The linear sampling method for the transmission problem in 2D anisotropic elasticity

In the present work, the problem of reconstructing the shape of two-dimensional elastic anisotropic inclusions embedded in isotropic media is investigated within the framework of the linear sampling method. It is well known that the latter approach has been extensively used as an inverse solver in acoustic, electromagnetic and elastic scattering problems dealing with isotropic media and only recently in anisotropic acoustics and electromagnetics. The work at hand aims at contributing to the extension of the linear sampling method to anisotropic elastic inverse scattering. As in the previous works referring to the aforementioned reconstruction method, the proposed inversion scheme is based on the unboundedness of the solution of a linear integral equation of the first kind. Numerical results are also presented for several inclusion geometries and a system thereof exhibiting the applicability of the method.