Multi-Grid Methods and Applications

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Springer Science & Business Media, Mar 9, 2013 - Mathematics - 378 pages
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Multi-grid methods are the most efficient tools for solving elliptic boundary value problems. The reader finds here an elementary introduction to multi-grid algorithms as well as a comprehensive convergence analysis. One section describes special applications (convection-diffusion equations, singular perturbation problems, eigenvalue problems, etc.). The book also contains a complete presentation of the multi-grid method of the second kind, which has important applications to integral equations (e.g. the "panel method") and to numerous other problems. Readers with a practical interest in multi-grid methods will benefit from this book as well as readers with a more theoretical interest.

 

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Contents

Preliminaries
1
Introductory Model Problem
17
General TwoGrid Method
41
General MultiGrid Iteration
80
Nested Iteration Technique
98
Convergence of the TwoGrid Iteration
112
Fourier Analysis
169
Nonlinear MultiGrid Methods
181
Elliptic Systems
231
Eigenvalue Problems and Singular Equations
252
Continuation Techniques
270
Extrapolation and Defect Correction Techniques
277
Local Techniques
293
The MultiGrid Method of the Second Kind
305
Bibliography
354
Subject Index
375

Singular Perturbation Problems
201

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