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

This paper is concerned with modeling the performance of high-order fi nite-difference schemes for hyperbolic problems on the Connection Mach ine CM-2. Specifically, we would like to determine whether the higher communication cost of higher-order methods makes them less favorable i n a parallel setting than in a sequential setting. Since most differen ce methods are implemented using the cshift operator, we first derive a timing model for it in CM-Fortran under the new slicewise compiler m odel. This model is then used to predict the performance of the differ ence methods with different orders applied to the 2D Burgers' equation s. In addition, we study the effect of varying different machine perfo rmance parameters, such as the communication time and floating-point o peration time, as well as problem parameters such as mesh size. Our an alysis and numerical results indicate that among high-order finite dif ference methods, the fourth-order one is the most efficient method in that it achieves a moderate error tolerance (a few percent) with]east running time.