Matrix Based Multigrid
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Matrix Based Multigrid
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Author : Yair Shapira
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Matrix Based Multigrid written by Yair Shapira and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
Many important problems in applied science and engineering, such as the Navier Stokes equations in fluid dynamics, the primitive equations in global climate mod eling, the strain-stress equations in mechanics, the neutron diffusion equations in nuclear engineering, and MRIICT medical simulations, involve complicated sys tems of nonlinear partial differential equations. When discretized, such problems produce extremely large, nonlinear systems of equations, whose numerical solution is prohibitively costly in terms of time and storage. High-performance (parallel) computers and efficient (parallelizable) algorithms are clearly necessary. Three classical approaches to the solution of such systems are: Newton's method, Preconditioned Conjugate Gradients (and related Krylov-space acceleration tech niques), and multigrid methods. The first two approaches require the solution of large sparse linear systems at every iteration, which are themselves often solved by multigrid methods. Developing robust and efficient multigrid algorithms is thus of great importance. The original multigrid algorithm was developed for the Poisson equation in a square, discretized by finite differences on a uniform grid. For this model problem, multigrid exhibits extremely rapid convergence, and actually solves the problem in the minimal possible time. The original algorithm uses rediscretization of the partial differential equation (POE) on each grid in the hierarchy of coarse grids that are used. However, this approach would not work for more complicated problems, such as problems on complicated domains and nonuniform grids, problems with variable coefficients, and non symmetric and indefinite equations. In these cases, matrix-based multi grid methods are in order.
Matrix Based Multigrid
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Author : Yair Shapira
language : en
Publisher: Springer
Release Date : 2008-11-01
Matrix Based Multigrid written by Yair Shapira and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-01 with Mathematics categories.
Matrix-Based Multigrid introduces and analyzes the multigrid approach for the numerical solution of large sparse linear systems arising from the discretization of elliptic partial differential equations. Special attention is given to the powerful matrix-based-multigrid approach, which is particularly useful for problems with variable coefficients and nonsymmetric and indefinite problems. This book can be used as a textbook in courses in numerical analysis, numerical linear algebra, and numerical PDEs at the advanced undergraduate and graduate levels in computer science, math, and applied math departments. The theory is written in simple algebraic terms and therefore requires preliminary knowledge only in basic linear algebra and calculus.
Multilevel Block Factorization Preconditioners
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Author : Panayot S. Vassilevski
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-22
Multilevel Block Factorization Preconditioners written by Panayot S. Vassilevski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-22 with Mathematics categories.
This monograph is the first to provide a comprehensive, self-contained and rigorous presentation of some of the most powerful preconditioning methods for solving finite element equations in a common block-matrix factorization framework. The book covers both algorithms and analysis using a common block-matrix factorization approach which emphasizes its unique feature. Topics covered include the classical incomplete block-factorization preconditioners, the most efficient methods such as the multigrid, algebraic multigrid, and domain decomposition. This text can serve as an indispensable reference for researchers, graduate students, and practitioners. It can also be used as a supplementary text for a topics course in preconditioning and/or multigrid methods at the graduate level.
Multigrid Methods
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Author : Stephen F. Mccormick
language : en
Publisher: CRC Press
Release Date : 2020-08-11
Multigrid Methods written by Stephen F. Mccormick and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-11 with Mathematics categories.
This book is a collection of research papers on a wide variety of multigrid topics, including applications, computation and theory. It represents proceedings of the Third Copper Mountain Conference on Multigrid Methods, which was held at Copper Mountain, Colorado.
A Multigrid Tutorial
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Author : William L. Briggs
language : en
Publisher: SIAM
Release Date : 2000-07-01
A Multigrid Tutorial written by William L. Briggs and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-07-01 with Mathematics categories.
Mathematics of Computing -- Numerical Analysis.
Matrix Computations
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Author : Gene H. Golub
language : en
Publisher: JHU Press
Release Date : 2013-02-15
Matrix Computations written by Gene H. Golub and has been published by JHU Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-15 with Mathematics categories.
This revised edition provides the mathematical background and algorithmic skills required for the production of numerical software. It includes rewritten and clarified proofs and derivations, as well as new topics such as Arnoldi iteration, and domain decomposition methods.
Multigrid Methods
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Author : Ulrich Trottenberg
language : en
Publisher: Academic Press
Release Date : 2001
Multigrid Methods written by Ulrich Trottenberg and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
Mathematics of Computing -- Numerical Analysis.
Towards Robust Algebraic Multigrid Methods For Nonsymmetric Problems
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Author : James Lottes
language : en
Publisher: Springer
Release Date : 2017-03-24
Towards Robust Algebraic Multigrid Methods For Nonsymmetric Problems written by James Lottes and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-24 with Mathematics categories.
This thesis presents a rigorous, abstract analysis of multigrid methods for positive nonsymmetric problems, particularly suited to algebraic multigrid, with a completely new approach to nonsymmetry which is based on a new concept of absolute value for nonsymmetric operators. Multigrid, and in particular algebraic multigrid, has become an indispensable tool for the solution of discretizations of partial differential equations. While used in both the symmetric and nonsymmetric cases, the theory for the nonsymmetric case has lagged substantially behind that for the symmetric case. This thesis closes some of this gap, presenting a major and highly original contribution to an important problem of computational science. The new approach to nonsymmetry will be of interest to anyone working on the analysis of discretizations of nonsymmetric operators, even outside the context of multigrid. The presentation of the convergence theory may interest even those only concerned with the symmetric case, as it sheds some new light on and extends existing results.
Multigrid Methods
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Author : James H Bramble
language : en
Publisher: Routledge
Release Date : 2019-01-22
Multigrid Methods written by James H Bramble and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-22 with Mathematics categories.
Multigrid methods are among the most efficient iterative methods for the solution of linear systems which arise in many large scale scientific calculations. Every researcher working with the numerical solution of partial differential equations should at least be familiar with this powerful technique. This invaluable book presents results concerning the rates of convergence of multigrid iterations.
An Introduction To Multigrid Methods
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Author : Pieter Wesseling
language : en
Publisher: R.T. Edwards, Inc.
Release Date : 2004
An Introduction To Multigrid Methods written by Pieter Wesseling and has been published by R.T. Edwards, Inc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
Introduces the principles, techniques, applications and literature of multigrid methods. Aimed at an audience with non-mathematical but computing-intensive disciplines and basic knowledge of analysis, partial differential equations and numerical mathematics, it is packed with helpful exercises, examples and illustrations.