%0 Unpublished work %T A hybrid parareal Monte Carlo algorithm for parabolic problems * %+ Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)) %+ Commissariat à l'énergie atomique et aux énergies alternatives (CEA) %+ Université Paris-Saclay %A Dabaghi, Jad %A Maday, Yvon %A Zoia, Andrea %8 2021-03-11 %D 2021 %K parareal-in-time algorithm %K time-dependent problems %K predictor-corrector %K Galerkin schemes %K Monte Carlo method %Z Mathematics [math]/Numerical Analysis [math.NA]Preprints, Working Papers, ... %X In this work, we propose a novel hybrid Monte Carlo/deterministic “parareal-in-time” approachdedicated to further speed up to solution time of unsteady Monte Carlo simulations over massivelyparallel computing environments.This parareal approach iterates on two different solvers: a low-cost “coarse” solver based on a verycheap deterministic Galerkin scheme and a “fine” solver based on a precise Monte Carlo resolution.In a set of benchmark numerical experiments based on a toy model concerning the time-dependentdiffusion 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 reducesthe computational time of the simulation while preserving its accuracy. The convergence properties ofthe proposed Monte Carlo/deterministic parareal strategy are also discussed. %G English %2 https://hal.science/hal-03143554v2/document %2 https://hal.science/hal-03143554v2/file/manuscript.pdf %L hal-03143554 %U https://hal.science/hal-03143554 %~ TEST-HALCNRS