On selecting coarse-grid operators for Parareal and MGRIT applied to linear advection
Abstract
We consider the parallel time integration of the linear advection equation with the Parareal and two-level multigrid-reduction-in-time (MGRIT) algorithms. Our aim is to develop a better understanding of the convergence behaviour of these algorithms for this problem, which is known to be poor relative to the diffusion equation, its model parabolic counterpart. Using Fourier analysis, we derive new convergence estimates for these algorithms which, in conjunction with existing convergence theory, provide insight into the origins of this poor performance. We then use this theory to explore improved coarse-grid time-stepping operators. For several high-order discretizations of the advection equation, we demonstrate that there exist non-standard coarse-grid time stepping operators that yield significant improvements over the standard choice of rediscretization.
Cite
@article{arxiv.1902.07757,
title = {On selecting coarse-grid operators for Parareal and MGRIT applied to linear advection},
author = {Oliver A. Krzysik and Hans De Sterck and Scott P. MacLachlan and Stephanie Friedhoff},
journal= {arXiv preprint arXiv:1902.07757},
year = {2019}
}
Comments
This work was submitted to the Student Paper Competition of the 19th Copper Mountain Conference On Multigrid Methods, Copper Mountain, CO, USA. Much of this manuscript has formed the foundations of a full-length manuscript for which a preprint is available at arXiv:1910.03726