Qualitative Methods for Inverse Scattering by an Impedant Crack

Overview & Synopsis

The inverse scattering problem for crack identification is increasingly gaining applications in many domains. Examples of applications include non destructive testing, geophysical prospection... The research work in this thesis focuses on the crack identification using qualitative methods, particularly the sampling methods. We use the Linear Sampling Method and the Factorization method to retrieve the geometry of cracks from multi-static far field data in the case of impedance boundary conditions on both sides of the crack embedded in a homogeneous domain. Moreover, an application of the Reciprocity Gap Linear Sampling Method is proposed to retrieve the geometry of cracks embedded in an inhomogeneous domain with the same boundary conditions. A completion method for the Helmholtz-Cauchy problem is also proposed to widen the applicability of the latter method. The efficiency of the proposed methods is shown through numerical experiments for different crack shapes and for several impedance values.