Domain Decomposition Algorithms for Indefinite Elliptic Problems

Xiao-Chuan Cai

ISBN 10: 1332088570 / ISBN 13: 9781332088577

Published by Forgotten Books, 2024

About this Item

Print on Demand. In this book, the author presents an iterative method that solves linear systems of algebraic equations that arise from finite element problems of elliptic nature. These issues are common in computational mechanics and the finite element method is a modern technique for finding approximate solutions to partial differential equations. The text focuses on problems with symmetric or non-symmetric and indefinite properties. The indefinite case includes some eigenvalues in the left half plane, which is a situation that can lead to difficulties with convergence. The author was able to find an alternative linear system that has the same solution as the original problem, thus allowing a solution via GMRES, a generalized conjugate residual method. In each iteration step, local problems are solved on small overlapping subregions of the original area, and a coarse mesh finite element problem is also solved, yielding a method that provides a way to construct preconditioners for many problems in terms of partitioning a certain finite element space into subspaces. 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 # 9781332088577_0

Bibliographic Details

• Title: Domain Decomposition Algorithms for Indefinite Elliptic Problems
• Publisher: Forgotten Books
• Publication Date: 2024
• Language: English
• ISBN 10: 1332088570
• ISBN 13: 9781332088577
• Binding: Paperback
• Condition: New
• Book Type: print-on-demand item
• Seller catalogs:
  • Calculus

About this title

Synopsis

Excerpt from Domain Decomposition Algorithms for Indefinite Elliptic Problems<br/><br/>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.