Matrix-Based Multigrid

Theory and Applications

AvYair Shapira

Häftad, Engelska, 2010

Del i serien Numerical Methods and Algorithms

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Beskrivning

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.This second edition offers improved content and provides more explanation for the non-expert.

Produktinformation

Utgivningsdatum:2010-11-29
Mått:155 x 235 x 19 mm
Vikt:522 g
Format:Häftad
Språk:Engelska
Serie:Numerical Methods and Algorithms
Antal sidor:318
Upplaga:2
Förlag:Springer-Verlag New York Inc.
ISBN:9781441943217

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Recensioner i media

From 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 fur Mathematik, Vol. 156 (3), March, 2009)

Innehållsförteckning

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.