Local Uniform Mesh Refinement on Loosely-Coupled Parallel Processors

摘要

Multiprocessor systems offer large gains in performance if algorithms for real problems can be found. We show how one algorithm for solving time dependent partial differential equations, Local Uniform Mesh Refinement, can be implemented on a multiprocessor system. Care is taken to insure that communications costs are kept under control, and an estimate of the performance of this algorithm for a range of configurations is presented. Experiments on a multiprocessor system are compared with the theory. Local Uniform Mesh Refinement (LUMR) is a powerful technique for the solution of partial differential equations. It is basically a strategy for the placement of uniform grids on a coarsest mesh which reduces the amount of work by attempting to equidistribute the error committed during the calculation. The use of the uniform grids allows the computation on each of the refined grids to be done efficiently, particulary on modern vector and parallel computers. In this paper, we discuss issues in implementing LUMR on a loosely coupled system of parallel processors.