IMEX Runge-Kutta Parareal for Non-Diffusive Equations

Tommaso Buvoli; Michael L. Minion

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arXiv · 2011.01604

IMEX Runge-Kutta Parareal for Non-Diffusive Equations

Tommaso Buvoli·Michael L. Minion

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Abstract

Parareal is a widely studied parallel-in-time method that can achieve meaningful speedup on certain problems. However, it is well known that the method typically performs poorly on non-diffusive equations. This paper analyzes linear stability and convergence for IMEX Runge-Kutta Parareal methods on non-diffusive equations. By combining standard linear stability analysis with a simple convergence analysis, we find that certain Parareal configurations can achieve parallel speedup on non-diffusive equations. These stable configurations all posses low iteration counts, large block sizes, and a large number of processors. Numerical examples using the nonlinear Schrodinger equation demonstrate the analytical conclusions.

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Tommaso Buvoli, Michael L. Minion. 2020-11-03. IMEX Runge-Kutta Parareal for Non-Diffusive Equations. https://arxiv.org/abs/2011.01604

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