Shapira Matrix-Based Multigrid
2. Auflage 2008
ISBN: 978-0-387-49765-5
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark
Theory and Applications
E-Book, Englisch, Band 2, 341 Seiten, eBook
Reihe: Numerical Methods and Algorithms
ISBN: 978-0-387-49765-5
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark
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 powerful matrix-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. Because it is self contained and includes useful exercises, the book is also suitable for self study by research students, researchers, engineers, and others interested in the numerical solution of partial differential equations.
Zielgruppe
Research
Autoren/Hrsg.
Weitere Infos & Material
Concepts and Preliminaries.- The Multilevel-Multiscale Approach.- Preliminaries.- Partial Differential Equations and Their Discretization.- Finite Differences and Volumes.- Finite Elements.- The Numerical Solution of Large Sparse Linear Systems of Algebraic Equations.- Iterative Linear System Solvers.- The Multigrid Iteration.- Matrix-Based Multigrid for Structured Grids.- The Automatic Multigrid Method.- Applications in Image Processing.- The Black-Box Multigrid Method.- The Indefinite Helmholtz Equation.- Matrix-Based Semicoarsening Method.- Matrix-Based Multigrid for Semistructured Grids.- Matrix-Based Multigrid for Locally Refined Meshes.- Application to Semistructured Grids.- Matrix-Based Multigrid for Unstructured Grids.- The Domain-Decomposition Multigrid Method.- The Algebraic Multilevel Method.- Applications.- Semialgebraic Multilevel Method for Systems of Partial Differential Equations.- Appendices.- Time-Dependent Parabolic PDEs.- Nonlinear Equations.
