Performance evaluation of mixed-precision Runge-Kutta methods for the solution of partial differential equations

TL;DR

This paper evaluates the performance of mixed-precision Runge-Kutta methods for solving partial differential equations, demonstrating potential speedups on modern hardware with careful consideration of solver parameters and software efficiency.

Contribution

It provides a numerical analysis of mixed-precision Runge-Kutta methods applied to PDEs, highlighting their computational advantages and hardware compatibility.

Findings

Significant speedups are achievable with mixed-precision methods.

Performance depends on solver parameters and software kernel efficiency.

Compatibility varies across GPU and CPU architectures.

Abstract

This work focuses on the numerical study of a recently published class of Runge-Kutta methods designed for mixed-precision arithmetic. We employ the methods in solving partial differential equations on modern hardware. In particular we investigate what speedups are achievable by the use of mixed precision and the dependence of the methods algorithmic compatibility with the computational hardware. We use state-of-the-art software, utilizing the Ginkgo library, which is designed to incorporate mixed precision arithmetic, and perform numerical tests of 3D problems on both GPU and CPU architectures. We show that significant speedups can be achieved but that performance depends on solver parameters and performance of software kernels.