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Foundations of the multigrid method. Introduction to standard procedures. (Grundlagen der Mehrgittermethode. Einführung in Standardverfahren.) (German)
Berichte aus der Mathematik. Aachen: Shaker (ISBN 978-3-8322-9963-7/pbk). xiv, 194~p. (2011).
These are lecture notes suitable for a self-contained first course for engineering or applied mathematics undergraduate students, based on the mature state of multigrid practice dating to 1980s and early 1990s. The book starts with an brief explanation of basic concepts of partial differential equations and their discretization by finite elements and finite differences. The principles of multigrid are then explained using the Poisson equation on a rectangle as a model problem. Convergence analysis is intuitive by the use of Fourier modes (local mode analysis). The classical nonlinear FAS scheme and refinement (MLAT) are also presented. The treatment of parabolic equations consists of a presentation the Crank-Nicolson scheme for the heat equation, with multigrid used in every time step. The book is concluded by an example code in Fortran 77 and an explanation of a Matlab code, available from the author’s website.
Reviewer: Jan Mandel (Denver)
Classification: N15 N45 U55
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