A hybrid parareal Monte Carlo algorithm for parabolic problems

Abstract

In this work, we propose a hybrid Monte Carlo/deterministic “parareal-in-time” approach devoted to accelerating Monte Carlo simulations over massively parallel computing environments for the simulation of time-dependent problems.This parareal approach iterates on two different solvers: a low-cost “coarse” solver based on a very cheap deterministic Galerkin scheme and a “fine” solver based on a high-fidelity Monte Carlo resolution.In a set of benchmark numerical experiments based on a toy model concerning the time-dependent diffusion equation, we compare our hybrid parareal strategy with a standard full Monte Carlo solution. In particular, we show that for a large number of processors, our hybrid strategy significantly reduces the computational time of the simulation while preserving its accuracy. The convergence properties of the proposed Monte Carlo/deterministic parareal strategy are also discussed.