%0 Journal Article
%T Optimization of the Multigrid-Convergence Rate on Semi-structured Meshes by Local Fourier Analysis
%A B. Gmeiner
%A T. Gradl
%A F. Gaspar
%A U. R¨ąde
%J Computer Science
%D 2014
%I arXiv
%R 10.1016/j.camwa.2012.12.006
%X In this paper a local Fourier analysis for multigrid methods on tetrahedral grids is presented. Different smoothers for the discretization of the Laplace operator by linear finite elements on such grids are analyzed. A four-color smoother is presented as an efficient choice for regular tetrahedral grids, whereas line and plane relaxations are needed for poorly shaped tetrahedra. A novel partitioning of the Fourier space is proposed to analyze the four-color smoother. Numerical test calculations validate the theoretical predictions. A multigrid method is constructed in a block-wise form, by using different smoothers and different numbers of pre- and post-smoothing steps in each tetrahedron of the coarsest grid of the domain. Some numerical experiments are presented to illustrate the efficiency of this multigrid algorithm.
%U http://arxiv.org/abs/1410.7254v1