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Some Domain Decomposition Algorithms for Nonselfadjoint Elliptic and Parabolic Partial Differential Equations: Technical Report 461; September, 1989 (Classic Reprint) - Softcover
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Excerpt from Some Domain Decomposition Algorithms for Nonselfadjoint Elliptic and Parabolic Partial Differential Equations: Technical Report 461; September, 1989
The iterative methods most commonly used are the conjugate gradient method for the symmetric, positive definite case and the generalized conju gate residual methods (gmres) for the general, nonsymmetric case. If the symmetric part of the operator is positive definite, with respect to a suitable inner product, convergence can be guaranteed. In this thesis, the rate of convergence of all algorithms will be estimated. We show that the additive Schwarz algorithm is optimal for both elliptic and parabolic problems in R2 and R3 in the sense that the rate of convergence is independent of both the coarse mesh size, defined by the substructures, and the fine mesh size. The iterative substructuring algorithm is not optimal in the above sense, however, in the R2 case the corresponding rate of convergence depends only mildly on the mesh parameters. A modified additive Schwarz algorithm is also introduced for parabolic problems in R2. The rate of convergence is independent of the fine mesh size.
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- PublisherForgotten Books
- Publication date2018
- ISBN 10 1333219601
- ISBN 13 9781333219604
- BindingPaperback
- LanguageEnglish
- Number of pages93
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Some Domain Decomposition Algorithms for Nonselfadjoint Elliptic and Parabolic
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Paperback. Condition: New. Print on Demand. This book presents numerical methods for solving large linear systems that emerge from finite element discretizations of partial differential equations. The author presents a unified abstract theory for additive Schwarz-type methods for general linear, non-selfadjoint, second order elliptic and parabolic problems. The convergence rate of the algorithms is estimated and shown to be optimal in both the elliptic and parabolic problems in R2 and R3. Numerical experiments are also presented. The algorithms introduced in this book are promising for parallel computation because they involve solving a number of smaller linear systems, which correspond to the restriction of the original problem to subregions, instead of the large original system. 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. Seller Inventory # 9781333219604_0
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Some Domain Decomposition Algorithms for Nonselfadjoint Elliptic and Parabolic Partial Differential Equations Technical Report 461 September, 1989 Classic Reprint
Seller: PBShop.store US, Wood Dale, IL, U.S.A.
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781333219604
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Some Domain Decomposition Algorithms for Nonselfadjoint Elliptic and Parabolic Partial Differential Equations Technical Report 461 September, 1989 Classic Reprint
Seller: PBShop.store UK, Fairford, GLOS, United Kingdom
Seller rating 4 out of 5 stars
PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781333219604
Quantity: 15 available