Coupling discontinuous Galerkin methods and retarded potentials for transient wave propagation on unbounded domains

Toufic Abboud 1 Patrick Joly 2 Jeronimo Rodríguez 2, 3 Isabelle Terrasse 4
1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
3 Departamento de Matemática Aplicada
4 CCR - Corporate Research Center France
Abstract : This work deals with the numerical simulation of wave propagation on unbounded domains with localized heterogeneities. To do so, we propose to combine a discretization based on a discontinuous Galerkin method in space and explicit finite differences in time on the regions containing heterogeneities with the retarded potential method to account the unbounded nature of the computational domain. The coupling formula enforces a discrete energy identity ensuring the stability under the usual CFL condition in the interior. Moreover, the scheme allows to use a smaller time step in the interior domain yielding to quasi-optimal discretization parameters for both methods. The aliasing phenomena introduced by the local time stepping are reduced by a post-processing by averaging in time obtaining a stable and second order consistent (in time) coupling algorithm. We compute the numerical rate of convergence of the method for an academic problem. The numerical results show the feasibility of the whole discretization procedure. © 2011 Elsevier Inc.
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Journal articles
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Submitted on : Friday, August 30, 2013 - 3:06:12 PM
Last modification on : Tuesday, July 9, 2019 - 2:52:30 PM

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Toufic Abboud, Patrick Joly, Jeronimo Rodríguez, Isabelle Terrasse. Coupling discontinuous Galerkin methods and retarded potentials for transient wave propagation on unbounded domains. Journal of Computational Physics, Elsevier, 2011, 230 (15), pp.5877-5907. ⟨10.1016/j.jcp.2011.03.062⟩. ⟨hal-00849573⟩

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