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

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.