The convergence of parallel multiblock multigrid methods

In this paper possibilities to obtain a satisfactory multigrid convergence when a domain is partitioned into blocks are discussed. First, standard parallel multigrid with alternating line Gauss-Seidel as smoother is investigated for the Euler equations in a partitioned domain. When the domain is partitioned into blocks the smoother updates lines per block. A possibility to regain the single block multigrid convergence for many block splittings for this problem is given. For singular perturbed problems with strongly coupled unknowns in one direction only this method will not be satisfactory. Therefore, the research for nonstandard multigrid methods that are based on point smoothers and are robust is sketched. Another flexible nonstandard multigrid method, called MG-S, is introduced. Because the method is equivalent with standard multigrid with a lower dimensional multigrid smoother the behaviour of the method is quite clear. Finally, the nonstandard multigrid method is tested for two-dimensional model equations, the rotated anisotropic diffusion equation and the convection diffusion equation.