Implementing the beam and warming method on the hypercube

Abstract

Numerical simulation of a wide range of physical phenomena typically involves enormous amounts of computation and, for scores of practical problems, these simulations cannot be carried out even on today's fastest supercomputers. The economic and scientific importance of many of these problems is driving the explosive research in computer architecture, especially the work aimed at achieving ultra high-speed computation by exploiting concurrent processing. Correspondingly, there is great interest in the design and analysis of numerical algorithms which are suitable for implementation on concurrent processor systems. In this paper we consider the implementation of the Beam and Warming implicit factored method on a hypercube concurrent processor system. We present a set of equations and give the numerical method in sufficient detail to illustrate and analyze the problems which arise in implementing this numerical method. We show that there are mappings of the computational domain onto the nodes of a hypercube concurrent processor system which maintain the efficiency of the numerical method. We also show that better methods do not exist.