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

This article describes a method to accelerate parallel, explicit time integration of two-dimensional unsteady PDEs. The method is motivated by our observation that latency, not bandwidth, 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 ping-pong latency of the network. The article presents simple theoretical analysis to the performance of the swept rule in two spatial dimensions, and supports the analysis with numerical experiments

Decomposition of stencil update formula into atomic stages

In parallel solution of partial differential equations, a complex stencil update formula that accesses multiple layers of neighboring grid points sometimes must be decomposed into atomic stages, ones that access only immediately neighboring grid points. This paper shows that this requirement can be formulated as constraints of an optimization problem, which is equivalent to the dual of a minimum-cost network flow problem. An optimized decomposition of a single stencil on one set of grid points can thereby be computed efficiently