An application of partition method for solving 3D Stokes equation

Abstract

In our previous work we have studied the performance of a parallel algorithm, based on a direction splitting approach, for solving of time dependent Stokes equation. We used a rectangular uniform mesh, combined with a central difference scheme for the second derivatives. Hence, the proposed algorithm required only solution of tridiagonal linear systems.In our work, we are targeting massively parallel computers, as well as clusters of multi-core nodes. The somehow slower (experimentally-established) performance of the proposed approach was observed when using all cores on a single node of a cluster. To remedy this problem, we tried to use LAPACK subroutines from the multi-threaded layer library, but the parallel performance of the code (while improved) was still not satisfactory on a single (multi-core) node.Our current work considers hybrid parallelization based on the MPI and OpenMP standards. It is motivated by the need to maximize the parallel efficiency of our implementation of the proposed algorithm. Essential improvements of the parallel algorithm are achieved by introducing two levels of parallelism: (i) between-node parallelism based on the MPI and (ii) inside-node parallelism based on the OpenMP. The implementation was tested on Linux clusters with Intel processors and on the IBM supercomputer.