Perfectly matched layers for convex truncated domains with discontinuous Galerkin time domain simulations

Axel Modave; Jonathan Lambrechts; Christophe Geuzaine

doi:10.1016/j.camwa.2016.12.027

Perfectly matched layers for convex truncated domains with discontinuous Galerkin time domain simulations

Axel Modave ^{1, 2} Jonathan Lambrechts ³ Christophe Geuzaine ⁴

1 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

2 Virginia Tech [Blacksburg]

3 UCL - Université Catholique de Louvain

4 University of Liège (ULg)

Abstract : This paper deals with the design of perfectly matched layers (PMLs) for transient acoustic wave propagation in generally-shaped convex truncated domains. After reviewing key elements to derive PML equations for such domains, we present two time-dependent formulations for the pressure-velocity system. These formulations are obtained by using a complex coordinate stretching of the time-harmonic version of the equations in a specific curvilinear coordinate system. The final PML equations are written in a general tensor form, which can easily be projected in Cartesian coordinates to facilitate implementation with classical discretization methods. Discontinuous Galerkin finite element schemes are proposed for both formulations. They are tested and compared using a three-dimensional benchmark with an ellipsoidal truncated domain. Our approach can be generalized to domains with corners.

Keywords : Absorbing boundary condition PML Wave propagation Discontinuous Galerkin Unbounded domain Absorbing layer

Document type :

Journal articles

Domain :

Computer Science [cs] / Modeling and Simulation

Engineering Sciences [physics] / Mechanics [physics.med-ph]

Mathematics [math] / Analysis of PDEs [math.AP]

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https://hal.archives-ouvertes.fr/hal-01378501
Contributor : Axel Modave <>
Submitted on : Friday, January 20, 2017 - 12:40:53 PM
Last modification on : Thursday, February 7, 2019 - 5:49:36 PM
Document(s) archivé(s) le : Friday, April 21, 2017 - 2:24:00 PM

PreprintPMLconvex_FINAL.pdf

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