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

Anne-Sophie Bonnet-Ben Dhia (1) , Colin Chambeyron (1) , Guillaume Legendre (2)

1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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 propagative 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.

Domaines: Mécanique des solides [physics.class-ph]; Mécanique des solides [physics.class-ph]; Analyse numérique [math.NA]

Anne-Sophie Bonnet-Ben Dhia, Colin Chambeyron, Guillaume Legendre. On the use of perfectly matched layers in the presence of long or backward guided elastic waves. 2013. ⟨hal-00816895v1⟩