Error bound analysis of the stochastic parareal algorithm
Numerical Analysis
2023-03-13 v2 Numerical Analysis
Computation
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.
Cite
@article{arxiv.2211.05496,
title = {Error bound analysis of the stochastic parareal algorithm},
author = {Kamran Pentland and Massimiliano Tamborrino and T. J. Sullivan},
journal= {arXiv preprint arXiv:2211.05496},
year = {2023}
}