Parallel implementation of a multigrid method on the experimental 1CAP supercomputer

摘要

A parallel multigrid method for the resolution of elliptic partial differential equations has been implemented on the loosely Coupled Array of Processors system at IBM Kingston, an experimental MIMD machine with communications occuring via shared memories. We consider various smoothers, restrictions, and prolongations, using multicolor ordering of the grid points. The parallelization is obtained by an a priori decomposition of the finest grid; each step of the multigrid method is then parallelized, up to the direct solve on the coarse grid, which is done sequentially: data communication via the shared memory occurs at the boundaries of the subregions thus defined. We present the numerical results that we obtain for the parallel code, along with the efficiencies according to the number of processors that we use. A finer analysis of the parallel code is carried out by a precise timing of the various procedures, leading to a number of conclusions as to the optimal way of parallelizing the multigrid method with this kind of approach.