The Two-Dimensional Swept Rule Applied on Heterogeneous Architectures

TL;DR

This paper explores the application of the two-dimensional swept rule on heterogeneous computing architectures to improve the efficiency of solving PDEs, demonstrating variable speedup results.

Contribution

It implements and tests the swept rule for 2D PDEs on heterogeneous systems, providing insights into its performance and potential benefits.

Findings

Speedup of 0.22-2.71 for heat diffusion

Speedup of 0.52-1.46 for Euler equations

Performance varies depending on system and problem

Abstract

The partial differential equations describing compressible fluid flows can be notoriously difficult to resolve on a pragmatic scale and often require the use of high performance computing systems and/or accelerators. However, these systems face scaling issues such as latency, the fixed cost of communicating information between devices in the system. The swept rule is a technique designed to minimize these costs by obtaining a solution to unsteady equations at as many possible spatial locations and times prior to communicating. In this study, we implemented and tested the swept rule for solving two-dimensional problems on heterogeneous computing systems across two distinct systems. Our solver showed a speedup range of 0.22-2.71 for the heat diffusion equation and 0.52-1.46 for the compressible Euler equations. We can conclude from this study that the swept rule offers both potential for speedups and slowdowns and that care should be taken when designing such a solver to maximize benefits. These results can help make decisions to maximize these benefits and inform designs.