Optimization of the multigrid-convergence rate on semi-structured meshes by local Fourier analysis

B. Gmeiner, T. Gradl, F. Gaspar, U. Rüde
2013 Computers and Mathematics with Applications  
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
more » ... 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.
doi:10.1016/j.camwa.2012.12.006 fatcat:al7ipzs3nvb3zert3v6q7jw5hm