trivigno, Soledad; Püschel, Thomas A.; Fortuny, Josep
2017-01-01
Background In this paper, we propose a new method, named the intervals’ method, to analyse data from finite element models in a comparative multivariate framework. As a case study, several armadillo mandibles are analysed, showing that the proposed method is useful to distinguish and characterise biomechanical differences related to diet/ecomorphology. Methods The intervals’ method consists of generating a set of variables, each one defined by an interval of stress values. Each variable is expressed as a percentage of the area of the mandible occupied by those stress values. Afterwards these newly generated variables can be analysed using multivariate methods. Results Applying this novel method to the biological case study of whether armadillo mandibles differ according to dietary groups, we show that the intervals’ method is a powerful tool to characterize biomechanical performance and how this relates to different diets. This allows us to positively discriminate between specialist and generalist species. Discussion We show that the proposed approach is a useful methodology not affected by the characteristics of the finite element mesh. Additionally, the positive discriminating results obtained when analysing a difficult case study suggest that the proposed method could be a very useful tool for comparative studies in finite element analysis using multivariate statistical approaches. PMID:29043107
Implicit time-dependent finite different algorithm for quench simulation
International Nuclear Information System (INIS)
Koizumi, Norikiyo; Takahashi, Yoshikazu; Tsuji, Hiroshi
1994-12-01
A magnet in a fusion machine has many difficulties in its application because of requirement of a large operating current, high operating field and high breakdown voltage. A cable-in-conduit (CIC) conductor is the best candidate to overcome these difficulties. However, there remained uncertainty in a quench event in the cable-in-conduit conductor because of a difficulty to analyze a fluid dynamics equation. Several scientists, then, developed the numerical code for the quench simulation. However, most of them were based on an explicit time-dependent finite difference scheme. In this scheme, a discrete time increment is strictly restricted by CFL (Courant-Friedrichs-Lewy) condition. Therefore, long CPU time was consumed for the quench simulation. Authors, then, developed a new quench simulation code, POCHI1, which is based on an implicit time dependent scheme. In POCHI1, the fluid dynamics equation is linearlized according to a procedure applied by Beam and Warming and then, a tridiagonal system can be offered. Therefore, no iteration is necessary to solve the fluid dynamics equation. This leads great reduction of the CPU time. Also, POCHI1 can cope with non-linear boundary condition. In this study, comparison with experimental results was carried out. The normal zone propagation behavior was investigated in two samples of CIC conductors which had different hydraulic diameters. The measured and simulated normal zone propagation length showed relatively good agreement. However, the behavior of the normal voltage shows a little disagreement. These results indicate necessity to improve the treatment of the heat transfer coefficient in the turbulent flow region and the electric resistivity of the copper stabilizer in high temperature and high field region. (author)
International Nuclear Information System (INIS)
Kobayashi, Keisuke; Kikuchi, Hirohiko; Tsutsuguchi, Ken
1993-01-01
A neutron multigroup transport equation in x-y-z geometry is solved by the spherical harmonics method using finite Fourier transformation. Using the first term of the Fourier series for the space variables of spherical harmonics moments, three-point finite difference like equations are derived for x-, y- and z-axis directions, which are more consistent and accurate than those derived using the usual finite difference approximation, and these equations are solved by the iteration method in each axis direction alternatively. A method to find an optimum acceleration factor for this inner iteration is described. It is shown in the numerical examples that the present method gives higher accuracy with less mesh points that the usual finite difference method. (author)
The Galerkin finite element method for a multi-term time-fractional diffusion equation
Jin, Bangti
2015-01-01
© 2014 The Authors. We consider the initial/boundary value problem for a diffusion equation involving multiple time-fractional derivatives on a bounded convex polyhedral domain. We analyze a space semidiscrete scheme based on the standard Galerkin finite element method using continuous piecewise linear functions. Nearly optimal error estimates for both cases of initial data and inhomogeneous term are derived, which cover both smooth and nonsmooth data. Further we develop a fully discrete scheme based on a finite difference discretization of the time-fractional derivatives, and discuss its stability and error estimate. Extensive numerical experiments for one- and two-dimensional problems confirm the theoretical convergence rates.
Hybrid Fundamental Solution Based Finite Element Method: Theory and Applications
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Changyong Cao
2015-01-01
Full Text Available An overview on the development of hybrid fundamental solution based finite element method (HFS-FEM and its application in engineering problems is presented in this paper. The framework and formulations of HFS-FEM for potential problem, plane elasticity, three-dimensional elasticity, thermoelasticity, anisotropic elasticity, and plane piezoelectricity are presented. In this method, two independent assumed fields (intraelement filed and auxiliary frame field are employed. The formulations for all cases are derived from the modified variational functionals and the fundamental solutions to a given problem. Generation of elemental stiffness equations from the modified variational principle is also described. Typical numerical examples are given to demonstrate the validity and performance of the HFS-FEM. Finally, a brief summary of the approach is provided and future trends in this field are identified.
Perfectly matched layer for the time domain finite element method
International Nuclear Information System (INIS)
Rylander, Thomas; Jin Jianming
2004-01-01
A new perfectly matched layer (PML) formulation for the time domain finite element method is described and tested for Maxwell's equations. In particular, we focus on the time integration scheme which is based on Galerkin's method with a temporally piecewise linear expansion of the electric field. The time stepping scheme is constructed by forming a linear combination of exact and trapezoidal integration applied to the temporal weak form, which reduces to the well-known Newmark scheme in the case without PML. Extensive numerical tests on scattering from infinitely long metal cylinders in two dimensions show good accuracy and no signs of instabilities. For a circular cylinder, the proposed scheme indicates the expected second order convergence toward the analytic solution and gives less than 2% root-mean-square error in the bistatic radar cross section (RCS) for resolutions with more than 10 points per wavelength. An ogival cylinder, which has sharp corners supporting field singularities, shows similar accuracy in the monostatic RCS
A collocation finite element method with prior matrix condensation
International Nuclear Information System (INIS)
Sutcliffe, W.J.
1977-01-01
For thin shells with general loading, sixteen degrees of freedom have been used for a previous finite element solution procedure using a Collocation method instead of the usual variational based procedures. Although the number of elements required was relatively small, nevertheless the final matrix for the simultaneous solution of all unknowns could become large for a complex compound structure. The purpose of the present paper is to demonstrate a method of reducing the final matrix size, so allowing solution for large structures with comparatively small computer storage requirements while retaining the accuracy given by high order displacement functions. Collocation points, a number are equilibrium conditions which must be satisfied independently of the overall compatibility of forces and deflections for a complete structure. (Auth.)
Application of Finite Layer Method in Pavement Structural Analysis
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Pengfei Liu
2017-06-01
Full Text Available The finite element (FE method has been widely used in predicting the structural responses of asphalt pavements. However, the three-dimensional (3D modeling in general-purpose FE software systems such as ABAQUS requires extensive computations and is relatively time-consuming. To address this issue, a specific computational code EasyFEM was developed based on the finite layer method (FLM for analyzing structural responses of asphalt pavements under a static load. Basically, it is a 3D FE code that requires only a one-dimensional (1D mesh by incorporating analytical methods and using Fourier series in the other two dimensions, which can significantly reduce the computational time and required resources due to the easy implementation of parallel computing technology. Moreover, a newly-developed Element Energy Projection (EEP method for super-convergent calculations was implemented in EasyFEM to improve the accuracy of solutions for strains and stresses over the whole pavement model. The accuracy of the program is verified by comparing it with results from BISAR and ABAQUS for a typical asphalt pavement structure. The results show that the predicted responses from ABAQUS and EasyFEM are in good agreement with each other. The EasyFEM with the EEP post-processing technique converges faster compared with the results derived from ordinary EasyFEM applications, which proves that the EEP technique can improve the accuracy of strains and stresses from EasyFEM. In summary, the EasyFEM has a potential to provide a flexible and robust platform for the numerical simulation of asphalt pavements and can easily be post-processed with the EEP technique to enhance its advantages.
Zhou, Wenjie; Wei, Xuesong; Wang, Leqin; Wu, Guangkuan
2017-05-01
Solving the static equilibrium position is one of the most important parts of dynamic coefficients calculation and further coupled calculation of rotor system. The main contribution of this study is testing the superlinear iteration convergence method-twofold secant method, for the determination of the static equilibrium position of journal bearing with finite length. Essentially, the Reynolds equation for stable motion is solved by the finite difference method and the inner pressure is obtained by the successive over-relaxation iterative method reinforced by the compound Simpson quadrature formula. The accuracy and efficiency of the twofold secant method are higher in comparison with the secant method and dichotomy. The total number of iterative steps required for the twofold secant method are about one-third of the secant method and less than one-eighth of dichotomy for the same equilibrium position. The calculations for equilibrium position and pressure distribution for different bearing length, clearance and rotating speed were done. In the results, the eccentricity presents linear inverse proportional relationship to the attitude angle. The influence of the bearing length, clearance and bearing radius on the load-carrying capacity was also investigated. The results illustrate that larger bearing length, larger radius and smaller clearance are good for the load-carrying capacity of journal bearing. The application of the twofold secant method can greatly reduce the computational time for calculation of the dynamic coefficients and dynamic characteristics of rotor-bearing system with a journal bearing of finite length.
Expanded Mixed Multiscale Finite Element Methods and Their Applications for Flows in Porous Media
Jiang, L.; Copeland, D.; Moulton, J. D.
2012-01-01
We develop a family of expanded mixed multiscale finite element methods (MsFEMs) and their hybridizations for second-order elliptic equations. This formulation expands the standard mixed multiscale finite element formulation in the sense that four
The Finite-Surface Method for incompressible flow: a step beyond staggered grid
Hokpunna, Arpiruk; Misaka, Takashi; Obayashi, Shigeru
2017-11-01
We present a newly developed higher-order finite surface method for the incompressible Navier-Stokes equations (NSE). This method defines the velocities as a surface-averaged value on the surfaces of the pressure cells. Consequently, the mass conservation on the pressure cells becomes an exact equation. The only things left to approximate is the momentum equation and the pressure at the new time step. At certain conditions, the exact mass conservation enables the explicit n-th order accurate NSE solver to be used with the pressure treatment that is two or four order less accurate without loosing the apparent convergence rate. This feature was not possible with finite volume of finite difference methods. We use Fourier analysis with a model spectrum to determine the condition and found that the range covers standard boundary layer flows. The formal convergence and the performance of the proposed scheme is compared with a sixth-order finite volume method. Finally, the accuracy and performance of the method is evaluated in turbulent channel flows. This work is partially funded by a research colloaboration from IFS, Tohoku university and ASEAN+3 funding scheme from CMUIC, Chiang Mai University.
Hannah, S. R.; Palazotto, A. N.
1978-01-01
A new trigonometric approach to the finite difference calculus was applied to the problem of beam buckling as represented by virtual work and equilibrium equations. The trigonometric functions were varied by adjusting a wavelength parameter in the approximating Fourier series. Values of the critical force obtained from the modified approach for beams with a variety of boundary conditions were compared to results using the conventional finite difference method. The trigonometric approach produced significantly more accurate approximations for the critical force than the conventional approach for a relatively wide range in values of the wavelength parameter; and the optimizing value of the wavelength parameter corresponded to the half-wavelength of the buckled mode shape. It was found from a modal analysis that the most accurate solutions are obtained when the approximating function closely represents the actual displacement function and matches the actual boundary conditions.
International Nuclear Information System (INIS)
Kriventsev, Vladimir
2000-09-01
Most of thermal hydraulic processes in nuclear engineering can be described by general convection-diffusion equations that are often can be simulated numerically with finite-difference method (FDM). An effective scheme for finite-difference discretization of such equations is presented in this report. The derivation of this scheme is based on analytical solutions of a simplified one-dimensional equation written for every control volume of the finite-difference mesh. These analytical solutions are constructed using linearized representations of both diffusion coefficient and source term. As a result, the Efficient Finite-Differencing (EFD) scheme makes it possible to significantly improve the accuracy of numerical method even using mesh systems with fewer grid nodes that, in turn, allows to speed-up numerical simulation. EFD has been carefully verified on the series of sample problems for which either analytical or very precise numerical solutions can be found. EFD has been compared with other popular FDM schemes including novel, accurate (as well as sophisticated) methods. Among the methods compared were well-known central difference scheme, upwind scheme, exponential differencing and hybrid schemes of Spalding. Also, newly developed finite-difference schemes, such as the the quadratic upstream (QUICK) scheme of Leonard, the locally analytic differencing (LOAD) scheme of Wong and Raithby, the flux-spline scheme proposed by Varejago and Patankar as well as the latest LENS discretization of Sakai have been compared. Detailed results of this comparison are given in this report. These tests have shown a high efficiency of the EFD scheme. For most of sample problems considered EFD has demonstrated the numerical error that appeared to be in orders of magnitude lower than that of other discretization methods. Or, in other words, EFD has predicted numerical solution with the same given numerical error but using much fewer grid nodes. In this report, the detailed
Generalized multiscale finite element methods (GMsFEM)
Efendiev, Yalchin R.; Galvis, Juan; Hou, Thomasyizhao
2013-01-01
In this paper, we propose a general approach called Generalized Multiscale Finite Element Method (GMsFEM) for performing multiscale simulations for problems without scale separation over a complex input space. As in multiscale finite element methods (MsFEMs), the main idea of the proposed approach is to construct a small dimensional local solution space that can be used to generate an efficient and accurate approximation to the multiscale solution with a potentially high dimensional input parameter space. In the proposed approach, we present a general procedure to construct the offline space that is used for a systematic enrichment of the coarse solution space in the online stage. The enrichment in the online stage is performed based on a spectral decomposition of the offline space. In the online stage, for any input parameter, a multiscale space is constructed to solve the global problem on a coarse grid. The online space is constructed via a spectral decomposition of the offline space and by choosing the eigenvectors corresponding to the largest eigenvalues. The computational saving is due to the fact that the construction of the online multiscale space for any input parameter is fast and this space can be re-used for solving the forward problem with any forcing and boundary condition. Compared with the other approaches where global snapshots are used, the local approach that we present in this paper allows us to eliminate unnecessary degrees of freedom on a coarse-grid level. We present various examples in the paper and some numerical results to demonstrate the effectiveness of our method. © 2013 Elsevier Inc.
Generalized multiscale finite element methods (GMsFEM)
Efendiev, Yalchin R.
2013-10-01
In this paper, we propose a general approach called Generalized Multiscale Finite Element Method (GMsFEM) for performing multiscale simulations for problems without scale separation over a complex input space. As in multiscale finite element methods (MsFEMs), the main idea of the proposed approach is to construct a small dimensional local solution space that can be used to generate an efficient and accurate approximation to the multiscale solution with a potentially high dimensional input parameter space. In the proposed approach, we present a general procedure to construct the offline space that is used for a systematic enrichment of the coarse solution space in the online stage. The enrichment in the online stage is performed based on a spectral decomposition of the offline space. In the online stage, for any input parameter, a multiscale space is constructed to solve the global problem on a coarse grid. The online space is constructed via a spectral decomposition of the offline space and by choosing the eigenvectors corresponding to the largest eigenvalues. The computational saving is due to the fact that the construction of the online multiscale space for any input parameter is fast and this space can be re-used for solving the forward problem with any forcing and boundary condition. Compared with the other approaches where global snapshots are used, the local approach that we present in this paper allows us to eliminate unnecessary degrees of freedom on a coarse-grid level. We present various examples in the paper and some numerical results to demonstrate the effectiveness of our method. © 2013 Elsevier Inc.
Multiscale Finite Element Methods for Flows on Rough Surfaces
Efendiev, Yalchin
2013-01-01
In this paper, we present the Multiscale Finite Element Method (MsFEM) for problems on rough heterogeneous surfaces. We consider the diffusion equation on oscillatory surfaces. Our objective is to represent small-scale features of the solution via multiscale basis functions described on a coarse grid. This problem arises in many applications where processes occur on surfaces or thin layers. We present a unified multiscale finite element framework that entails the use of transformations that map the reference surface to the deformed surface. The main ingredients of MsFEM are (1) the construction of multiscale basis functions and (2) a global coupling of these basis functions. For the construction of multiscale basis functions, our approach uses the transformation of the reference surface to a deformed surface. On the deformed surface, multiscale basis functions are defined where reduced (1D) problems are solved along the edges of coarse-grid blocks to calculate nodalmultiscale basis functions. Furthermore, these basis functions are transformed back to the reference configuration. We discuss the use of appropriate transformation operators that improve the accuracy of the method. The method has an optimal convergence if the transformed surface is smooth and the image of the coarse partition in the reference configuration forms a quasiuniform partition. In this paper, we consider such transformations based on harmonic coordinates (following H. Owhadi and L. Zhang [Comm. Pure and Applied Math., LX(2007), pp. 675-723]) and discuss gridding issues in the reference configuration. Numerical results are presented where we compare the MsFEM when two types of deformations are used formultiscale basis construction. The first deformation employs local information and the second deformation employs a global information. Our numerical results showthat one can improve the accuracy of the simulations when a global information is used. © 2013 Global-Science Press.
Paulina Krolo; Davor Grandić; Mladen Bulić
2016-01-01
The aim of this paper is the development of the two different numerical techniques for the preloading of bolts by the finite element method using the software Abaqus Standard. Furthermore, this paper gave detailed guidelines for modelling contact, method for solving the numerical error problems such as numerical singularity error and negative eigenvalues due to rigid body motion or the problem of the extensive elongation of bolts after pretension which is occurring during the analysis. The be...
A simple finite-difference scheme for handling topography with the first-order wave equation
Mulder, W. A.; Huiskes, M. J.
2017-07-01
One approach to incorporate topography in seismic finite-difference codes is a local modification of the difference operators near the free surface. An earlier paper described an approach for modelling irregular boundaries in a constant-density acoustic finite-difference code, based on the second-order formulation of the wave equation that only involves the pressure. Here, a similar method is considered for the first-order formulation in terms of pressure and particle velocity, using a staggered finite-difference discretization both in space and in time. In one space dimension, the boundary conditions consist in imposing antisymmetry for the pressure and symmetry for particle velocity components. For the pressure, this means that the solution values as well as all even derivatives up to a certain order are zero on the boundary. For the particle velocity, all odd derivatives are zero. In 2D, the 1-D assumption is used along each coordinate direction, with antisymmetry for the pressure along the coordinate and symmetry for the particle velocity component parallel to that coordinate direction. Since the symmetry or antisymmetry should hold along the direction normal to the boundary rather than along the coordinate directions, this generates an additional numerical error on top of the time stepping errors and the errors due to the interior spatial discretization. Numerical experiments in 2D and 3D nevertheless produce acceptable results.
induction motor, unbalance, electrical loss, finite element method.
Directory of Open Access Journals (Sweden)
Camilo Andrés Cortés
2008-09-01
Full Text Available This paper shows the pattern of a 7.5 kW squirrel-cage induction motor’s electrical loss in balanced and unbalanced conditions, modelling the motor using the finite element method and comparing the results with experimental data obtained in the laboratory for the selected motor. Magnetic flux density variation was analysed at four places in the machine. The results so obtained sho- wed that the undervoltage unbalanced condition was the most critical from the motor’s total loss point of view. Regarding varia- tion of loss in parts of the motor, a constant iron loss pattern was found when the load was changed for each type of voltage supply and that the place where the loss had the largest rise was in the machine’s rotor.
A finite-elements method for turbulent flow analysis
International Nuclear Information System (INIS)
Autret, A.
1986-03-01
The work discussed here covers turbulent flow calculations using GALERKIN's finite-element method. Turbulence effects on the mean field are taken into account by the k-epsilon model with two evolution equations: one for the kinetic energy of the turbulence, and one for the energy dissipation rate. The wall zone is covered by wall laws, and by REICHARDT's law in particular. A law is advanced for the epsilon input profile, and a numerical solution is proposed for the physically aberrant values of k and epsilon generated by the model. Single-equation models are reviewed comparatively with the k-epsilon model. A comparison between calculated and analytical solutions or calculated and experimental results is presented for decreasing turbulence behind a grid, for the flow between parallel flat plates with three REYNOLDS numbers, and for backward facing step. This part contains graphs and curves corresponding to results of the calculations presented in part one [fr
A mixed finite element method for nonlinear diffusion equations
Burger, Martin; Carrillo, José
2010-01-01
We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model. © American Institute of Mathematical Sciences.
Two different hematocrit detection methods: Different methods, different results?
Directory of Open Access Journals (Sweden)
Schuepbach Reto A
2010-03-01
Full Text Available Abstract Background Less is known about the influence of hematocrit detection methodology on transfusion triggers. Therefore, the aim of the present study was to compare two different hematocrit-assessing methods. In a total of 50 critically ill patients hematocrit was analyzed using (1 blood gas analyzer (ABLflex 800 and (2 the central laboratory method (ADVIA® 2120 and compared. Findings Bland-Altman analysis for repeated measurements showed a good correlation with a bias of +1.39% and 2 SD of ± 3.12%. The 24%-hematocrit-group showed a correlation of r2 = 0.87. With a kappa of 0.56, 22.7% of the cases would have been transfused differently. In the-28%-hematocrit group with a similar correlation (r2 = 0.8 and a kappa of 0.58, 21% of the cases would have been transfused differently. Conclusions Despite a good agreement between the two methods used to determine hematocrit in clinical routine, the calculated difference of 1.4% might substantially influence transfusion triggers depending on the employed method.
Huang, Chih-Hsu; Lin, Chou-Ching K; Ju, Ming-Shaung
2015-02-01
Compared with the Monte Carlo method, the population density method is efficient for modeling collective dynamics of neuronal populations in human brain. In this method, a population density function describes the probabilistic distribution of states of all neurons in the population and it is governed by a hyperbolic partial differential equation. In the past, the problem was mainly solved by using the finite difference method. In a previous study, a continuous Galerkin finite element method was found better than the finite difference method for solving the hyperbolic partial differential equation; however, the population density function often has discontinuity and both methods suffer from a numerical stability problem. The goal of this study is to improve the numerical stability of the solution using discontinuous Galerkin finite element method. To test the performance of the new approach, interaction of a population of cortical pyramidal neurons and a population of thalamic neurons was simulated. The numerical results showed good agreement between results of discontinuous Galerkin finite element and Monte Carlo methods. The convergence and accuracy of the solutions are excellent. The numerical stability problem could be resolved using the discontinuous Galerkin finite element method which has total-variation-diminishing property. The efficient approach will be employed to simulate the electroencephalogram or dynamics of thalamocortical network which involves three populations, namely, thalamic reticular neurons, thalamocortical neurons and cortical pyramidal neurons. Copyright © 2014 Elsevier Ltd. All rights reserved.
Numerically stable finite difference simulation for ultrasonic NDE in anisotropic composites
Leckey, Cara A. C.; Quintanilla, Francisco Hernando; Cole, Christina M.
2018-04-01
Simulation tools can enable optimized inspection of advanced materials and complex geometry structures. Recent work at NASA Langley is focused on the development of custom simulation tools for modeling ultrasonic wave behavior in composite materials. Prior work focused on the use of a standard staggered grid finite difference type of mathematical approach, by implementing a three-dimensional (3D) anisotropic Elastodynamic Finite Integration Technique (EFIT) code. However, observations showed that the anisotropic EFIT method displays numerically unstable behavior at the locations of stress-free boundaries for some cases of anisotropic materials. This paper gives examples of the numerical instabilities observed for EFIT and discusses the source of instability. As an alternative to EFIT, the 3D Lebedev Finite Difference (LFD) method has been implemented. The paper briefly describes the LFD approach and shows examples of stable behavior in the presence of stress-free boundaries for a monoclinic anisotropy case. The LFD results are also compared to experimental results and dispersion curves.
Kou, Jisheng
2017-06-09
In this paper, a new three-field weak formulation for Stokes problems is developed, and from this, a dual-mixed finite element method is proposed on a rectangular mesh. In the proposed mixed methods, the components of stress tensor are approximated by piecewise constant functions or Q1 functions, while the velocity and pressure are discretized by the lowest-order Raviart-Thomas element and the piecewise constant functions, respectively. Using quadrature rules, we demonstrate that this scheme can be reduced into a finite volume method on staggered grid, which is extensively used in computational fluid mechanics and engineering.
A simple finite-difference scheme for handling topography with the first-order wave equation
Mulder, W.A.; Huiskes, M.J.
2017-01-01
One approach to incorporate topography in seismic finite-difference codes is a local modification of the difference operators near the free surface. An earlier paper described an approach for modelling irregular boundaries in a constant-density acoustic finite-difference code, based on the
A Coupled Finite Difference and Moving Least Squares Simulation of Violent Breaking Wave Impact
DEFF Research Database (Denmark)
Lindberg, Ole; Bingham, Harry B.; Engsig-Karup, Allan Peter
2012-01-01
feature of this model is a generalized finite point set method which is applied to the solution of the Poisson equation on an unstructured point distribution. The presented finite point set method is generalized to arbitrary order of approximation. The two models are applied to simulation of steep...
Enhanced finite difference scheme for the neutron diffusion equation using the importance function
International Nuclear Information System (INIS)
Vagheian, Mehran; Vosoughi, Naser; Gharib, Morteza
2016-01-01
Highlights: • An enhanced finite difference scheme for the neutron diffusion equation is proposed. • A seven-step algorithm is considered based on the importance function. • Mesh points are distributed through entire reactor core with respect to the importance function. • The results all proved that the proposed algorithm is highly efficient. - Abstract: Mesh point positions in Finite Difference Method (FDM) of discretization for the neutron diffusion equation can remarkably affect the averaged neutron fluxes as well as the effective multiplication factor. In this study, by aid of improving the mesh point positions, an enhanced finite difference scheme for the neutron diffusion equation is proposed based on the neutron importance function. In order to determine the neutron importance function, the adjoint (backward) neutron diffusion calculations are performed in the same procedure as for the forward calculations. Considering the neutron importance function, the mesh points can be improved through the entire reactor core. Accordingly, in regions with greater neutron importance, density of mesh elements is higher than that in regions with less importance. The forward calculations are then performed for both of the uniform and improved non-uniform mesh point distributions and the results (the neutron fluxes along with the corresponding eigenvalues) for the two cases are compared with each other. The results are benchmarked against the reference values (with fine meshes) for Kang and Rod Bundle BWR benchmark problems. These benchmark cases revealed that the improved non-uniform mesh point distribution is highly efficient.
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
Kou, Jisheng; Sun, Shuyu
2017-01-01
In this paper, a new three-field weak formulation for Stokes problems is developed, and from this, a dual-mixed finite element method is proposed on a rectangular mesh. In the proposed mixed methods, the components of stress tensor are approximated
Parallelized implicit propagators for the finite-difference Schrödinger equation
Parker, Jonathan; Taylor, K. T.
1995-08-01
We describe the application of block Gauss-Seidel and block Jacobi iterative methods to the design of implicit propagators for finite-difference models of the time-dependent Schrödinger equation. The block-wise iterative methods discussed here are mixed direct-iterative methods for solving simultaneous equations, in the sense that direct methods (e.g. LU decomposition) are used to invert certain block sub-matrices, and iterative methods are used to complete the solution. We describe parallel variants of the basic algorithm that are well suited to the medium- to coarse-grained parallelism of work-station clusters, and MIMD supercomputers, and we show that under a wide range of conditions, fine-grained parallelism of the computation can be achieved. Numerical tests are conducted on a typical one-electron atom Hamiltonian. The methods converge robustly to machine precision (15 significant figures), in some cases in as few as 6 or 7 iterations. The rate of convergence is nearly independent of the finite-difference grid-point separations.
Ghil, M.; Balgovind, R.
1979-01-01
The inhomogeneous Cauchy-Riemann equations in a rectangle are discretized by a finite difference approximation. Several different boundary conditions are treated explicitly, leading to algorithms which have overall second-order accuracy. All boundary conditions with either u or v prescribed along a side of the rectangle can be treated by similar methods. The algorithms presented here have nearly minimal time and storage requirements and seem suitable for development into a general-purpose direct Cauchy-Riemann solver for arbitrary boundary conditions.
A 3D Finite Element Method for Flexible Multibody Systems
International Nuclear Information System (INIS)
Gerstmayr, Johannes; Schoeberl, Joachim
2006-01-01
An efficient finite element (FE) formulation for the simulation of multibody systems is derived from Hamilton's principle. According to the classical assumptions of multibody systems, a large rotation formulation has been chosen, where large rotations and large displacements, but only small deformations of the single bodies are taken into account. The strain tensor is linearized with respect to a co-rotated frame. The present approach uses absolute coordinates for the degrees of freedom and forms an alternative to the floating frame of reference formulation that is based on relative coordinates and describes deformation with respect to a co-rotated frame. Due to the modified strain tensor, the present formulation distinguishes significantly from standard nodal based nonlinear FE methods. Constraints are defined in integral form for every pair of surfaces of two bodies. This leads to a small number of constraint equations and avoids artificial stress singularities. The resulting mass and stiffness matrices are constant apart from a transformation based on a single rotation matrix for each body. The particular structure of this transformation allows to prevent from the usually expensive factorization of the system Jacobian within implicit time--integration methods. The present method has been implemented and tested with the FE-package NGSolve and specific 3D examples are verified with a standard beam formulation
An enhanced finite volume method to model 2D linear elastic structures
CSIR Research Space (South Africa)
Suliman, Ridhwaan
2014-04-01
Full Text Available . Suliman) Preprint submitted to Applied Mathematical Modelling July 22, 2013 Keywords: finite volume, finite element, locking, error analysis 1. Introduction Since the 1960s, the finite element method has mainly been used for modelling the mechanics... formulation provides higher accuracy 2 for displacement solutions. It is well known that the linear finite element formulation suffers from sensitivity to element aspect ratio or shear locking when subjected to bend- ing [16]. Fallah [8] and Wheel [6] present...
International Nuclear Information System (INIS)
Liang, Hongbo; Fan, Man; You, Shijun; Zheng, Wandong; Zhang, Huan; Ye, Tianzhen; Zheng, Xuejing
2017-01-01
Highlights: •Four optical models for parabolic trough solar collectors were compared in detail. •Characteristics of Monte Carlo Method and Finite Volume Method were discussed. •A novel method was presented combining advantages of different models. •The method was suited to optical analysis of collectors with different geometries. •A new kind of cavity receiver was simulated depending on the novel method. -- Abstract: The PTC (parabolic trough solar collector) is widely used for space heating, heat-driven refrigeration, solar power, etc. The concentrated solar radiation is the only energy source for a PTC, thus its optical performance significantly affects the collector efficiency. In this study, four different optical models were constructed, validated and compared in detail. On this basis, a novel coupled method was presented by combining advantages of these models, which was suited to carry out a mass of optical simulations of collectors with different geometrical parameters rapidly and accurately. Based on these simulation results, the optimal configuration of a collector with highest efficiency can be determined. Thus, this method was useful for collector optimization and design. In the four models, MCM (Monte Carlo Method) and FVM (Finite Volume Method) were used to initialize photons distribution, as well as CPEM (Change Photon Energy Method) and MCM were adopted to describe the process of reflecting, transmitting and absorbing. For simulating reflection, transmission and absorption, CPEM was more efficient than MCM, so it was utilized in the coupled method. For photons distribution initialization, FVM saved running time and computation effort, whereas it needed suitable grid configuration. MCM only required a total number of rays for simulation, whereas it needed higher computing cost and its results fluctuated in multiple runs. In the novel coupled method, the grid configuration for FVM was optimized according to the “true values” from MCM of
A simple finite-difference scheme for handling topography with the second-order wave equation
Mulder, W.A.
2017-01-01
The presence of topography poses a challenge for seismic modeling with finite-difference codes. The representation of topography by means of an air layer or vacuum often leads to a substantial loss of numerical accuracy. A suitable modification of the finite-difference weights near the free
The computation of pressure waves in shock tubes by a finite difference procedure
International Nuclear Information System (INIS)
Barbaro, M.
1988-09-01
A finite difference solution of one-dimensional unsteady isentropic compressible flow equations is presented. The computer program has been tested by solving some cases of the Riemann shock tube problem. Predictions are in good agreement with those presented by other authors. Some inaccuracies may be attributed to the wave smearing consequent of the finite-difference treatment. (author)
International Nuclear Information System (INIS)
Ibral, Asmaa; Zouitine, Asmaa; Assaid, El Mahdi
2015-01-01
Poisson equation is solved analytically in the case of a point charge placed anywhere in a spherical core/shell nanostructure, immersed in aqueous or organic solution or embedded in semiconducting or insulating matrix. Conduction and valence band-edge alignments between core and shell are described by finite height barriers. Influence of polarization charges induced at the surfaces where two adjacent materials meet is taken into account. Original expressions of electrostatic potential created everywhere in the space by a source point charge are derived. Expressions of self-polarization potential describing the interaction of a point charge with its own image–charge are deduced. Contributions of double dielectric constant mismatch to electron and hole ground state energies as well as nanostructure effective gap are calculated via first order perturbation theory and also by finite difference approach. Dependencies of electron, hole and gap energies against core to shell radii ratio are determined in the case of ZnS/CdSe core/shell nanostructure immersed in water or in toluene. It appears that finite difference approach is more efficient than first order perturbation method and that the effect of polarization charge may in no case be neglected as its contribution can reach a significant proportion of the value of nanostructure gap
Energy Technology Data Exchange (ETDEWEB)
Ibral, Asmaa [Equipe d' Optique et Electronique du Solide, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B. P. 20 El Jadida principale, El Jadida, Royaume du Maroc (Morocco); Laboratoire d' Instrumentation, Mesure et Contrôle, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B. P. 20 El Jadida principale, El Jadida, Royaume du Maroc (Morocco); Zouitine, Asmaa [Département de Physique, Ecole Nationale Supérieure d' Enseignement Technique, Université Mohammed V Souissi, B. P. 6207 Rabat-Instituts, Rabat, Royaume du Maroc (Morocco); Assaid, El Mahdi, E-mail: eassaid@yahoo.fr [Equipe d' Optique et Electronique du Solide, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B. P. 20 El Jadida principale, El Jadida, Royaume du Maroc (Morocco); Laboratoire d' Instrumentation, Mesure et Contrôle, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B. P. 20 El Jadida principale, El Jadida, Royaume du Maroc (Morocco); and others
2015-02-01
Poisson equation is solved analytically in the case of a point charge placed anywhere in a spherical core/shell nanostructure, immersed in aqueous or organic solution or embedded in semiconducting or insulating matrix. Conduction and valence band-edge alignments between core and shell are described by finite height barriers. Influence of polarization charges induced at the surfaces where two adjacent materials meet is taken into account. Original expressions of electrostatic potential created everywhere in the space by a source point charge are derived. Expressions of self-polarization potential describing the interaction of a point charge with its own image–charge are deduced. Contributions of double dielectric constant mismatch to electron and hole ground state energies as well as nanostructure effective gap are calculated via first order perturbation theory and also by finite difference approach. Dependencies of electron, hole and gap energies against core to shell radii ratio are determined in the case of ZnS/CdSe core/shell nanostructure immersed in water or in toluene. It appears that finite difference approach is more efficient than first order perturbation method and that the effect of polarization charge may in no case be neglected as its contribution can reach a significant proportion of the value of nanostructure gap.
Quiney, H. M.; Glushkov, V. N.; Wilson, S.; Sabin,; Brandas, E
2001-01-01
A comparison is made of the accuracy achieved in finite difference and finite basis set approximations to the Dirac equation for the ground state of the hydrogen molecular ion. The finite basis set calculations are carried out using a distributed basis set of Gaussian functions the exponents and
Finite Element Modeling of Thermo Creep Processes Using Runge-Kutta Method
Directory of Open Access Journals (Sweden)
Yu. I. Dimitrienko
2015-01-01
Full Text Available Thermo creep deformations for most heat-resistant alloys, as a rule, nonlinearly depend on stresses and are practically non- reversible. Therefore, to calculate the properties of these materials the theory of plastic flow is most widely used. Finite-element computations of a stress-strain state of structures with account of thermo creep deformations up to now are performed using main commercial software, including ANSYS package. However, in most cases to solve nonlinear creep equations, one should apply explicit or implicit methods based on the Euler method of approximation of time-derivatives. The Euler method is sufficiently efficient in terms of random access memory in computations, however this method is cumbersome in computation time and does not always provide a required accuracy for creep deformation computations.The paper offers a finite-element algorithm to solve a three-dimensional problem of thermo creep based on the Runge-Kutta finite-difference schemes of different orders with respect to time. It shows a numerical test example to solve the problem on the thermo creep of a beam under tensile loading. The computed results demonstrate that using the Runge-Kutta method with increasing accuracy order allows us to obtain a more accurate solution (with increasing accuracy order by 1 a relative error decreases, approximately, by an order too. The developed algorithm proves to be efficient enough and can be recommended for solving the more complicated problems of thermo creep of structures.
Finite-Time Synchronization of Chaotic Systems with Different Dimension and Secure Communication
Directory of Open Access Journals (Sweden)
Shouquan Pang
2016-01-01
Full Text Available Finite-time synchronization of chaotic systems with different dimension and secure communication is investigated. It is rigorously proven that global finite-time synchronization can be achieved between three-dimension Lorenz chaotic system and four-dimension Lorenz hyperchaotic system which have certain parameters or uncertain parameters. The electronic circuits of finite-time synchronization using Multisim 12 are designed to verify our conclusion. And the application to the secure communications is also analyzed and discussed.
Generalized multiscale finite element method for elasticity equations
Chung, Eric T.
2014-10-05
In this paper, we discuss the application of generalized multiscale finite element method (GMsFEM) to elasticity equation in heterogeneous media. We consider steady state elasticity equations though some of our applications are motivated by elastic wave propagation in subsurface where the subsurface properties can be highly heterogeneous and have high contrast. We present the construction of main ingredients for GMsFEM such as the snapshot space and offline spaces. The latter is constructed using local spectral decomposition in the snapshot space. The spectral decomposition is based on the analysis which is provided in the paper. We consider both continuous Galerkin and discontinuous Galerkin coupling of basis functions. Both approaches have their cons and pros. Continuous Galerkin methods allow avoiding penalty parameters though they involve partition of unity functions which can alter the properties of multiscale basis functions. On the other hand, discontinuous Galerkin techniques allow gluing multiscale basis functions without any modifications. Because basis functions are constructed independently from each other, this approach provides an advantage. We discuss the use of oversampling techniques that use snapshots in larger regions to construct the offline space. We provide numerical results to show that one can accurately approximate the solution using reduced number of degrees of freedom.
Randomized Oversampling for Generalized Multiscale Finite Element Methods
Calo, Victor M.
2016-03-23
In this paper, we develop efficient multiscale methods for flows in heterogeneous media. We use the generalized multiscale finite element (GMsFEM) framework. GMsFEM approximates the solution space locally using a few multiscale basis functions. This approximation selects an appropriate snapshot space and a local spectral decomposition, e.g., the use of oversampled regions, in order to achieve an efficient model reduction. However, the successful construction of snapshot spaces may be costly if too many local problems need to be solved in order to obtain these spaces. We use a moderate quantity of local solutions (or snapshot vectors) with random boundary conditions on oversampled regions with zero forcing to deliver an efficient methodology. Motivated by the randomized algorithm presented in [P. G. Martinsson, V. Rokhlin, and M. Tygert, A Randomized Algorithm for the approximation of Matrices, YALEU/DCS/TR-1361, Yale University, 2006], we consider a snapshot space which consists of harmonic extensions of random boundary conditions defined in a domain larger than the target region. Furthermore, we perform an eigenvalue decomposition in this small space. We study the application of randomized sampling for GMsFEM in conjunction with adaptivity, where local multiscale spaces are adaptively enriched. Convergence analysis is provided. We present representative numerical results to validate the method proposed.
Finite-difference solution of the space-angle-lethargy-dependent slowing-down transport equation
Energy Technology Data Exchange (ETDEWEB)
Matausek, M V [Boris Kidric Vinca Institute of Nuclear Sciences, Vinca, Belgrade (Yugoslavia)
1972-07-01
A procedure has been developed for solving the slowing-down transport equation for a cylindrically symmetric reactor system. The anisotropy of the resonance neutron flux is treated by the spherical harmonics formalism, which reduces the space-angle-Iethargy-dependent transport equation to a matrix integro-differential equation in space and lethargy. Replacing further the lethargy transfer integral by a finite-difference form, a set of matrix ordinary differential equations is obtained, with lethargy-and space dependent coefficients. If the lethargy pivotal points are chosen dense enough so that the difference correction term can be ignored, this set assumes a lower block triangular form and can be solved directly by forward block substitution. As in each step of the finite-difference procedure a boundary value problem has to be solved for a non-homogeneous system of ordinary differential equations with space-dependent coefficients, application of any standard numerical procedure, for example, the finite-difference method or the method of adjoint equations, is too cumbersome and would make the whole procedure practically inapplicable. A simple and efficient approximation is proposed here, allowing analytical solution for the space dependence of the spherical-harmonics flux moments, and hence the derivation of the recurrence relations between the flux moments at successive lethargy pivotal points. According to the procedure indicated above a computer code has been developed for the CDC -3600 computer, which uses the KEDAK nuclear data file. The space and lethargy distribution of the resonance neutrons can be computed in such a detailed fashion as the neutron cross-sections are known for the reactor materials considered. The computing time is relatively short so that the code can be efficiently used, either autonomously, or as part of some complex modular scheme. Typical results will be presented and discussed in order to prove and illustrate the applicability of the
Analysis of the neutron flux in an annular pulsed reactor by using finite volume method
Energy Technology Data Exchange (ETDEWEB)
Silva, Mário A.B. da; Narain, Rajendra; Bezerra, Jair de L., E-mail: mabs500@gmail.com, E-mail: narain@ufpe.br, E-mail: jairbezerra@gmail.com [Universidade Federal de Pernambuco (UFPE), Recife, PE (Brazil). Centro de Tecnologia e Geociências. Departamento de Energia Nuclear
2017-07-01
Production of very intense neutron sources is important for basic nuclear physics and for material testing and isotope production. Nuclear reactors have been used as sources of intense neutron fluxes, although the achievement of such levels is limited by the inability to remove fission heat. Periodic pulsed reactors provide very intense fluxes by a rotating modulator near a subcritical core. A concept for the production of very intense neutron fluxes that combines features of periodic pulsed reactors and steady state reactors was proposed by Narain (1997). Such a concept is known as Very Intense Continuous High Flux Pulsed Reactor (VICHFPR) and was analyzed by using diffusion equation with moving boundary conditions and Finite Difference Method with Crank-Nicolson formalism. This research aims to analyze the flux distribution in the Very Intense Continuous Flux High Pulsed Reactor (VICHFPR) by using the Finite Volume Method and compares its results with those obtained by the previous computational method. (author)
Analysis of the neutron flux in an annular pulsed reactor by using finite volume method
International Nuclear Information System (INIS)
Silva, Mário A.B. da; Narain, Rajendra; Bezerra, Jair de L.
2017-01-01
Production of very intense neutron sources is important for basic nuclear physics and for material testing and isotope production. Nuclear reactors have been used as sources of intense neutron fluxes, although the achievement of such levels is limited by the inability to remove fission heat. Periodic pulsed reactors provide very intense fluxes by a rotating modulator near a subcritical core. A concept for the production of very intense neutron fluxes that combines features of periodic pulsed reactors and steady state reactors was proposed by Narain (1997). Such a concept is known as Very Intense Continuous High Flux Pulsed Reactor (VICHFPR) and was analyzed by using diffusion equation with moving boundary conditions and Finite Difference Method with Crank-Nicolson formalism. This research aims to analyze the flux distribution in the Very Intense Continuous Flux High Pulsed Reactor (VICHFPR) by using the Finite Volume Method and compares its results with those obtained by the previous computational method. (author)
SLIC: an interactive mesh generator for finite element and finite difference application programs
International Nuclear Information System (INIS)
Gerhard, M.A.; Greenlaw, R.C.
1979-01-01
Computers with extended memory, such as the CDC STAR 100 and the CRAY 1 with mega-word capacities, are greatly enlarging the size of finite element problems which can be solved. The cost of developing and testing large meshes can be prohibitive unless one uses a computer program for mesh generation and plotting. SLIC is an interactive mesh program which builds and plots 2- and 3-D continuum meshes from interactive terminal or disc input. The user inputs coordinates for certain key points and enters commands which complete the description of the geometry. Entire surfaces and volumes are then generated from the geometric skeleton. SLIC allows the user to correct input errors and saves the corrected command list for later reuse. The mesh can be plotted on a video display at any stage of development to evaluate the work in progress. Output is in the form of an input file to a user-selected computer code. Among the available output types are ADINA, SAP4, and NIKE2D. 11 figures
High Order Finite Element Method for the Lambda modes problem on hexagonal geometry
International Nuclear Information System (INIS)
Gonzalez-Pintor, S.; Ginestar, D.; Verdu, G.
2009-01-01
A High Order Finite Element Method to approximate the Lambda modes problem for reactors with hexagonal geometry has been developed. This method is based on the expansion of the neutron flux in terms of the modified Dubiner's polynomials on a triangular mesh. This mesh is fixed and the accuracy of the method is improved increasing the degree of the polynomial expansions without the necessity of remeshing. The performance of method has been tested obtaining the dominant Lambda modes of different 2D reactor benchmark problems.
Numerical simulation of subwoofer array congurations using the Finite Element Method
Directory of Open Access Journals (Sweden)
Xavier Banyuls-Juan
2017-08-01
Full Text Available Teaching in the Master of Acoustic Engineering includes contents that require the modeling of acoustic systems of two types: simple systems through analytical theory and complex models using simulation techniques. In the present work, we describe an example of complex acoustic sources modeling using the finite element method: subwoofer sound radiation in different configurations. Numerical simulations in the frequency domain can calculate the radiation pattern of systems that do not have a simple analytical solution.
Topology optimization of bounded acoustic problems using the hybrid finite element-wave based method
DEFF Research Database (Denmark)
Goo, Seongyeol; Wang, Semyung; Kook, Junghwan
2017-01-01
This paper presents an alternative topology optimization method for bounded acoustic problems that uses the hybrid finite element-wave based method (FE-WBM). The conventional method for the topology optimization of bounded acoustic problems is based on the finite element method (FEM), which...
Reactor calculation in coarse mesh by finite element method applied to matrix response method
International Nuclear Information System (INIS)
Nakata, H.
1982-01-01
The finite element method is applied to the solution of the modified formulation of the matrix-response method aiming to do reactor calculations in coarse mesh. Good results are obtained with a short running time. The method is applicable to problems where the heterogeneity is predominant and to problems of evolution in coarse meshes where the burnup is variable in one same coarse mesh, making the cross section vary spatially with the evolution. (E.G.) [pt
Non linear permanent magnets modelling with the finite element method
International Nuclear Information System (INIS)
Chavanne, J.; Meunier, G.; Sabonnadiere, J.C.
1989-01-01
In order to perform the calculation of permanent magnets with the finite element method, it is necessary to take into account the anisotropic behaviour of hard magnetic materials (Ferrites, NdFeB, SmCo5). In linear cases, the permeability of permanent magnets is a tensor. This one is fully described with the permeabilities parallel and perpendicular to the easy axis of the magnet. In non linear cases, the model uses a texture function which represents the distribution of the local easy axis of the cristallytes of the magnet. This function allows a good representation of the angular dependance of the coercitive field of the magnet. As a result, it is possible to express the magnetic induction B and the tensor as functions of the field and the texture parameter. This model has been implemented in the software FLUX3D where the tensor is used for the Newton-Raphson procedure. 3D demagnetization of a ferrite magnet by a NdFeB magnet is a suitable representative example. They analyze the results obtained for an ideally oriented ferrite magnet and a real one using a measured texture parameter
Fluid-film bearings: a finite element method of analysis
International Nuclear Information System (INIS)
Pururav, T.; Soni, R.S.; Kushwaha, H.S.; Mahajan, S.C.
1995-01-01
Finite element method (FEM) has become a very popular technique for the analysis of fluid-film bearings in the last few years. These bearings are extensively used in nuclear industry applications such as in moderator pumps and main coolant pumps. This report gives the methodology for the solution of Reynold's equation using FEM and its implementation in FE software LUBAN developed in house. It also deals with the mathematical basis and algorithm to account for the cavitation phenomena which makes these problems non-linear in nature. The dynamic coefficients of bearings are evaluated by one-step approach using variational principles. These coefficients are useful for the dynamic characterisation of fluid-film bearings. Several problems have been solved using this code including two real life problems, a circumferentially grooved journal bearing for which experimental results are available and the bearing of moderator pump of 500 MWe PHWR, have been solved. The results obtained for sample problems are in good agreement with the published literature. (author). 9 refs., 14 figs., 5 tabs., 2 ills
Well balanced finite volume methods for nearly hydrostatic flows
International Nuclear Information System (INIS)
Botta, N.; Klein, R.; Langenberg, S.; Luetzenkirchen, S.
2004-01-01
In numerical approximations of nearly hydrostatic flows, a proper representation of the dominant hydrostatic balance is of crucial importance: unbalanced truncation errors can induce unacceptable spurious motions, e.g., in dynamical cores of models for numerical weather prediction (NWP) in particular near steep topography. In this paper we develop a new strategy for the construction of discretizations that are 'well-balanced' with respect to dominant hydrostatics. The classical idea of formulating the momentum balance in terms of deviations of pressure from a balanced background distribution is realized here through local, time dependent hydrostatic reconstructions. Balanced discretizations of the pressure gradient and of the gravitation source term are achieved through a 'discrete Archimedes' buoyancy principle'. This strategy is applied to extend an explicit standard finite volume Godunov-type scheme for compressible flows with minimal modifications. The resulting method has the following features: (i) It inherits its conservation properties from the underlying base scheme. (ii) It is exactly balanced, even on curvilinear grids, for a large class of near-hydrostatic flows. (iii) It solves the full compressible flow equations without reference to a background state that is defined for an entire vertical column of air. (iv) It is robust with respect to details of the implementation, such as the choice of slope limiting functions, or the particularities of boundary condition discretizations
Moving finite element method for ICF target implosion
Furuta, J.; Kawata, S.; Niu, K.
1985-03-01
One dimensional hydrodynamic codes for the analysis of internal confinement fusion (ICF) target implosion which include various effects were developed, but most of them utilize the artificial viscosity (e.g., Von Neumann's viscosity) which cannot reveal accurately the shock waves. A gain of ICF target implosion is much due to the dissipation at the shock fronts, so it is necessary to express correctly the shock waves which are affected by the viscosity. The width of the shock waves is usually a few times as large as the length of mean free path, therefore the meshes for the shock waves must be set to about 10 to the 4th to 10 to the 5th power. It is a serious problem because of the computational memories or CPU time. In the moving finite element (MPE) method, both nodal amplitudes and nodal positions move continuously with time in such a way as to satisfy simultaneous ordinary differential equations (OPDs) which minimize partial differential equation (PDE) residuals.
A finite-elements method for turbulent flow analysis
International Nuclear Information System (INIS)
Autret, A.
1986-03-01
The work discussed here covers turbulent flow calculations using GALERKIN's finite-element method. In our specific case, we have to deal with monophasic incompressible flow in Boussinesq approximation in the normal operating conditions of a primary circuit of nuclear power plant. Turbulence effects on the mean field are taken into account by the k-epsilon model with two evolution equations: one for the kinetic energy of the turbulence, and one for the energy dissipation rate. The wall zone is covered by wall laws, and by REICHARDT's law in particular. A Law is advanced for the epsilon input profile, and a numerical solution is proposed for the physically aberrant values of k and epsilon generated by the model. Single-equation models are reviewed comparatively with the k-epsilon model. A comparison between calculated and analytical solutions or calculated and experimental results is presented for decreasing turbulence behind a grid, for the flow between parallel flat plates with three REYNOLDS numbers, and for backward facing step [fr
Finite element analysis of CFRP reinforced silo structure design method
Yuan, Long; Xu, Xinsheng
2017-11-01
Because of poor construction, there is a serious problem of concrete quality in the silo project, which seriously affects the safe use of the structure. Concrete quality problems are mainly seen in three aspects: concrete strength cannot meet the design requirements, concrete cracking phenomenon is serious, and the unreasonable concrete vibration leads to a lot of honeycombs and surface voids. Silos are usually reinforced by carbon fiber cloth in order to ensure the safe use of silos. By the example of an alumina silo in a fly ash plant in Binzhou, Shandong Province, the alumina silo project was tested and examined on site. According to filed test results, the actual concrete strength was determined, and the damage causes of the silo was analysed. Then, a finite element analysis model of this silo was established, the CFRP cloth reinforcement method was adopted to strengthen the silo, and other technology like additional reinforcement, rebar planting, carbon fiber bonding technology was also expounded. The research of this paper is of great significance to the design and construction of silo structure.
Analysis of gear reducer housing using the finite element method
Miklos, I. Zs; Miklos, C. C.; Alic, C. I.; Raţiu, S.
2018-01-01
The housing is an important component in the construction of gear reducers, having the role of fixing the relative position of the shafts and toothed wheels. At the same time, the housing takes over, via the bearings, the shaft loads resulting when the toothed wheel is engaging another toothed mechanism (i.e. power transmission through belts or chains), and conveys them to the foundation on which it is anchored. In this regard, in order to ensure the most accurate gearing, a high stiffness of the housing is required. In this paper, we present the computer-aided 3D modelling of the housing (in cast version) of a single stage cylindrical gear reducer, using the Autodesk Inventor Professional software, on the principle of constructive sizing. For the housing resistance calculation, we carried out an analysis using the Autodesk Simulation Mechanical software to apply the finite element method, based on the actual loads, as well as a comparative study of the stress and strain distribution, for several tightening values of the retaining bolts that secure the cover and the foundation housing.
COVE-1: a finite difference creep collapse code for oval fuel pin cladding material
International Nuclear Information System (INIS)
Mohr, C.L.
1975-03-01
COVE-1 is a time-dependent incremental creep collapse code that estimates the change in ovality of a fuel pin cladding tube. It uses a finite difference method of solving the differential equations which describe the deflection of the tube walls as a function of time. The physical problem is nonlinear, both with respect to geometry and material properties, which requires the use of an incremental, analytical, path-dependent solution. The application of this code is intended primarily for tubes manufactured from Zircaloy. Therefore, provision has been made to include some of the effects of anisotropy in the flow equations for inelastic incremental deformations. 10 references. (U.S.)
Directory of Open Access Journals (Sweden)
Yuan Zhang
2016-01-01
Full Text Available Based on finite difference method, a mathematical model and a numerical model written by Fortran language were established in the paper. Then a series of experiments were conducted to figure out the evolution law of temperature field in high geothermal roadway. Research results indicate that temperature disturbance range increases gradually as the unsteady heat conduction goes on and it presents power function relationship with dimensionless time. Based on the case analysis, there is no distinct expansion of temperature disturbance range after four years of ventilation, when the temperature disturbance range R=13.6.
Four-level conservative finite-difference schemes for Boussinesq paradigm equation
Kolkovska, N.
2013-10-01
In this paper a two-parametric family of four level conservative finite difference schemes is constructed for the multidimensional Boussinesq paradigm equation. The schemes are explicit in the sense that no inner iterations are needed for evaluation of the numerical solution. The preservation of the discrete energy with this method is proved. The schemes have been numerically tested on one soliton propagation model and two solitons interaction model. The numerical experiments demonstrate that the proposed family of schemes has second order of convergence in space and time steps in the discrete maximal norm.
Scattering analysis of periodic structures using finite-difference time-domain
ElMahgoub, Khaled; Elsherbeni, Atef Z
2012-01-01
Periodic structures are of great importance in electromagnetics due to their wide range of applications such as frequency selective surfaces (FSS), electromagnetic band gap (EBG) structures, periodic absorbers, meta-materials, and many others. The aim of this book is to develop efficient computational algorithms to analyze the scattering properties of various electromagnetic periodic structures using the finite-difference time-domain periodic boundary condition (FDTD/PBC) method. A new FDTD/PBC-based algorithm is introduced to analyze general skewed grid periodic structures while another algor
Solution to PDEs using radial basis function finite-differences (RBF-FD) on multiple GPUs
International Nuclear Information System (INIS)
Bollig, Evan F.; Flyer, Natasha; Erlebacher, Gordon
2012-01-01
This paper presents parallelization strategies for the radial basis function-finite difference (RBF-FD) method. As a generalized finite differencing scheme, the RBF-FD method functions without the need for underlying meshes to structure nodes. It offers high-order accuracy approximation and scales as O(N) per time step, with N being with the total number of nodes. To our knowledge, this is the first implementation of the RBF-FD method to leverage GPU accelerators for the solution of PDEs. Additionally, this implementation is the first to span both multiple CPUs and multiple GPUs. OpenCL kernels target the GPUs and inter-processor communication and synchronization is managed by the Message Passing Interface (MPI). We verify our implementation of the RBF-FD method with two hyperbolic PDEs on the sphere, and demonstrate up to 9x speedup on a commodity GPU with unoptimized kernel implementations. On a high performance cluster, the method achieves up to 7x speedup for the maximum problem size of 27,556 nodes.
Containment penetration design and analysis by finite element methods
International Nuclear Information System (INIS)
Perry, R.F.; Rigamonti, G.; Dainora, J.
1975-01-01
Containment penetration designs which provide complete support to process piping containing high pressure and high temperature fluids and which do not employ cooling coils, require special provisions to sustain loadings associated with normal/abnormal conditions and to limit maximum temperature transmitted to the containment concrete wall. In order to accomodate piping loads and fluid temperatures within code and regulatory limitations, the containment penetration designs require careful analysis of two critical regions: 1) the portion of the penetration sleeve which is exposed to containment ambient conditions and 2) the portion of the penetration which connects the sleeve to process piping (flued head). Analytical models using finite element representation of process piping, penetration flued head, and exposed sleeve were employed to investigate the penetration assembly design. By application of flexible multi-step analyses, different penetration configurations were evaluated to determine the effects of key design parameters. Among the parameters studied were flued head angles with the process piping, sleeve length and wall thickness. Special designs employing fins welded to the sleeve to further lower the temperature at the concrete wall interface were also investigated and fin geometry effects reported. (Auth.)
Seismic Analysis of Concrete Dam by Using Finite Element Method
Directory of Open Access Journals (Sweden)
Rozaina Ismail
2017-01-01
Full Text Available This paper reports a brief study on linear seismic analysis of Sg. Kinta Concrete Dam. The analysis was conducted in order to determine the performance and behaviour of the dam under seismic excitation. The dam was modelled as two-dimensional and developed based on the design drawing that is obtained from Angkasa Consulting Services Sdn. Bhd. The seismic analysis of the dam is conducted using finite element analysis software package LUSAS 14.3 and the dam has been analyse as a plain stress problem with a linear consideration. A set of historic data, with E1 Centro earthquake acceleration of about 0.50g is used as an earthquake excitation. The natural frequency and mode shape up to fifth mode of the dam has been obtained from the analysis to show the differences of the stress and deformation between each mode. The maximum horizontal and vertical stress of Sg. Kinta dam was found and the distribution of them was discussed in form of contours. The deformation of the dam were also been discussed by comparing the maximum displacement for each mode shaped.
Application of compact finite-difference schemes to simulations of stably stratified fluid flows
Czech Academy of Sciences Publication Activity Database
Bodnár, Tomáš; Beneš, L.; Fraunie, P.; Kozel, Karel
2012-01-01
Roč. 219, č. 7 (2012), s. 3336-3353 ISSN 0096-3003 Institutional support: RVO:61388998 Keywords : stratification * finite- difference * finite-volume * Runge-Kutta Subject RIV: BA - General Mathematics Impact factor: 1.349, year: 2012 http://www.sciencedirect.com/science/article/pii/S0096300311010988
On the application of finite element method in the solution of steady state diffusion equation
International Nuclear Information System (INIS)
Ono, S.
1982-01-01
The solution of the steady state neutron diffusion equation is obtained by using the finite element method. Specifically the variational approach is used for one dimensional problems and the weighted residual method (Galerkin) for one and two dimensional problems. The spatial domain is divided into retangular elements and the neutron flux is approximated by linear (one dimensional case), and bilinear (two-dimensional case) functions. Numerical results are obtained with a FORTRAN IV computer program and compared with those obtained by the finite difference CITATION code. The results show that linear or bilinear functions, do not satisfactorily describe the differential parameters in highly heterogeneous reactor cases, but provide good results for integral parameters such as multiplication factor. (Author) [pt
HYFRAC3D, 3-D Hydraulic Rock Fracture Propagation by Finite Element Method
International Nuclear Information System (INIS)
Advani, S.H.; Lee, J.K.; Lee, T.S.
2001-01-01
1 - Description of program or function: HYFRAC3D is a finite element program for simulation of three-dimensional fracture geometries with a two-dimensional planar solution. The model predicts the height, width and wing length over time for a hydraulic fracture propagating in a multi-layered system of rock with variable fluid flow and rock mechanics properties. 2 - Method of solution: The program uses the finite element Method of solution. A backward difference scheme is used by taking the weight functions on the time axis. This implicit time matching scheme requires iteration since the fracture configuration at time t+dt is not known. 3 - Restrictions on the complexity of the problem: Graphics output is not available and program is limited to fracture propagation in a single plane without proppant transport
An object-oriented decomposition of the adaptive-hp finite element method
Energy Technology Data Exchange (ETDEWEB)
Wiley, J.C.
1994-12-13
Adaptive-hp methods are those which use a refinement control strategy driven by a local error estimate to locally modify the element size, h, and polynomial order, p. The result is an unstructured mesh in which each node may be associated with a different polynomial order and which generally require complex data structures to implement. Object-oriented design strategies and languages which support them, e.g., C++, help control the complexity of these methods. Here an overview of the major classes and class structure of an adaptive-hp finite element code is described. The essential finite element structure is described in terms of four areas of computation each with its own dynamic characteristics. Implications of converting the code for a distributed-memory parallel environment are also discussed.
International Nuclear Information System (INIS)
Chernyshenko, Dmitri; Fangohr, Hans
2015-01-01
In the finite difference method which is commonly used in computational micromagnetics, the demagnetizing field is usually computed as a convolution of the magnetization vector field with the demagnetizing tensor that describes the magnetostatic field of a cuboidal cell with constant magnetization. An analytical expression for the demagnetizing tensor is available, however at distances far from the cuboidal cell, the numerical evaluation of the analytical expression can be very inaccurate. Due to this large-distance inaccuracy numerical packages such as OOMMF compute the demagnetizing tensor using the explicit formula at distances close to the originating cell, but at distances far from the originating cell a formula based on an asymptotic expansion has to be used. In this work, we describe a method to calculate the demagnetizing field by numerical evaluation of the multidimensional integral in the demagnetizing tensor terms using a sparse grid integration scheme. This method improves the accuracy of computation at intermediate distances from the origin. We compute and report the accuracy of (i) the numerical evaluation of the exact tensor expression which is best for short distances, (ii) the asymptotic expansion best suited for large distances, and (iii) the new method based on numerical integration, which is superior to methods (i) and (ii) for intermediate distances. For all three methods, we show the measurements of accuracy and execution time as a function of distance, for calculations using single precision (4-byte) and double precision (8-byte) floating point arithmetic. We make recommendations for the choice of scheme order and integrating coefficients for the numerical integration method (iii). - Highlights: • We study the accuracy of demagnetization in finite difference micromagnetics. • We introduce a new sparse integration method to compute the tensor more accurately. • Newell, sparse integration and asymptotic method are compared for all ranges
hpGEM -- A software framework for discontinuous Galerkin finite element methods
Pesch, L.; Bell, A.; Sollie, W.E.H.; Ambati, V.R.; Bokhove, Onno; van der Vegt, Jacobus J.W.
2006-01-01
hpGEM, a novel framework for the implementation of discontinuous Galerkin finite element methods, is described. We present structures and methods that are common for many (discontinuous) finite element methods and show how we have implemented the components as an object-oriented framework. This
International Nuclear Information System (INIS)
Coulomb, F.
1989-06-01
The aim of this work is to study methods for solving the diffusion equation, based on a primal or mixed-dual finite elements discretization and well suited for use on multiprocessors computers; domain decomposition methods are the subject of the main part of this study, the linear systems being solved by the block-Jacobi method. The origin of the diffusion equation is explained in short, and various variational formulations are reminded. A survey of iterative methods is given. The elemination of the flux or current is treated in the case of a mixed method. Numerical tests are performed on two examples of reactors, in order to compare mixed elements and Lagrange elements. A theoretical study of domain decomposition is led in the case of Lagrange finite elements, and convergence conditions for the block-Jacobi method are derived; the dissection decomposition is previously the purpose of a particular numerical analysis. In the case of mixed-dual finite elements, a study is led on examples and is confirmed by numerical tests performed for the dissection decomposition; furthermore, after being justified, decompositions along axes of symmetry are numerically tested. In the case of a decomposition into two subdomains, the dissection decomposition and the decomposition with an integrated interface are compared. Alternative directions methods are defined; the convergence of those relative to Lagrange elements is shown; in the case of mixed elements, convergence conditions are found [fr