Generating Eecient Parallel Code for Successive Over-relaxation Generating Eecient Parallel Code for Successive Over-relaxation

Successive Over-Relaxation (SOR) is a method used extensively for solving partial diierential equations by nite diierence. Compared with the Jacobi method for the same class of problems, SOR (of which the Gauss-Seidel method is a special case) ooers faster convergence. All of the schemes of parallelizing SOR proposed require two-way communication between neighbor processors. The number of the messages a processor needs to send at the end of each iteration can be as large as 3 n ?1 for a n-dimensional grid points space. In this paper, we propose a new method of parallelization which converts the two-way data communication to one-way data communication. The number of messages can be reduced from 3 n ? 1 to 2 n ? 1. By using the indirect message passing technique, this number can be further reduced to n. The new method in this paper can be used by parallelizing compilers to generate eecient parallel code for SOR programs. It can also be used to generate the parallel code directly from high-level numerical computing tools such as Matlab.