This book 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 powerfulmatrix-based-multigrid approach, which is particularly useful for problems with variable coefficients and nonsymmetric and indefinite problems. This approach applies not only to model problems on rectangular grids but also to more realistic applications with complicated grids and domains and discontinuous coefficients. Matrix-Based Multigrid 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 in basic linear algebra and calculus only. Second edition is a much improved version of the book, with more explanation included for the non-expert INDICE: List of Figures.- List of Tables.- Preface.- Part I. Concepts and Preliminaries.- 1. The Multilevel–Multiscale Approach.- 2. Preliminaries.- Part II. Partial Differential Equations and Their Discretization.- 3. Finite Differences and Volumes.- 4. Finite Elements.- Part III. Numerical Solution of Linear Systems.- 5. Iterative Linear System Solvers.- 6. The Multigrid Iteration.- Part IV. Multigrid for Structured Grids.- 7. Automatic Multigrid.- 8. Applications in Image Processing.- 9. Black-Box Multigrid.- 10. The Indefinite Helmholtz Equation.- 11. Matrix-Based Semicoarsening.- Part V. Multigrid for Semistructured Grids.- 12. Multigrid for Locally Refined Meshes.- 13. Application toSemistructured Grids.- Part VI. Multigrid for Unstructured Grids.- 14. DomainDecomposition.- 15. The Algebraic Multilevel Method.- 16. Applications.- 17. Semialgebraic Multilevel for Systems of PDEs.- Part VII. Appendices.- 18. Time-Dependent Parabolic PDEs.- 19. Nonlinear Equations.- References.- Index.
- ISBN: 978-0-387-49764-8
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 345
- Fecha Publicación: 01/06/2008
- Nº Volúmenes: 1
- Idioma: Inglés