hal-03143554
https://hal.science/hal-03143554
https://hal.science/hal-03143554v3/document
https://hal.science/hal-03143554v3/file/manuscript_revised_second.pdf
[ENPC] Ecole des Ponts ParisTech
[INRIA] INRIA - Institut National de Recherche en Informatique et en Automatique
[INRIA-ROCQ] INRIA Paris - Rocquencourt
[PARISTECH] ParisTech
[PREPRINT] Preprint HAL Ecole des Ponts ParisTech
[TESTALAIN1] TESTALAIN1
A hybrid parareal Monte Carlo algorithm for parabolic problems
Dabaghi, Jad
Maday, Yvon
Zoia, Andrea
[MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA]
UNDEFINED
Parareal-in-time algorithm
Time-dependent problems
Predictor-corrector
Galerkin schemes
Monte Carlo method
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.
2022-06-23
2022-06-23
en