×

zbMATH — the first resource for mathematics

An introduction to multigrid methods. (English) Zbl 0760.65092
Pure and Applied Mathematics. A Wiley-Interscience Series of Texts, Monographs & Tracts. Chichester: John Wiley & Sons Ltd. vii, 284 p. (1992).
This book gives a complete introduction to multigrid methods for partial differential equations. Only a basic understanding of analysis, partial differential equations and numerical analysis is necessary. First the essential principle of multigrid methods is introduced. Then finite difference and finite volume discretizations are given. A basic smoothing analysis is presented and convergence results for the whole multigrid algorithm are derived. Finally applications to computational fluid dynamics are discussed.

MSC:
65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
76M99 Basic methods in fluid mechanics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65N06 Finite difference methods for boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65N99 Numerical methods for partial differential equations, boundary value problems
Software:
HLLE; Wesseling
PDF BibTeX XML Cite