Parallel Algorithms for Solving Partial Differential Equations

This paper describes the use of a parallel computer system in applying a finite difference method to solve various types of partial differential equations. A sequential implementation of this method was made parallel by essentially spatially decomposing the problem domain into pieces that could be separately analyzed and assigning each piece to a processor in a large, multi-processor system. Although this approach is attractive in theory, it suffers in practice because of inter-processor interactions. Thus, particular emphasis was placed on developing efficient methods for the sharing of information among the processors. Initially, a simple two-dimensional board game, life, was implemented and used to develop inter-processor communication techniques. These techniques were then applied to parallel solutions of the one-dimensional wave equation and of the two-dimensional Laplace\u27s equation. Different initial conditions were used to illustrate the feasibility of this approach