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

TL;DR

This paper introduces the swept rule, a space-time domain decomposition method that reduces communication frequency in parallel PDE solving, effectively breaking the latency barrier and enabling faster time integration.

Contribution

The paper presents a novel swept rule for space-time decomposition that minimizes communication, exploits influence domains, and improves parallel PDE solution speed beyond traditional methods.

Findings

Achieves more than one time step per network ping-pong latency.

Reduces communication messages compared to conventional methods.

Supports theoretical analysis with numerical experiments.

Abstract

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.