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A hybrid parareal Monte Carlo algorithm for parabolic problems *

Abstract : In this work, we propose a novel hybrid Monte Carlo/deterministic “parareal-in-time” approach dedicated to further speed up to solution time of unsteady Monte Carlo simulations over massively parallel computing environments. This parareal approach iterates on two different solvers: a low-cost “coarse” solver based on a very cheap 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-dependent diffusion 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 reduces the computational time of the simulation while preserving its accuracy. The convergence properties of the proposed Monte Carlo/deterministic parareal strategy are also discussed.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03143554
Contributor : Jad Dabaghi Connect in order to contact the contributor
Submitted on : Thursday, March 11, 2021 - 2:06:23 PM
Last modification on : Thursday, April 7, 2022 - 1:58:31 PM

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  • HAL Id : hal-03143554, version 2

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Jad Dabaghi, Yvon Maday, Andrea Zoia. A hybrid parareal Monte Carlo algorithm for parabolic problems *. 2021. ⟨hal-03143554v2⟩

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