IMEX Runge-Kutta Parareal for Non-Diffusive Equations
Numerical Analysis
2021-08-03 v2 Numerical Analysis
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.
Cite
@article{arxiv.2011.01604,
title = {IMEX Runge-Kutta Parareal for Non-Diffusive Equations},
author = {Tommaso Buvoli and Michael L. Minion},
journal= {arXiv preprint arXiv:2011.01604},
year = {2021}
}