Algorithms For Elliptic Problems
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Algorithms For Elliptic Problems
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Author : Marián Vajtersic
language : en
Publisher: Springer Science & Business Media
Release Date : 1993-04-30
Algorithms For Elliptic Problems written by Marián Vajtersic 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 1993-04-30 with Computers categories.
This volume deals with problems of modern effective algorithms for the numerical solution of the most frequently occurring elliptic partial differential equations. From the point of view of implementation, attention is paid to algorithms for both classical sequential and parallel computer systems. The first two chapters are devoted to fast algorithms for solving the Poisson and biharmonic equation. In the third chapter, parallel algorithms for model parallel computer systems of the SIMD and MIMD types are described. The implementation aspects of parallel algorithms for solving model elliptic boundary value problems are outlined for systems with matrix, pipeline and multiprocessor parallel computer architectures. A modern and popular multigrid computational principle which offers a good opportunity for a parallel realization is described in the next chapter. More parallel variants based in this idea are presented, whereby methods and assignments strategies for hypercube systems are treated in more detail. The last chapter presents VLSI designs for solving special tridiagonal linear systems of equations arising from finite-difference approximations of elliptic problems. For researchers interested in the development and application of fast algorithms for solving elliptic partial differential equations using advanced computer systems.
Towards An Unified Theory Of Domain Decomposition Algorithms For Elliptic Problems Classic Reprint
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Author : Maksymilian Dryja
language : en
Publisher: Forgotten Books
Release Date : 2016-10-20
Towards An Unified Theory Of Domain Decomposition Algorithms For Elliptic Problems Classic Reprint written by Maksymilian Dryja and has been published by Forgotten Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-20 with Mathematics categories.
Excerpt from Towards an Unified Theory of Domain Decomposition Algorithms for Elliptic Problems The paper is organized as follows. After introducing two elliptic model problems and certain finite element methods in Section 2, we begin Section 3 by reviewing Schwarz's alternating algorithm in its classical setting. Following Sobolev [50] and P. L. Lions we indicate how this algorithm can be expressed in a variational form. Since this formulation is very convenient for the analysis of finite element problems, we work in this Hilbert space setting throughout the paper. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Towards A Unified Theory Of Domain Decomposition Algorithms For Elliptic Problems
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Author : Maksymilian Dryja
language : en
Publisher: Palala Press
Release Date : 2018-02-20
Towards A Unified Theory Of Domain Decomposition Algorithms For Elliptic Problems written by Maksymilian Dryja and has been published by Palala Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-20 with History categories.
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Some Domain Decomposition Algorithms For Elliptic Problems Classic Reprint
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Author : M. Dryja
language : en
Publisher:
Release Date : 2016-06-26
Some Domain Decomposition Algorithms For Elliptic Problems Classic Reprint written by M. Dryja and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-26 with Mathematics categories.
Excerpt from Some Domain Decomposition Algorithms for Elliptic Problems This paper is organized as follows. In Section 2, we review some of the ideas of substructuring that are very important in the development of computational methods of structural engineering. This discussion naturally leads to matrix splittings, which provide preconditioners for the large lin ear systems of algebraic equations, which arises in finite element work. In section 3, we discuss different Schwarz methods and some general tools for estimating their rates of convergence. In the concluding sections, we show how two types of domain decomposition algorithms can be analyzed by using relatively simple tools of mathematical and finite element analysis. While we can do much with linear algebra, we ultimately have to resort to tools of analysis in order to complete the proofs of our main results. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Some Domain Decomposition Algorithms For Elliptic Problems
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Author : Olof B. Widlund
language : en
Publisher: Legare Street Press
Release Date : 2022-10-27
Some Domain Decomposition Algorithms For Elliptic Problems written by Olof B. Widlund and has been published by Legare Street Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-27 with Education categories.
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Towards A Unified Theory Of Domain Decomposition Algorithms For Elliptic Problems
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Author : M. Dryja
language : en
Publisher:
Release Date : 1989
Towards A Unified Theory Of Domain Decomposition Algorithms For Elliptic Problems written by M. Dryja and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with categories.
Optimization In Solving Elliptic Problems
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Author : Eugene G. D'yakonov
language : en
Publisher: CRC Press
Release Date : 1995-10-20
Optimization In Solving Elliptic Problems written by Eugene G. D'yakonov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-10-20 with Mathematics categories.
Optimization in Solving Elliptic Problems focuses on one of the most interesting and challenging problems of computational mathematics - the optimization of numerical algorithms for solving elliptic problems. It presents detailed discussions of how asymptotically optimal algorithms may be applied to elliptic problems to obtain numerical solutions meeting certain specified requirements. Beginning with an outline of the fundamental principles of numerical methods, this book describes how to construct special modifications of classical finite element methods such that for the arising grid systems, asymptotically optimal iterative methods can be applied. Optimization in Solving Elliptic Problems describes the construction of computational algorithms resulting in the required accuracy of a solution and having a pre-determined computational complexity. Construction of asymptotically optimal algorithms is demonstrated for multi-dimensional elliptic boundary value problems under general conditions. In addition, algorithms are developed for eigenvalue problems and Navier-Stokes problems. The development of these algorithms is based on detailed discussions of topics that include accuracy estimates of projective and difference methods, topologically equivalent grids and triangulations, general theorems on convergence of iterative methods, mixed finite element methods for Stokes-type problems, methods of solving fourth-order problems, and methods for solving classical elasticity problems. Furthermore, the text provides methods for managing basic iterative methods such as domain decomposition and multigrid methods. These methods, clearly developed and explained in the text, may be used to develop algorithms for solving applied elliptic problems. The mathematics necessary to understand the development of such algorithms is provided in the introductory material within the text, and common specifications of algorithms that have been developed for typical problems in mathematical physics are identified. These features of the book make it more widely accessible to those interested in numerical methods and their optimization, including students and researchers in mathematical physics, functional analysis, theory of differential equations, approximation theory of functions, and geometry.
Some Domain Decomposition Algorithms For Elliptic Problems
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Author : Courant Institute of Mathematical Sciences Ultracomputer Research Laboratory
language : en
Publisher:
Release Date : 1989
Some Domain Decomposition Algorithms For Elliptic Problems written by Courant Institute of Mathematical Sciences Ultracomputer Research Laboratory and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Finite element method categories.
One of them is a Schwarz-type method, for which the subregions overlap, while the others are so called iterative substructuring methods, where the subregions do not overlap. Compared to previous studies of iterative substructuring methods, our proof is simpler and in one case it can be completed without using a finite element extension theorem. Such a theorem has, to our knowledge, always been used in the previous analysis in all but the very simplest cases."
Schwarz Analysis Of Iterative Substructuring Algorithms For Elliptic Problems In Three Dimensions
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Author : M. Dryja
language : en
Publisher:
Release Date : 1993
Schwarz Analysis Of Iterative Substructuring Algorithms For Elliptic Problems In Three Dimensions written by M. Dryja and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.
Two Color Fourier Analysis Of Iterative Algorithms For Elliptic Problems With Red Black Ordering
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Author : Chung-Chieh Jay Kuo
language : en
Publisher:
Release Date : 1988
Two Color Fourier Analysis Of Iterative Algorithms For Elliptic Problems With Red Black Ordering written by Chung-Chieh Jay Kuo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with categories.