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

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.

Domaines: Equations aux dérivées partielles [math.AP]; Modélisation et simulation; Analyse numérique [math.NA]; Physique mathématique [math-ph]; Optimisation et contrôle [math.OC]; Théorie spectrale [math.SP]

Laurent Bourgeois, Éric Lunéville. On the use of the Linear Sampling Method to identify cracks in elastic waveguides. Inverse Problems, 2013, 29, pp.025017. ⟨10.1088/0266-5611/29/2/025017⟩. ⟨hal-00937686⟩