A hybrid parareal Monte Carlo algorithm for parabolic problems

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