On the use of perfectly matched layers in the presence of long or backward propagating guided elastic waves

Anne-Sophie Bonnet-Ben Dhia 1 Colin Chambeyron 1 Guillaume Legendre 2
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
Abstract : An efficient method to compute the scattering of a guided wave by a localized defect, in an elastic waveguide of infinite extent and bounded cross section, is considered. It relies on the use of perfectly matched layers (PML) to reduce the problem to a bounded portion of the guide, allowing for a classical finite element discretization. The difficulty here comes from the existence of backward propagating modes, which are not correctly handled by the PML. We propose a simple strategy, based on finite-dimensional linear algebra arguments and using the knowledge of the modes, to recover a correct approximation to the solution with a low additional cost compared to the standard PML approach. Numerical experiments are presented in the two-dimensional case involving Rayleigh--Lamb modes.
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Anne-Sophie Bonnet-Ben Dhia, Colin Chambeyron, Guillaume Legendre. On the use of perfectly matched layers in the presence of long or backward propagating guided elastic waves. Wave Motion, Elsevier, 2014, 51 (2), pp.266-283. 〈10.1016/j.wavemoti.2013.08.001〉. 〈hal-00816895v2〉

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