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arXiv · 2211.05496

Error bound analysis of the stochastic parareal algorithm

Kamran Pentland·Massimiliano Tamborrino·T. J. Sullivan
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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 ordinary differential equation (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.

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Kamran Pentland, Massimiliano Tamborrino, T. J. Sullivan. 2023-03-10. Error bound analysis of the stochastic parareal algorithm. https://arxiv.org/abs/2211.05496

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