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Error bound analysis of the stochastic parareal algorithm
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Pentland, Kamran, Tamborrino, Massimiliano and Sullivan, T. J. (2023) Error bound analysis of the stochastic parareal algorithm. SIAM Journal on Scientific Computing, 45 (5). A2657-A2678. doi:10.1137/22M1533062 ISSN 1064-8275.
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Official URL: https://doi.org/10.1137/22M1533062
Abstract
Stochastic Parareal (SParareal) is a probabilistic variant of the popular parallel-in-time algorithm known as Parareal. Similarly to Parareal, it combines fine- and coarse-grained solutions to an ODE using a predictor-corrector (PC) scheme. The key difference is that carefully chosen random perturbations are added to the PC to try to accelerate the location of a stochastic solution to the ODE. In this paper, we derive superlinear and linear mean-square error bounds for SParareal applied to nonlinear systems of ODEs using different types of perturbations. We illustrate these bounds numerically on a linear system of ODEs and a scalar nonlinear ODE, showing a good match between theory and numerics.
Item Type: | Journal Article | |||||||||
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Subjects: | Q Science > QA Mathematics | |||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Engineering > Engineering Faculty of Science, Engineering and Medicine > Science > Mathematics Faculty of Science, Engineering and Medicine > Science > Statistics |
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Library of Congress Subject Headings (LCSH): | Numerical analysis, Differential equations, Stochastic differential equations , Parallel algorithms | |||||||||
Journal or Publication Title: | SIAM Journal on Scientific Computing | |||||||||
Publisher: | Society for Industrial and Applied Mathematics | |||||||||
ISSN: | 1064-8275 | |||||||||
Official Date: | 6 October 2023 | |||||||||
Dates: |
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Volume: | 45 | |||||||||
Number: | 5 | |||||||||
Page Range: | A2657-A2678 | |||||||||
DOI: | 10.1137/22M1533062 | |||||||||
Status: | Peer Reviewed | |||||||||
Publication Status: | Published | |||||||||
Access rights to Published version: | Restricted or Subscription Access | |||||||||
Copyright Holders: | © 2023 Society for Industrial and Applied Mathematics. | |||||||||
Date of first compliant deposit: | 22 June 2023 | |||||||||
Date of first compliant Open Access: | 9 October 2023 | |||||||||
RIOXX Funder/Project Grant: |
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Open Access Version: |
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