Domain Decomposition Algorithms For Indefinite Elliptic Problems Classic Reprint
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Domain Decomposition Algorithms for Indefinite Elliptic Problems (Classic Reprint)
Excerpt from Domain Decomposition Algorithms for Indefinite Elliptic Problems Domain decomposition techniques are powerful iterative methods for solving lin ear systems oi equations that arise from finite element problems. In each iteration step, a coarse mesh finite element problem and a number of smaller linear sys tems, which correspond to the restriction of the original problem to subregions, are solved instead of the large original system. These algorithms can be regarded as divide and conquer methods. The number of subproblems can be large and these methods are therefore promising for parallel computation. The central mathematical question is to obtain estimates on the rate of convergence of the iteration by deriving bounds on the spectrum of the iteration operator. We are able to establish quite satisfactory bounds if the coarse mesh is fine enough. 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 (Classic Reprint)
Excerpt from Some Domain Decomposition Algorithms for Elliptic Problems We consider a linear, self adjoint, elliptic problem, which is discretized by a finite element method on a bounded Lipschitz region. The region Q is a subset of R, n=2 or 3, the differential operator is the Laplacian, and zero Dirichlet conditions and continuous, piecewise linear finite elements are used. The theory could equally well be developed for much more general linear elliptic problems, which can be formulated as minimization problems. Arbitrary conforming finite elements could also be considered without fur ther major complications. Nonconforming finite elements, non-self adjoint problems and problems that give rise to indefinite symmetric systems of equations are also quite important. Some progress has already been made in such cases. 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.
Domain Decomposition Algorithms for Indefinite Elliptic Problems
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