\theta-parareal schemes
Numerical Analysis
2018-02-09 v2
Abstract
A weighted version of the parareal method for parallel-in-time computation of time dependent problems is presented. Linear stability analysis for a scalar weighing strategy shows that the new scheme may enjoy favorable stability properties with marginal reduction in accuracy at worse. More complicated matrix-valued weights are applied in numerical examples. The weights are optimized using information from past iterations, providing a systematic framework for using the parareal iterations as an approach to multiscale coupling. The advantage of the method is demonstrated using numerical examples, including some well-studied nonlinear Hamiltonian systems.
Cite
@article{arxiv.1704.06882,
title = {\theta-parareal schemes},
author = {Gil Ariel and Hieu Nguyen and Richard Tsai},
journal= {arXiv preprint arXiv:1704.06882},
year = {2018}
}
Comments
32 pages, 14 figures