Performance Modeling for High-Order Finite Difference Methods On the Connection Machine Cm-2

Abstract

This paper is concerned with modeling the perfor mance of high-order finite-difference schemes for hy perbolic problems on the Connection Machine CM-2. Specifically, we would like to determine whether the higher communication cost of higher-order methods makes them less favorable in a parallel setting than in a sequential setting. Since most difference methods are implemented using the cshift operator, we first de rive a timing model for it in CM-Fortran under the new slicewise compiler model. This model is then used to predict the performance of the difference methods with different orders applied to the 2D Bürgers' equa tions. In addition, we study the effect of varying differ ent machine performance parameters, such as the communication time and floating-point operation time, as well as problem parameters such as mesh size. Our analysis and numerical results indicate that among high-order finite difference methods, the fourth-order one is the most efficient method in that it achieves a moderate error tolerance (a few percent) with least running time.