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Coupling Parareal with Optimized Schwarz waveform relaxation for parabolic problems

Abstract : We propose and analyse a parallel method, both in the time and space directions, that couples the Parareal algorithm with the Optimized Schwarz waveform relaxation (OSWR) method, with only few OSWR iterations in the fine propagator and with a simple coarse propagator deduced from the Backward Euler method. The analysis of this coupled method is presented for a one-dimensional advection-reaction-diffusion equation. We prove a general convergence result for this method via energy estimates. Numerical results for two-dimensional advection-diffusion problems and for a diffusion equation with strong heterogeneities are presented, to illustrate the performance of the coupled Parareal-OSWR algorithm.
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https://hal.inria.fr/hal-03167571
Contributor : Caroline Japhet Connect in order to contact the contributor
Submitted on : Friday, August 5, 2022 - 4:29:46 PM
Last modification on : Tuesday, August 9, 2022 - 11:59:21 AM

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  • HAL Id : hal-03167571, version 2

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Duc Quang Bui, Caroline Japhet, Yvon Maday, Pascal Omnes. Coupling Parareal with Optimized Schwarz waveform relaxation for parabolic problems. SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2022. ⟨hal-03167571v2⟩

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