Performance of iterative methods for distributed memory machines

We consider iterative methods for the large linear systems arising from partial differential equation problems on nonrectangular domains. These are somewhat banded but otherwise of no special structure beyond being sparse. We study the implementations and performance of several iterative methods on hypercube machines and we examine in detail the effects of communication and synchronization delays. Models are presented for these computations and projections made about performance for massively parallel machines. We conclude that it is currently difficult to achieve the potential of parallel machines for such methods. Some approaches for improving efficiency are suggested.