# IMEX Runge-Kutta Parareal for Non-diffusive Equations

@inproceedings{Buvoli2021IMEXRP,
title={IMEX Runge-Kutta Parareal for Non-diffusive Equations},
author={Tommaso Buvoli and Michael L. Minion},
year={2021}
}
• Published 3 November 2020
• Mathematics, Computer Science
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…

## References

SHOWING 1-10 OF 39 REFERENCES
Analysis of the Parareal Algorithm Applied to Hyperbolic Problems Using Characteristics
This paper proves in this paper a convergence result for the advection equation using the technique of characteristics and reveals limitations of the method when applied to the second order wave equation.
Parareal Algorithms Implemented with IMEX Runge-Kutta Methods
• Computer Science
• 2015
A stability criterion of the parareal algorithm coupled with IMEX RK methods is established and the advantage (in the sense of stability) of implementing with this kind of Rk methods is numerically investigated.
Tight two-level convergence of Linear Parareal and MGRIT: Extensions and implications in practice
• Mathematics
ArXiv
• 2020
A new and simplified analysis of linear error and residual propagation of Parareal, wherein the norm of error or residual propagation is given by one over the minimum singular value of a certain block bidiagonal operator.
Implicit-explicit methods for time-dependent partial differential equations
• Computer Science
• 1995
This work systematically analyze the performance of implicit-explicit IMEX schemes, propose improved new schemes, and pay particular attention to their relative performance in the context of fast multigrid algorithms and of aliasing reduction for spectral methods.
On a Class of Uniformly Accurate IMEX Runge--Kutta Schemes and Applications to Hyperbolic Systems with Relaxation
• Computer Science
SIAM J. Sci. Comput.
• 2009
New IMEX R-K schemes for hyperbolic systems with relaxation that present better uniform accuracy than the ones existing in the literature are developed and produce good behavior with high order accuracy in the asymptotic limit, i.e., when $\varepsilon$ is very small.
A HYBRID PARAREAL SPECTRAL DEFERRED CORRECTIONS METHOD
This paper investigates a variant of the parareal algorithm first outlined by Minion and Williams in 2008 that utilizes a deferred correction strategy within theParareal iterations that utilizes the parallel speedup and efficiency of the hybrid methods.
Semi-implicit spectral deferred correction methods for ordinary differential equations
The results suggest that higher-order SISDC methods are more efficient than semi-implicit Runge-Kutta methods for moderately stiff problems in terms of accuracy per function evaluation.