Alternating-Direction Line-Relaxation Methods on Multicomputers

We study the multicomputer performance of a three-dimensional Navier-Stokes solver based on alternating-direction line-relaxation methods. We compare several multicomputer implementations, each of which combines a particular line-relaxation method and a particular distributed block-tridiagonal solver. In our experiments, the problem size was determined by resolution requirements of the application. As a result, the granularity of the computations of our study is finer than is customary in the performance analysis of concurrent block-tridiagonal solvers. Our best results were obtained with a modified half-Gauss-Seidel line-relaxation method implemented by means of a new iterative block-tridiagonal solver that is developed here. Most computations were performed on the Intel Touchstone Delta, but we also used the Intel Paragon XP]S, the Parsytec SC-256, and the Fujitsu S-600 for comparison. 1. Introduction. When using alternating-direction line-relaxation methods for systems of partial-differential equations discretized on a rectangular grid, one must solve many block-tridiagonal systems of linear equations in every relaxation step. This type of computation surfaces in many applications. In our work, we faced it when parallelizing a highly vectorized solver for the three-dimensional, unsteady, and incompressible Navier-Stokes equations [4] for use on multicomputers. In this paper, we shall discuss and analyze five line-relaxation methods and six distributed block-tridiagonal solvers used during the course of this project. We have measured the performance of several combinations of relaxation methods and block