Extremely fast finite difference techniques for the Connection Machine

The acoustic-wave equation with sponge boundary conditions is used to illustrate the mapping and optimization of an explicit finite-difference algorithm onto a massively parallel machine. The program has achieved a sustained performance of 5.6 Gigaflops (including I/O) on a 65536-processor CM2 supercomputer. The algorithm was implemented in a CM FORTRAN program enhanced by a fourth-order, two-dimensional Laplacian stencil operator. The algorithm is noted to have used almost 70 percent of the available memory bandwidth of the CM2, while maintaining considerable data communication between processors.