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Modified parareal method for solving the two-dimensional nonlinear shallow water equations using finite volumes

Abstract : In this work, the POD-DEIM-based parareal method introduced in [6] is implemented for the resolution of the two-dimensional nonlinear shallow water equations using a finite volume scheme. This method is a variant of the traditional parareal method, first introduced by [19], that improves the stability and convergence for nonlinear hyperbolic problems, and uses reduced-order models constructed via the Proper Orthogonal Decomposition-Discrete Empirical Interpolation Method (POD-DEIM) applied to snapshots of the solution of the parareal iterations. We propose a modification of this parareal method for further stability and convergence improvements. It consists in enriching the snapshots set for the POD-DEIM procedure with extra snapshots whose computation does not require any additional computational cost. The performances of the classical parareal method, the POD-DEIM-based parareal method and our proposed modification are compared using numerical tests with increasing complexity. Our modified method shows a more stable behaviour and converges in fewer iterations than the other two methods.
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https://hal.inria.fr/hal-02894841
Contributor : Joao Guilherme Caldas Steinstraesser <>
Submitted on : Thursday, July 9, 2020 - 11:50:10 AM
Last modification on : Tuesday, May 11, 2021 - 1:53:48 PM
Long-term archiving on: : Monday, November 30, 2020 - 5:41:29 PM

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  • HAL Id : hal-02894841, version 1

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Joao Guilherme Caldas Steinstraesser, Vincent Guinot, Antoine Rousseau. Modified parareal method for solving the two-dimensional nonlinear shallow water equations using finite volumes. In press. ⟨hal-02894841⟩

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