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This article describes a method to accelerate parallel, explicit timeintegration of two-dimensional unsteady PDEs. The method is motivated by ourobservation that latency, not bandwidth, often limits how fast PDEs can besolved in parallel. The method is called the swept rule of space-time domaindecomposition. Compared to conventional, space-only domain decomposition, itcommunicates similar amount of data, but in fewer messages. The swept ruleachieves this by decomposing space and time among computing nodes in ways thatexploit the domains of influence and the domain of dependency, making itpossible to communicate once per many time steps with no redundant computation.By communicating less often, the swept rule effectively breaks the latencybarrier, advancing on average more than one time step per ping-pong latency ofthe network. The article presents simple theoretical analysis to theperformance of the swept rule in two spatial dimensions, and supports theanalysis with numerical experiments.

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