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arXiv · 2401.01798

Micro-macro Parareal, from ODEs to SDEs and back again

Ignace Bossuyt·Stefan Vandewalle·Giovanni Samaey
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Abstract

In this paper, we are concerned with the micro-macro Parareal algorithm for the simulation of initial-value problems. In this algorithm, a coarse (fast) solver is applied sequentially over the time domain, and a fine (time-consuming) solver is applied as a corrector in parallel over smaller chunks of the time interval. Moreover, the coarse solver acts on a reduced state variable, which is coupled to the fine state variable through appropriate coupling operators. We first provide a contribution to the convergence analysis of the micro-macro Parareal method for multiscale linear ordinary differential equations (ODEs). Then, we extend a variant of the micro-macro Parareal algorithm for scalar stochastic differential equations (SDEs) to higher-dimensional SDEs.

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Ignace Bossuyt, Stefan Vandewalle, Giovanni Samaey. 2024-01-03. Micro-macro Parareal, from ODEs to SDEs and back again. https://doi.org/10.1017/s1446181124000270

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