Some Domain Decomposition and Iterative Refinement Algorithms for Elliptic
Language: English
Published by Forgotten Books, 2018
- Softcover
- New
Seller: Forgotten Books, London, United KingdomForgotten Books
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Print on Demand. This book introduces the theory and application of two closely related families of iterative methods for solving elliptic finite element problems. Both methods have proven to be well-suited for parallel computing on many processors, especially for systems with strong grading of the mesh. For the first method, called the multiplicative Schwarz method, the author establishes optimal convergence rates independent of the number of subregions and the mesh size. The second method, called the additive Schwarz method, is shown to have the same property for a specific variant, and a convergence proof is given for a more general variant. The author also discusses optimal iterative refinement methods, which are closely related to the Schwarz methods. These methods can be used to improve the accuracy of finite element solutions by locally refining the mesh. The author provides a detailed analysis of these methods and establishes their optimal convergence rates. This book is a valuable resource for researchers and practitioners working in the fields of numerical analysis, scientific computing, and computational engineering. 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.…
Seller Inventory # 9781334016141_0
- Title
- Some Domain Decomposition and Iterative Refinement Algorithms for Elliptic
- Author
- Olof Widlund
- Publisher
- Forgotten Books
- Publication year
- 2018
- Condition
- New
- Book Type
- print-on-demand item
- Binding
- Paperback
- Language
- English
- ISBN 10
- 1334016143
- ISBN 13
- 9781334016141
- Seller catalogs
- Calculus
In the second section of this paper, we introduce a framework similar to Lions' and also an additive parallel) version of the Schwarz algorithm. While Lions considered the continuous problems, we work consistently with conforming finite element approximations; cf.
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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.
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