9422380 Lumsdaine Distributed-memory computers have been available for about a decade. Still, hard questions remain concerning the scalability of implicit numerical methods, and new, alternative numerical methods, in order to gauge the value of further, large-scale investment in parallelization of key applications. Furthermore, algorithms, even if developed to be suitably scalable for certain applications, must be represented in software cost-effectively in order to make the massively parallel systems economical overall. Therefore, we seek to answer fundamental questions about algorithms and software technology related to implicit numerical integration methods, and more generally, about trade-offs between concurrency and convergence of iterative methods.
