Description
Book SynopsisThis 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.
Trade ReviewFrom the reviews of the second edition:
"Shapira delivers a systematic and unified presentation of the multigrid method that is used for the efficient solution of partial differential equations. … The notations are consistent and the presentation is self-contained. The book is recommended to readers involved in the field of computational science and engineering, from the postgraduate to the expert level. Additionally, the book is suitable for courses in numerical analysis, numerical linear algebra, scientific computing, and numerical solution of partial differential equations." (George A. Gravvanis, ACM Computing Reviews, May, 2009)
“This book provides an introduction into this area. Basically, it presupposes only a sound knowledge of analysis and linear algebra and introduces all other necessary concepts on its own. … Many exercises are included. The presentation is well suited for seminars in this area.” (H. Muthsam, Monatshefte für Mathematik, Vol. 156 (3), March, 2009)
Table of ContentsList 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 Large Sparse 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 Semi-Structured Grids 12. Multigrid for Locally Refined Meshes 13. Application to Semi-Structured Grids Part VI. Multigrid for Unstructured Grids 14. Domain Decomposition 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
