PARALLELIZATION OF ROBUST MULTIGRID METHODS - ILU FACTORIZATION AND FREQUENCY DECOMPOSITION METHOD

The parallelization of two multigrid methods that are robust for systems of linear equations arising from the discretization of certain singularly perturbed elliptic partial differential equations is presented. The multigrid method with ILU smoother and the Frequency Decomposition Method, based on a multiple coarse grid correction, were implemented on a MIMD computer with distributed shared memory using a ring configuration for the first and a hypercube configuration for the second method. The speedups were determined for various grid sizes and numbers of processors. An objective comparison of both methods against the multigrid method with highly parallelizable red-black Gauss-Seidel smoother is made for the anisotropic equation and shows the superiority of both methods over the standard approach. The speedup of the ILU smoother is modelled and the influence of computer architecture on the speedup is discussed.