The convergence of parallel multiblock multigrid methods (Q1917407)

Multigrid convergence is shown for a domain which is partitioned into blocks. First, a standard parallel multigrid solver with alternating line Gauss-Seidel relaxation is investigated for the Euler equations in a partitioned domain. For a domain which is partitioned into blocks the smoother updates lines per block. For singularly perturbed problems this method will not be satisfactory. Hence a nonstandard multigrid method based on point relaxation (MG-S) is introduced. This method is essentially equivalent to a lower-dimensional multigrid smoother and therefore the behaviour is quite clear. The new method is tested for rotated anisotropic diffusion equations and the convection-diffusion equation.