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Remarks on the stability of Cartesian PMLs in corners

Eliane Bécache 1 Andrés Prieto 2
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
CNRS - Centre National de la Recherche Scientifique : UMR7231, UMA - Unité de Mathématiques Appliquées, Inria Saclay - Ile de France
Abstract : This work is a contribution to the understanding of the question of stability of Perfectly Matched Layers (PMLs) in corners, at continuous and discrete levels. First, stability results are presented for the Cartesian PMLs associated to a general first-order hyperbolic system. Then, in the context of the pressure–velocity formulation of the acoustic wave propagation, an unsplit PML formulation is discretized with spectral mixed finite elements in space and finite differences in time. It is shown, through the stability analysis of two different schemes, how a bad choice of the time discretization can deteriorate the CFL stability condition. Some numerical results are finally presented to illustrate these stability results.
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Submitted on : Friday, April 4, 2014 - 1:53:11 PM
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Eliane Bécache, Andrés Prieto. Remarks on the stability of Cartesian PMLs in corners. Applied Numerical Mathematics, Elsevier, 2012, 62 (11), pp.1639-1653. ⟨10.1016/j.apnum.2012.05.003⟩. ⟨hal-00973536⟩



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