Domain Decomposition Algorithms for Indefinite Elliptic Problems (Classic Reprint)

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Opis: Domain Decomposition Algorithms for Indefinite Elliptic Problems (Classic Reprint) - Cai Xiao-Chuan

Excerpt from Domain Decomposition Algorithms for Indefinite Elliptic Problems
Iterative methods for the linear systems of algebraic equations arising from elliptic finite element problems are considered. Methods previously known to work well for positive definite, symmetric problems are extended to certain nonsymmetric problems, which also can have some eigenvalues in the left half plane.
We first consider an additive Schwarz method applied to linear, second order, symmetric or nonsymmetric, indefinite elliptic boundary value problems in two and three dimensions. An alternative linear system, which has the same solution as the original problem, is derived and this system is then solved by using GMRES, an iterative method of conjugate gradient type. In each iteration step, a coarse mesh finite element problem and a number of local problems are solved on small, overlapping subregions into which the original region is subdivided. We show that the rate of convergence is independent of the number of degrees of freedom and the number of local problems if the coarse mesh is fine enough. The performance of the method is illustrated by results of several numerical experiments.
We also consider two other iterative method for solving the same class of elliptic problems in two dimensions. Using an observation of Dryja and Widlund, we show that the rate of convergence of certain iterative substructuring methods deteriorates only quite slowly when the local problems increase in size. A similar result is established for Yserentant shierarchical basis method.
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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.


Szczegóły: Domain Decomposition Algorithms for Indefinite Elliptic Problems (Classic Reprint) - Cai Xiao-Chuan

Tytuł: Domain Decomposition Algorithms for Indefinite Elliptic Problems (Classic Reprint)
Autor: Cai Xiao-Chuan
Wydawnictwo: FB &c Ltd
ISBN: 9781332088577
Języki: angielski
Rok wydania: 2015
Ilość stron: 30
Format: 15.2x22.9cm
Oprawa: Miękka


Recenzje: Domain Decomposition Algorithms for Indefinite Elliptic Problems (Classic Reprint) - Cai Xiao-Chuan

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Domain Decomposition Algorithms for Indefinite Elliptic Problems (Classic Reprint)

Excerpt from Domain Decomposition Algorithms for Indefinite Elliptic Problems
Iterative methods for the linear systems of algebraic equations arising from elliptic finite element problems are considered. Methods previously known to work well for positive definite, symmetric problems are extended to certain nonsymmetric problems, which also can have some eigenvalues in the left half plane.
We first consider an additive Schwarz method applied to linear, second order, symmetric or nonsymmetric, indefinite elliptic boundary value problems in two and three dimensions. An alternative linear system, which has the same solution as the original problem, is derived and this system is then solved by using GMRES, an iterative method of conjugate gradient type. In each iteration step, a coarse mesh finite element problem and a number of local problems are solved on small, overlapping subregions into which the original region is subdivided. We show that the rate of convergence is independent of the number of degrees of freedom and the number of local problems if the coarse mesh is fine enough. The performance of the method is illustrated by results of several numerical experiments.
We also consider two other iterative method for solving the same class of elliptic problems in two dimensions. Using an observation of Dryja and Widlund, we show that the rate of convergence of certain iterative substructuring methods deteriorates only quite slowly when the local problems increase in size. A similar result is established for Yserentant shierarchical basis method.
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.

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Szczegóły: Domain Decomposition Algorithms for Indefinite Elliptic Problems (Classic Reprint) - Cai Xiao-Chuan

Tytuł: Domain Decomposition Algorithms for Indefinite Elliptic Problems (Classic Reprint)
Autor: Cai Xiao-Chuan
Wydawnictwo: FB &c Ltd
ISBN: 9781332088577
Języki: angielski
Rok wydania: 2015
Ilość stron: 30
Format: 15.2x22.9cm
Oprawa: Miękka


Recenzje: Domain Decomposition Algorithms for Indefinite Elliptic Problems (Classic Reprint) - Cai Xiao-Chuan

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