Inverse Scattering by a Penetrable Conductive Medium and an Impenetrable Obstacle with Generalized Oblique Derivative Boundary Condition

Abstract

We consider an inverse problem of scattering by a mixed-type scatterer consisting of an inhomogeneous penetrable conductive medium and an impenetrable obstacle with generalized oblique derivative boundary condition induced by incident plane waves scattering. Relying on the well-posedness of the direct problem which can be proved directly by a variational method, we are interested in studying the inverse problem of developing a modified factorization method to simultaneously reconstruct the shape and location of the mixed-type scatterer. The complex refractive index and the generalized oblique derivative boundary condition may bring new challenges since the factorization method is closely related to the refractive index and the mixed boundary conditions. Finally, some numerical examples are given to show the effectiveness and feasibility of the inversion algorithm.