| Popis: |
Multigrid is a fast iterative method used to solve linear partial differential equations. However, because the solution of very small problems is inherent in the multigrid iteration, it is difficult to implement efficiently on a massively parallel computer. In this paper, we present an implementation of the multigrid v-cycle that has achieved 84% efficiency on the 1,024 processor NCUBE/ten. We also present a model for the efficiency of multigrid on a parallel computer that depends only on the efficiency of the smoother at each level. This model can be used to verify that it is indeed difficult to obtain extremely high efficiencies (95% to loo%), but that it is relatively easy to obtain moderately high efficiencies (70% to 85%). |
