50 jaar Anjerfonds
| Author | : |
| Publisher | : |
| Total Pages | : 30 |
| Release | : 1990 |
| Genre | : |
| ISBN | : |
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Analysis Of Projective Iterative Methods For Solving Multidimensional Transport Problems
Download Analysis Of Projective Iterative Methods For Solving Multidimensional Transport Problems full books in PDF, epub, and Kindle. Read online free Analysis Of Projective Iterative Methods For Solving Multidimensional Transport Problems ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Analysis of Projective-Iterative Methods for Solving Multidimensional Transport Problems
| Author | : |
| Publisher | : |
| Total Pages | : |
| Release | : 2004 |
| Genre | : |
| ISBN | : |
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The particle transport equation has a wide range of applications: nuclear engineering, astrophysics, atmospheric science, medical physics, microelectronics manufacturing, etc. It is an integro-differential equation with seven independent variables: 3 spatial, 2 angular, energy, and time, which cannot be solved analytically in most of the cases of interest. The way to solve this equation is to discretize it in space, angle, energy, and time. In practical cases, this leads to a huge sparse matrix. Iterative methods should be used even for solving transport problems on the most powerful computers available nowadays. The need to analyze the behavior of these methods is obvious: knowledge about behavior of methods can help us to improve them and avoid their use in cases in which they are not efficient. Also, if we can predict what should happen in specific cases, we can verify and validate transport codes. Analysis of iterative methods' behavior in highly scattering and strong heterogeneous medium is very important from the point of view of solving various radiative and particle transport problems. It became important for solving neutron transport equation in full-core, due to current industry's interest in obtaining very detailed transport solution without homogenization. For these reasons, the main target of this thesis was to analyze the convergence rate of four methods used to solve the steady state transport equation. We were interested in studying behavior of these methods in case of one and two dimensional strong heterogeneous and highly scattering medium with periodic structure, on rectangular grids. In order to understand better these methods, we analyzed them as well in cases of homogeneous and low scattering medium, uniform grids, etc. The main tool that we used is Fourier analysis. Iteration matrix analysis was a secondary tool that we consider. It proved to be restrictive in some cases but provided a good insight of the methods behavior. In several diffcult.
New Splitting Iterative Methods for Solving Multidimensional Neutron Transport Equations
| Author | : Jacques Tagoudjeu |
| Publisher | : Universal-Publishers |
| Total Pages | : 161 |
| Release | : 2011-04 |
| Genre | : Mathematics |
| ISBN | : 1599423960 |
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This thesis focuses on iterative methods for the treatment of the steady state neutron transport equation in slab geometry, bounded convex domain of Rn (n = 2,3) and in 1-D spherical geometry. We introduce a generic Alternate Direction Implicit (ADI)-like iterative method based on positive definite and m-accretive splitting (PAS) for linear operator equations with operators admitting such splitting. This method converges unconditionally and its SOR acceleration yields convergence results similar to those obtained in presence of finite dimensional systems with matrices possessing the Young property A. The proposed methods are illustrated by a numerical example in which an integro-differential problem of transport theory is considered. In the particular case where the positive definite part of the linear equation operator is self-adjoint, an upper bound for the contraction factor of the iterative method, which depends solely on the spectrum of the self-adjoint part is derived. As such, this method has been successfully applied to the neutron transport equation in slab and 2-D cartesian geometry and in 1-D spherical geometry. The self-adjoint and m-accretive splitting leads to a fixed point problem where the operator is a 2 by 2 matrix of operators. An infinite dimensional adaptation of minimal residual and preconditioned minimal residual algorithms using Gauss-Seidel, symmetric Gauss-Seidel and polynomial preconditioning are then applied to solve the matrix operator equation. Theoretical analysis shows that the methods converge unconditionally and upper bounds of the rate of residual decreasing which depend solely on the spectrum of the self-adjoint part of the operator are derived. The convergence of theses solvers is illustrated numerically on a sample neutron transport problem in 2-D geometry. Various test cases, including pure scattering and optically thick domains are considered.
Direct Methods of Solving Multidimensional Inverse Hyperbolic Problems
| Author | : Sergey I. Kabanikhin |
| Publisher | : Walter de Gruyter |
| Total Pages | : 188 |
| Release | : 2013-04-09 |
| Genre | : Mathematics |
| ISBN | : 3110960710 |
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The authors consider dynamic types of inverse problems in which the additional information is given by the trace of the direct problem on a (usually time-like) surface of the domain. They discuss theoretical and numerical background of the finite-difference scheme inversion, the linearization method, the method of Gel'fand-Levitan-Krein, the boundary control method, and the projection method and prove theorems of convergence, conditional stability, and other properties of the mentioned methods.
Nuclear Science Abstracts
| Author | : |
| Publisher | : |
| Total Pages | : 1298 |
| Release | : 1974 |
| Genre | : Nuclear energy |
| ISBN | : |
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Scientific and Technical Aerospace Reports
| Author | : |
| Publisher | : |
| Total Pages | : 702 |
| Release | : 1995 |
| Genre | : Aeronautics |
| ISBN | : |
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Innovative Methods for Numerical Solutions of Partial Differential Equations
| Author | : P. L. Roe |
| Publisher | : World Scientific |
| Total Pages | : 418 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : 9812810811 |
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This book consists of 20 review articles dedicated to Prof. Philip Roe on the occasion of his 60th birthday and in appreciation of his original contributions to computational fluid dynamics. The articles, written by leading researchers in the field, cover many topics, including theory and applications, algorithm developments and modern computational techniques for industry. Contents: OC A One-Sided ViewOCO: The Real Story (B van Leer); Collocated Upwind Schemes for Ideal MHD (K G Powell); The Penultimate Scheme for Systems of Conservation Laws: Finite Difference ENO with Marquina's Flux Splitting (R P Fedkiw et al.); A Finite Element Based Level-Set Method for Multiphase Flows (B Engquist & A-K Tornberg); The GHOST Fluid Method for Viscous Flows (R P Fedkiw & X-D Liu); Factorizable Schemes for the Equations of Fluid Flow (D Sidilkover); Evolution Galerkin Methods as Finite Difference Schemes (K W Morton); Fluctuation Distribution Schemes on Adjustable Meshes for Scalar Hyperbolic Equations (M J Baines); Superconvergent Lift Estimates Through Adjoint Error Analysis (M B Giles & N A Pierce); Somewhere between the LaxOCoWendroff and Roe Schemes for Calculating Multidimensional Compressible Flows (A Lerat et al.); Flux Schemes for Solving Nonlinear Systems of Conservation Laws (J M Ghidaglia); A LaxOCoWendroff Type Theorem for Residual Schemes (R Abgrall et al.); Kinetic Schemes for Solving SaintOCoVenant Equations on Unstructured Grids (M O Bristeau & B Perthame); Nonlinear Projection Methods for Multi-Entropies NavierOCoStokes Systems (C Berthon & F Coquel); A Hybrid Fluctuation Splitting Scheme for Two-Dimensional Compressible Steady Flows (P De Palma et al.); Some Recent Developments in Kinetic Schemes Based on Least Squares and Entropy Variables (S M Deshpande); Difference Approximation for Scalar Conservation Law. Consistency with Entropy Condition from the Viewpoint of Oleinik's E-Condition (H Aiso); Lessons Learned from the Blast Wave Computation Using Overset Moving Grids: Grid Motion Improves the Resolution (K Fujii). Readership: Researchers and graduate students in numerical and computational mathematics in engineering."
Handbook of Numerical Analysis
| Author | : Philippe G. Ciarlet |
| Publisher | : Gulf Professional Publishing |
| Total Pages | : 1187 |
| Release | : 1990 |
| Genre | : Numerical analysis |
| ISBN | : 9780444512246 |
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Includes following subjects: Solution of equations in Rn, Finite difference methods, Finite element methods, Techniques of scientific computing, Optimization theory and systems science, Numerical methods for fluids, Numerical methods for solids, Specific applications
Handbook of Numerical Methods for Hyperbolic Problems
| Author | : Remi Abgrall |
| Publisher | : Elsevier |
| Total Pages | : 612 |
| Release | : 2017-01-16 |
| Genre | : Mathematics |
| ISBN | : 044463911X |
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Handbook on Numerical Methods for Hyperbolic Problems: Applied and Modern Issues details the large amount of literature in the design, analysis, and application of various numerical algorithms for solving hyperbolic equations that has been produced in the last several decades. This volume provides concise summaries from experts in different types of algorithms, so that readers can find a variety of algorithms under different situations and become familiar with their relative advantages and limitations. Provides detailed, cutting-edge background explanations of existing algorithms and their analysis Presents a method of different algorithms for specific applications and the relative advantages and limitations of different algorithms for engineers or those involved in applications Written by leading subject experts in each field, the volumes provide breadth and depth of content coverage
Finite Element Methods for Computational Fluid Dynamics
| Author | : Dmitri Kuzmin |
| Publisher | : SIAM |
| Total Pages | : 321 |
| Release | : 2014-12-18 |
| Genre | : Science |
| ISBN | : 1611973600 |
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This informal introduction to computational fluid dynamics and practical guide to numerical simulation of transport phenomena covers the derivation of the governing equations, construction of finite element approximations, and qualitative properties of numerical solutions, among other topics. To make the book accessible to readers with diverse interests and backgrounds, the authors begin at a basic level and advance to numerical tools for increasingly difficult flow problems, emphasizing practical implementation rather than mathematical theory.?Finite Element Methods for Computational Fluid Dynamics: A Practical Guide?explains the basics of the finite element method (FEM) in the context of simple model problems, illustrated by numerical examples. It comprehensively reviews stabilization techniques for convection-dominated transport problems, introducing the reader to streamline diffusion methods, Petrov?Galerkin approximations, Taylor?Galerkin schemes, flux-corrected transport algorithms, and other nonlinear high-resolution schemes, and covers Petrov?Galerkin stabilization, classical projection schemes, Schur complement solvers, and the implementation of the k-epsilon turbulence model in its presentation of the FEM for incompressible flow problem. The book also describes the open-source finite element library ELMER, which is recommended as a software development kit for advanced applications in an online component.?
