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On the use of the Linear Sampling Method to identify cracks in elastic waveguides

Laurent Bourgeois 1 Éric Lunéville 1
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 : We consider the identification of cracks in an elastic 2D or 3D waveguide with the help of a modal version of the linear sampling method. The main objective of our paper is to show that since the usual crack in elasticity is traction free, that is, the boundary condition on the lips of the crack is a priori known to be of Neumann type, we shall adapt the formulation of the sampling method to such a boundary condition in order to improve the efficiency of the method. The need for such adaptation is proved theoretically and illustrated numerically with the help of 2D examples.
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Submitted on : Tuesday, January 28, 2014 - 5:06:33 PM
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Laurent Bourgeois, Éric Lunéville. On the use of the Linear Sampling Method to identify cracks in elastic waveguides. Inverse Problems, IOP Publishing, 2013, 29, pp.025017. ⟨10.1088/0266-5611/29/2/025017⟩. ⟨hal-00937686⟩



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