\theta-parareal schemes
Gil Ariel, Hieu Nguyen, Richard Tsai

TL;DR
This paper introduces a weighted parareal scheme for parallel-in-time computation, analyzing its stability and optimizing weights for multiscale coupling, demonstrated through numerical examples including nonlinear Hamiltonian systems.
Contribution
It proposes a weighted parareal method with stability analysis and weight optimization, enhancing multiscale coupling capabilities in parallel-in-time algorithms.
Findings
Favorable stability properties with marginal accuracy loss
Effective weight optimization using past iteration data
Successful application to nonlinear Hamiltonian systems
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematics and Applications
