On the Choice of Suitable Operators and Parameters in Multigrid Methods

摘要

Multigrid methods for the solution of elliptic boundary value problems are discussed. These methods are described by a simple Algol-like program. By special choices of some operators and parameters, almost every multigrid strategy proposed in the literature for linear problems can be recovered. Several possibilities for the restriction, prolongation, coarse grid, and smoothing operators are considered. Furthermore, the number of smoothing steps and the number of coarse grid corrections are discussed. Some comparitive experiments are described with the Poisson, anisotropic diffusion, and the convection-diffusion equations.