The swept rule for breaking the latency barrier in time-advancing PDEs

Abstract

This thesis describes a method to accelerate parallel, explicit time integration of unsteady PDEs. The method is motivated by our observation that network latency, not bandwidth or computing power, often limits how fast PDEs can be solved in parallel. The method is called the swept rule of space-time domain decomposition. Compared to conventional, space-only domain decomposition, it communicates similar amount of data, but in fewer messages. The swept rule achieves this by decomposing space and time among computing nodes in ways that exploit the domains of influence and the domain of dependency, making it possible to communicate once per many time steps with no redundant computation. By communicating less often, the swept rule effectively breaks the latency barrier, advancing on average more than one time step per round-trip latency of the network. The thesis describes the algorithms, presents simple theoretical analysis to the performance of the swept rule, and supports the analysis with numerical experiments.