Asynchronous parareal time discretization for partial differential equations
Abstract
Asynchronous iterations are more and more investigated for both scaling and fault-resilience purpose on high performance computing platforms. While so far, they have been exclusively applied within space domain decomposition frameworks, this paper advocates a novel application direction targeting time-decomposed time-parallel approaches. Specifically, an asynchronous iterative model is derived from the Parareal scheme, for which convergence and speedup analysis are then conducted. It turned out that Parareal and async-Parareal feature very close convergence conditions, asymptotically equivalent, including the finite-time termination property. Based on a computational cost model aware of unsteady communication delays, our speedup analysis shows the potential performance gain from asynchronous iterations, which is confirmed by some experimental case of heat evolution on a homogeneous supercomputer. This primary work clearly suggests possible further benefits from asynchronous iterations.
Cite
@article{arxiv.2110.10762,
title = {Asynchronous parareal time discretization for partial differential equations},
author = {Frederic Magoules and Guillaume Gbikpi-Benissan},
journal= {arXiv preprint arXiv:2110.10762},
year = {2021}
}