Experiments with an ordinary differential equation solver in the parallel solution of method of lines problems on a shared memory parallel computer, Part 2

摘要

The authors previously considered the use of parallel direct dense matrix techniques for the solution of method of lines problems on a shared memory parallel computer. It was found that substantial speedups can be obtained for dense problems involving spatially discretized systems containing from a few to several hundred ordinary differential equations. This paper reports the results for similar experiments with parallel direct sparse matrix techniques for the solution of such problems. The methods are implemented in the context of a well-known stiff ordinary differential equation solver. Parallelism is exploited by forming the Jacobian matrix in parallel and by using parallel direct sparse linear algebra matrix techniques for the solution of the corrector equations. Timing results are given for several representative problems involving spatially discretized systems containing from several hundred to a few thousand ordinary differential equations. The experiments reported in this paper were performed on a Sequent Balance computer which is a parallel computer with 8 processors sharing a global memory. The results demonstrate that substantial speedups can be obtained in this manner for sparse method of lines problems.