Matrix-Based Multigrid Theory and Applications [Hardcover]

Matrix-Based Multigrid introduces and analyzes the multigrid approach for the numerical solution of large sparse linear systems arising from the discretization of elliptic partial differential equations. Special attention is given to the powerful matrix-based-multigrid approach, which is particularly useful for problems with variable coefficients and nonsymmetric and indefinite problems.

This book can be used as a textbook in courses in numerical analysis, numerical linear algebra, and numerical PDEs at the advanced undergraduate and graduate levels in computer science, math, and applied math departments. The theory is written in simple algebraic terms and therefore requires preliminary knowledge only in basic linear algebra and calculus.

This book introduces the multigrid approach for the numerical solution of large sparse linear systems arising from the discretization of elliptic partial differential equations. This new edition offers improved content and more explanation for the non-expert.

List of FiguresList of TablesPrefacePart I. Concepts and Preliminaries1. The MultilevelMultiscale Approach2. PreliminariesPart II. Partial Differential Equations and Their Discretization3. Finite Differences and Volumes4. Finite ElementsPart III. Numerical Solution of Large Sparse Linear Systems5. Iterative Linear System Solvers6. The Multigrid IterationPart IV. Multigrid for Structured Grids7. Automatic Multigrid8. Applications in Image Processing9. Black-Box Multigrid10. The Indefinite Helmholtz Equation11. Matrix-Based SemicoarseningPart V. Multigrid for Semi-Structured Grids12. Multigrid for Locally Refined Meshes13. Application to Semi-Structured GridsPart VI. Multigrid for Unstructured Grids14. Domain Decomposition15. The Algebraic Multilevel Method16. Applications17. Semialgebraic Multilevel for Systems of PDEsPart VII. Appendices18. Time-Dependent Parabolic PDEs19. Nonlinear EquationsReferencesIndex