HAL CCSD
A hybrid parareal Monte Carlo algorithm for parabolic problems *
Dabaghi, Jad
Maday, Yvon
Zoia, Andrea
Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)) ; Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)
Commissariat à l'énergie atomique et aux énergies alternatives (CEA)
Université Paris-Saclay
hal-03143554
https://hal.science/hal-03143554
https://hal.science/hal-03143554v2/document
https://hal.science/hal-03143554v2/file/manuscript.pdf
https://hal.science/hal-03143554
2021
en
parareal-in-time algorithm
time-dependent problems
predictor-corrector
Galerkin schemes
Monte Carlo method
[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
info:eu-repo/semantics/preprint
Preprints, Working Papers, ...
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.
2021-03-11
info:eu-repo/semantics/OpenAccess