A parallelized point rowwise successive over-relaxation method on a multiprocessor

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 computational and 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 and may provide some guidelines for similar future coding since new approaches and restructuring techniques are required for programming a multiple instruction stream machine, which are totally different than those required for programming an algorithm on a vector processor. To assess the capabilitiesof the parallelized algorithm it was used to solve the 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 the algorithm for a realistic problem, it was used to obtain the numerical solution of a viscous incompressible fluid in a square cavity. Since point iterative relaxation schemes are at the core of many systems of elliptic as well as non-elliptic partial differential equations occuring in engineering and scientific applications, the present study suggests the possibility of both reducing the real time processing and increasing the scope of computational modeling.