Parallel Methods for PDES

This paper examines the potential of parallel computation methods for pamal differential equations (PDEs). We start by observing Utat linear algebra is nOI the right model for PDE methods, that data slructures should be based on the physical geometry. We observe that there is a naturally high level of parallelism in the physical world to be exploited. An analysis is made showing there is a natural level of granularity or degree of parallelism which depends on the accuracy needed and the complexity of the POE problem. It is noted that the granularity leads to the usc of superelemenlS and that computational efficiency suggeslS that these should be of higher accuracy. We discuss the inherent complexity of parallel mclhods and parallel machines and conclude that dramatically increased software support is needed for the general scientific and engineering community to exploit !.he power of highly parallel machines. The paper ends with a brief taxonomy of methods for PDEs. the classification is based on the method's use of three basic procedures: Partitioning, Discretization and Iteration. • To appear as chaptt-rin Taxooomy of Pal1l1lel Algorithms, GannOR and Iamieson, MIT press. 1987. ... This wOfk supported in pan by Air Force Office of Scientific R=rch granl AH)SR·84-0385"