Implementation and Performance Analysis of Numerical Algorithms on the MPP, Flex/32, and Cray/2

This dissertation presents the results of the implementation of a number of numerical algorithms on three parallel/vector computers. The object of this research is to determine how well, or poorly, a number of numerical algorithms would map onto three different architectures and to analyze the performance of these architectures using these algorithms. These algorithms are: a relaxation scheme for the solution of the Cauchy-Riemann equations, an ADI method for the solution of the diffusion equation, and a compact difference scheme for the solution of two-dimensional Navier-Stokes equations. The computers were chosen so as to encompass a variety of architectures. They are: the MPP, an SIMD machine with 16K bit serial processors; Flex/32, an MIMD machine with 20 processors; and the Cray/2. The machine architectures are briefly described. The implementation of these algorithms is discussed in relation to these architectures and measures of the performance on each machine are given. The basic comparison is among SIMD instruction parallelism on the MPP, MIMD process parallelism on the Flex/32, and vectorization of a serial code on the Cray/2. Simple performance models are used to describe the performance. These models highlight the bottlenecks and limiting factors for these algorithms on these architectures. Finally conclusions are presented