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Journal Articles Journal of Computational and Applied Mathematics Year : 2023

## A hybrid parareal Monte Carlo algorithm for parabolic problems

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#### Abstract

In this work, we propose a hybrid Monte Carlo/deterministic parareal-in-time'' approach devoted to accelerating Monte Carlo simulations over massively parallel 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” solver based on a high-fidelity 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.

#### Domains

Mathematics [math] Numerical Analysis [math.NA]

### 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 5
• DOI :

### Cite

Jad Dabaghi, Yvon Maday, Andrea Zoia. A hybrid parareal Monte Carlo algorithm for parabolic problems. Journal of Computational and Applied Mathematics, 2023, 420, ⟨10.1016/j.cam.2022.114800⟩. ⟨hal-03143554v5⟩

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