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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.
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Some Domain Decomposition Algorithms for Elliptic Problems (Classic Reprint)
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Paperback. Condizione: New. Print on Demand. This book explores domain decomposition methods that solve large linear systems of equations arising from elliptic boundary value problems. These equations often emerge when discretizing partial differential equations used in fluid dynamics, elasticity, and other important applications. The author discusses how to efficiently solve these problems using domain decomposition methods on parallel computers. The book provides a comprehensive framework for designing and analyzing these methods, and it highlights the importance of using subspaces and projections to accelerate convergence. The author also explores the use of iterative substructuring methods, which do not use any overlap between subregions, and shows how they can be used to obtain fast rates of convergence. Overall, this book offers a valuable resource for researchers and practitioners working on the numerical solution of partial differential equations. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Codice articolo 9781332961429_0
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