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978-3-8322-9963-7
Wolfgang Joppich
Grundlagen der Mehrgittermethode
Einführung in Standardverfahren
Mathematik
Book presentation
Zentralblatt MATH 1241|1, 08.01.2013

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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 1080s and early 1990s. The book starts with an brief explanation of basic concepts of partial diefferential equations and their discretization by finite elements and finite diffenrences.
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 ninlinear 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 bookk is concluded by an example code in Forran 77 and an explanation of a Matlab code, available from the author´s website.

Jan Mandel (Denver)

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