THE FACTORIZATION METHOD APPLIED TO CRACKS WITH IMPEDANCE BOUNDARY CONDITIONS

We use the Factorization method to retrieve the shape of cracks with impedance boundary conditions from far fields associated with incident plane waves at a fixed frequency. This work is an extension of the study initiated by Kirsch and Ritter [Inverse Problems, 16, pp. 89-105, 2000] where the case of sound soft cracks is considered. We address here the scalar problem and provide theoretical validation of the method when the impedance boundary conditions hold on both sides of the crack. We then deduce an inversion algorithm and present some validating numerical results in the case of simply and multiply connected cracks.