%0 Unpublished work
%T A hybrid parareal Monte Carlo algorithm for parabolic problems
%+ Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS)
%+ MATHematics for MatERIALS (MATHERIALS)
%+ 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
%Z This project has received funding from the ANR project “Ciné-Para” (ANR-15-CE23-0019). This work has received funding from the European Research Council (ERC) under theEuropean Union’s Horizon 2020 research and innovation program (grant agreement No 810367- project EMC2) (YM) and from the European High Performance Computing Joint Undertaking (EuroHPC JU) under the European Union’s Horizon 2020 research and innovationprogram (grant agreement No 955701 - project TIME-X) (YM
%8 2022-06-23
%D 2022
%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 hybrid Monte Carlo/deterministic “parareal-in-time” approach devoted to accelerating Monte Carlo simulations over massivelyparallel 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” solverbased on a high-fidelity Monte Carlo resolution.In a set of benchmark numerical experiments based on a toy model con-cerning the time-dependent diffusion equation, we compare our hybrid pararealstrategy with a standard full Monte Carlo solution. In particular, we show thatfor a large number of processors, our hybrid strategy significantly reduces thecomputational time of the simulation while preserving its accuracy. The conver-gence properties of the proposed Monte Carlo/deterministic parareal strategyare also discussed.
%G English
%2 https://hal.science/hal-03143554v3/document
%2 https://hal.science/hal-03143554v3/file/manuscript_revised_second.pdf
%L hal-03143554
%U https://hal.science/hal-03143554
%~ ENPC
%~ INRIA
%~ INRIA-ROCQ
%~ PARISTECH
%~ PREPRINT
%~ TESTALAIN1