#sparareal
Error analysis for SParareal in SISC
The final version of “Error bound analysis of the stochastic parareal algorithm” by Kamran Pentland, Massimiliano Tamborrino, and myself has just appeared online in the SIAM Journal on Scientific Computing (SISC).
K. Pentland, M. Tamborrino, and T. J. Sullivan. “Error bound analysis of the stochastic parareal algorithm.” SIAM Journal on Scientific Computing 45(5):A2657–A2678, 2023.
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.
Published on Monday 9 October 2023 at 09:00 UTC #publication #prob-num #sparareal #pentland #tamborrino #sisc
Error analysis for SParareal
Kamran Pentland, Massimiliano Tamborrino, and I have just uploaded a preprint of our latest article, “Error bound analysis of the stochastic parareal algorithm”, to the arXiv.
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.
Published on Thursday 10 November 2022 at 10:00 UTC #preprint #prob-num #sparareal #pentland #tamborrino