Abstract
This chapter provides a comparison of the performance of multi-grid and conjugate gradient (CG) algorithms on the Cray torus, three-dimensional (T3D) massively parallel platforms (MPP) system for solving very large systems of linear equations. The multigrid algorithm is used with a stationary-type solver and is frequently the method of choice for sequential machines. It is found that the T3D has very fast communication and, a low latency. Because of the good communication performance of the Cray T3D, the multi-grid algorithm is found quite competitive against the conjugate gradient algorithm from direct numerical simulation (DNS) of combustion. DNS of turbulent combustion involves the solution of the three-dimensional Navier-Stokes equations and a scalar transport equation that represents the reaction progress variable. To improve the communication time for the multi-grid, it is necessary to reduce the startup time of the communication as well as to improve the packing/unpacking speed. Results are compared to those obtained on the Intel iPSC/860.
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