Parallelized Point Successive Over-Relaxation Method on a Multiple Instruction Multiple Data Stream Computer

摘要

A parallelized point rowwise Successive Over-Relaxation (SOR) iterative algorithm is developed for the Heterogeneous Element Processor (HEP) multiple instruction stream computer. The classical point SOR method is not easily vectorizable with rowwise ordering of the grid points, but it can be effectively parallelized on a multiple instruction stream machine without suffering in convergence rate. The details of the implementation including restructuring of a serial FORTRAN program and techniques needed to exploit the parallel processing architectural concept of the HEP are presented. The parallelized algorithm is analyzed in detail. The lessons learned in this study are documented to provide guidelines for similar future coding since new approaches and restructuring techniques are required for programming a multiple instruction machine which are totally different than those required for programming an algorithm on a vector processor. To assess the capabilities of the parallelized algorithm, it was used to solve Laplace's equation on a rectangular field with Dirichlet boundary conditions. Computer run times are presented which indicate significant speed gain over a scalar version of the code. For a moderate to large size problem, seventeen or more processes are required to make efficient use of the parallel processing hardware. Also, to demonstrate the capability of viscous incompressible fluid in a square cavity.