Smoothing and Coarse Grid Approximation Properties of Multigrid Methods

摘要

Smoothing processes, which are used in multigrid methods, are analyzed with the smoothing analysis of Brandt. The smoothing processes are applied to model problems: the Poisson, anisotropic diffusion and convection diffusion equations. An estimate is given of the Galerkin coarse grid approximation. These and other theoretical results, in comparison with experiments with multigrid methods, are remarked on. Numerical experiments show that these methods are efficient and robust in the sense that they do not need to be adapted to the problem at hand.