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**A multigrid tutorial.**
*(English)*
Zbl 0659.65095

Philadelphia, Pa.: Society for Industrial and Applied Mathematics (SIAM). IX, 90 p.; $ 13.50 (1987).

This is a clear and concise development of basic multigrid principles for solving elliptic partial differential equations. It is well motivated and carefully illustrated with numerical examples. Using one- and two- dimensional Poisson equations, the development starts with a careful analysis of relaxation methods that focuses on their slow convergence properties. This paves the way for a natural introduction of the multigrid concept as a cure for this slowness. The multigrid method is then studied in terms of its numerical properties. An especially illuminating component of this study is the analysis of the interplay between algebraic and Fourier theories. This “Tutorial” is a must for anyone interested in an introduction to multigrid methods and for those who wish to solidify their present understanding.

Reviewer: S.McCormick

### MSC:

65N22 | Numerical solution of discretized equations for boundary value problems involving PDEs |

65-02 | Research exposition (monographs, survey articles) pertaining to numerical analysis |

65F10 | Iterative numerical methods for linear systems |

35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |