%0 Unpublished work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