A hybrid parareal Monte-Carlo algorithm for parabolic problems * - Université de Paris - Faculté des Sciences Access content directly
Preprints, Working Papers, ... Year : 2021

A hybrid parareal Monte-Carlo algorithm for parabolic problems *

Abstract

In this work, we examine a hybrid Monte-Carlo/deterministic approach for a toy model based on the parabolic time-dependent diffusion equation. We consider two different solvers: a low-cost "coarse" solver based on a deterministic Galerkin scheme and a "fine" solver based on a Monte-Carlo resolution. We use a hybrid "parareal-in-time" algorithm based on these two solvers to reduce the computational cost with respect to a full Monte-Carlo simulation. In a set of benchmark numerical experiments, we compare our hybrid parareal strategy with a standard full Monte-Carlo solution of the time-dependent diffusion equation. 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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Dates and versions

hal-03143554 , version 1 (16-02-2021)
hal-03143554 , version 2 (11-03-2021)
hal-03143554 , version 3 (23-06-2022)
hal-03143554 , version 4 (24-09-2022)
hal-03143554 , version 5 (11-10-2022)

Identifiers

  • HAL Id : hal-03143554 , version 1

Cite

Jad Dabaghi, Yvon Maday, Andrea Zoia. A hybrid parareal Monte-Carlo algorithm for parabolic problems *. 2021. ⟨hal-03143554v1⟩
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