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On the use of sampling methods to identify cracks in acoustic waveguides

Laurent Bourgeois 1 Éric Lunéville 1
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 : We consider the identification of cracks in an acoustic 2D/3D waveguide with the help of sampling methods such as the linear sampling method or the factorization method. A modal version of these sampling methods is used. Our paper emphasizes the fact that if one a priori knows the type of boundary condition which actually applies on the crack, then we shall adapt the formulation of our sampling method to such boundary conditions 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. We also show by using our modal formulation that the factorization method is applicable in a waveguide with the same data as the linear sampling method. © 2012 IOP Publishing Ltd.
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Laurent Bourgeois, Éric Lunéville. On the use of sampling methods to identify cracks in acoustic waveguides. Inverse Problems, IOP Publishing, 2012, 28 (10), pp.105011.1-105011.18. ⟨10.1088/0266-5611/28/10/105011⟩. ⟨hal-00849558⟩



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