Multi-Grid Methods and Applications

by Wolfgang Hackbusch

Overview

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.

Product Details

ISBN-13:	9783642057229
Publisher:	Springer Berlin Heidelberg
Publication date:	12/06/2010
Series:	Springer Series in Computational Mathematics , #4
Edition description:	Softcover reprint of hardcover 1st ed. 1985
Pages:	378
Product dimensions:	6.10(w) x 9.25(h) x 0.24(d)

Table of Contents

1. Preliminaries.- 2. Introductory Model Problem.- 3. General Two-Grid Method.- 4. General Multi-Grid Iteration.- 5. Nested Iteration Technique.- 6. Convergence of the Two-Grid Iteration.- 7. Convergence of the Multi-Grid Iteration.- 8. Fourier Analysis.- 9. Nonlinear Multi-Grid Methods.- 10. Singular Perturbation Problems.- 11. Elliptic Systems.- 12. Eigenvalue Problems and Singular Equations.- 13. Continuation Techniques.- 14. Extrapolation and Defect Correction Techniques.- 15. Local Techniques.- 16. The Multi-Grid Method of the Second Kind.