An accurate and time-parallel rational exponential integrator for hyperbolic and oscillatory PDEs

Rational exponential integrators (REXI) are a class of numerical methods that are well suited for the time integration of linear partial differential equations with imaginary eigenvalues. Since these methods can be parallelized in time (in addition to the spatial parallelization that is commonly performed) they are well suited to exploit modern high performance computing systems. In this paper, we propose a novel REXI scheme that drastically improves accuracy and efficiency. The chosen approach will also allow us to easily determine how many terms are required in the approximation in order to obtain accurate results. We provide comparative numerical simulations for a shallow water equation that highlight the efficiency of our approach and demonstrate that REXI schemes can be efficiently implemented on graphic processing units. (C) 2021 The Author(s). Published by Elsevier Inc.

Automated summary

Rational Exponential Integrators (REXI) are numerical methods suitable for time integration of linear partial differential equations with imaginary eigenvalues. A novel REXI scheme proposed in this paper drastically improves accuracy and efficiency, along with the ability to easily determine the required number of terms for accurate results. Comparative numerical simulations for a shallow water equation show the efficiency of the approach, indicating that REXI schemes can be efficiently implemented on graphic processing units.