Krylov methods preconditioned with incompletely factored matrices on the CM-2

In the work presented here, we measured the performance of the components of the key iterative kernel of a preconditioned Krylov space iterative linear system solver. In some sense, these numbers can be regarded as best case timings for these kernels. We timed sweeps over meshes, sparse triangular solves, and inner products on a large three-dimensional model problem over a cube-shaped domain discretized with a seven-point template. The performance of the CM-2 is highly dependent on the use of very specialized programs. These programs mapped a regular problem domain onto the processor topology in a careful manner and used the optimized local NEWS communications network. We also document rather dramatic deterioration in performance when these ideal conditions no longer apply. A synthetic work load generator was developed to produce and solve a parameterized family of increasingly irregular problems.