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

TL;DR

The paper introduces the swept rule, a space-time domain decomposition technique that reduces communication frequency in solving time-dependent PDEs, thereby overcoming latency barriers and improving computational efficiency.

Contribution

It presents a novel decomposition method leveraging domains of influence and dependency, with theoretical analysis and numerical validation demonstrating its effectiveness.

Findings

Reduced communication frequency in PDE solving

Theoretical analysis matches numerical experiments

Improved scalability in time-dependent PDE computations

Abstract

This article investigates the swept rule of space-time domain decomposition, an idea to break the latency barrier via communicating less often when explicitly solving time-dependent PDEs. The swept rule decomposes 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 timesteps without redundant computation. The article presents simple theoretical analysis to the performance of the swept rule which then was shown to be accurate by conducting numerical experiments.