Performance Evaluation of Mixed-Precision Runge-Kutta Methods

TL;DR

This paper evaluates mixed-precision additive Runge-Kutta methods for solving nonlinear ODEs, demonstrating they achieve high accuracy with reduced runtime and energy use on modern hardware.

Contribution

It develops a FORTRAN implementation and provides a comprehensive analysis of convergence, accuracy, runtime, and energy efficiency of MP-ARK methods on different architectures.

Findings

MP-ARK methods deliver accurate solutions efficiently.

Significant reductions in runtime and energy consumption observed.

Methods are effective on IBM POWER9 and Intel x86_64 chips.

Abstract

Additive Runge-Kutta methods designed for preserving highly accurate solutions in mixed-precision computation were proposed and analyzed in [8]. These specially designed methods use reduced precision or the implicit computations and full precision for the explicit computations. We develop a FORTRAN code to solve a nonlinear system of ordinary differential equations using the mixed precision additive Runge-Kutta (MP-ARK) methods on IBM POWER9 and Intel x86\_64 chips. The convergence, accuracy, runtime, and energy consumption of these methods is explored. We show that these MP-ARK methods efficiently produce accurate solutions with significant reductions in runtime (and by extension energy consumption).