Some Domain Decomposition Algorithms For Elliptic Problems
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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.
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."
Domain Decomposition Methods Algorithms And Theory
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Author : Andrea Toselli
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-20
Domain Decomposition Methods Algorithms And Theory written by Andrea Toselli 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 2006-06-20 with Mathematics categories.
This book offers a comprehensive presentation of some of the most successful and popular domain decomposition preconditioners for finite and spectral element approximations of partial differential equations. It places strong emphasis on both algorithmic and mathematical aspects. It covers in detail important methods such as FETI and balancing Neumann-Neumann methods and algorithms for spectral element methods.
Domain Decomposition Methods In Scientific And Engineering Computing
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Author : David E. Keyes
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
Domain Decomposition Methods In Scientific And Engineering Computing written by David E. Keyes and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
This book contains proceedings from the Seventh International Conference on Domain Decomposition Methods, held at Pennsylvania State University in October 1993. The term ``domain decomposition'' has for nearly a decade been associated with the partly iterative, partly direct algorithms explored in the proceedings of this conference. Noteworthy trends in the current volume include progress in dealing with so-called ``bad parameters'' in elliptic partial differential equation problems, as well as developments in partial differential equations outside of the elliptically-dominated framework. Also described here are convergence and complexity results for novel discretizations, which bring with them new challenges in the derivation of appropriate operators for coarsened spaces. Implementations and architectural considerations are discussed, as well as partitioning tools and environments. In addition, the book describes a wide array of applications, from semiconductor device simulation to structural mechanics to aerodynamics. Presenting many of the latest results in the field, this book offers readers an up-to-date guide to the many facets of the theory and practice of domain decomposition.
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.
Fifth International Symposium On Domain Decomposition Methods For Partial Differential Equations
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Author : David E. Keyes
language : en
Publisher: SIAM
Release Date : 1992-01-01
Fifth International Symposium On Domain Decomposition Methods For Partial Differential Equations written by David E. Keyes and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-01-01 with Mathematics categories.
Papers presented at the May 1991 symposium reflect continuing interest in the role of domain decomposition in the effective utilization of parallel systems; applications in fluid mechanics, structures, biology, and design optimization; and maturation of analysis of elliptic equations, with theoretic
Domain Decomposition Methods For Nonconforming Finite Element Discretizations
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Author : Jinsheng Gu
language : en
Publisher: Nova Publishers
Release Date : 1999
Domain Decomposition Methods For Nonconforming Finite Element Discretizations written by Jinsheng Gu and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
Domain decomposition refers to numerical methods for obtaining solutions of scientific and engineering problems by combining solutions to problems posed on physical subdomains, or, more generally, by combining solutions to appropriately constructed subproblems. It has been a subject of intense interest recently because of its suitability for implementation on high performance computer architectures. It is well known that the nonconforming finite elements are widely used in and effective for the solving of partial differential equations derived from mechanics and engineering, because they have fewer degrees of freedom, simpler basis functions and better convergence behavior. But, there has been no extensive study of domain decomposition methods with nonconforming finite elements which lack the global continuity. Therefore, a rather systematic investigation on domain decomposition methods with nonconforming elements is of great significance and this is what the present book achieves. The theoretical breakthrough is the establishment of a series of essential estimates, especially the extension theorems for nonconforming elements, which play key roles in domain decomposition analysis. There are also many originalities in the design of the domain decomposition algorithms for the nonconforming finite element discretizations, according to the features of the nonconforming elements. The existing domain decomposition methods developed in the conforming finite element discrete case can be revised properly and extended to the nonconforming finite element discrete case correspondingly. These algorithms, nonoverlap or overlap, are as efficient as their counterparts in the conforming cases, and even easier in implementation.
Domain Decomposition Methods In Science And Engineering
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Author : Alfio Quarteroni
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
Domain Decomposition Methods In Science And Engineering written by Alfio Quarteroni and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
This book contains the proceedings of the Sixth International Conference on Domain Decomposition, held in June 1992 in Como, Italy. Much of the work in this field focuses on developing numerical methods for large algebraic systems.
Third International Symposium On Domain Decomposition Methods For Partial Differential Equations
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Author : Tony F. Chan
language : en
Publisher: SIAM
Release Date : 1990-01-01
Third International Symposium On Domain Decomposition Methods For Partial Differential Equations written by Tony F. Chan and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-01-01 with Mathematics categories.