The linear sampling method for a mixed scattering problem

Abstract

This paper is concerned with the scattering problem of time-harmonic acoustic plane waves by a mixed scatterer, which is a combination of an open crack and an impenetrable obstacle. Firstly, the well-posedness of the solution to the direct scattering problem is established using the variational method. Then, a uniqueness result for the inverse scattering problem is proved, that is, both of the crack and the impenetrable obstacle can be uniquely determined simultaneously by the knowledge of the far-field pattern. Furthermore, a mathematical basis is given to reconstruct the shape of the crack and the impenetrable obstacle using the linear sampling method, and some numerical examples are given to establish the viability of our approach.