Optimized partial semicoarsening multigrid algorithm for heat diffusion problems and anisotropic grids

The purpose of this work is to reduce the CPU time necessary to solve three two-dimensional linear diffusive problems governed by Laplace and Poisson equations, discretized with anisotropic grids. The Finite Difference Method is used to discretizate the differential equations with central differencing scheme. The systems of equations are solved with the lexicographic and red–black Gauss–Seidel methods associated to the geometric multigrid with correction scheme and V-cycle. The anisotropic grids considered have aspect ratios varying from 1/1024 up to 16,384. Four algorithms are compared: full coarsening, semicoarsening, full coarsening followed by semicoarsening and partial semicoarsening. Three new restriction schemes for anisotropic grids are proposed: geometric half weighting, geometric full weighting and partial weighting. Comparisons are made among these three new schemes and some restriction schemes presented in literature: injection, half weighting and full weighting. The prolongation process used is the bilinear interpolation. It is also investigated the effects on the CPU time caused by: the number of inner iterations of the smoother, the number of grids and the number of grid elements. It was verified that the partial semicoarsening algorithm is the fastest. This work also provides the optimum values of the multigrid components for this algorithm.