PERFORMANCE MODELING FOR HIGH-ORDER FINITE DIFFERENCE METHODS ON THE CONNECTION MACHINE CM-2

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