Direct and inverse acoustic scattering by a mixed-type scatterer (original) (raw)

The scattering of time-harmonic acoustic plane waves by a mixed-type scatterer is considered. Such a scatterer is given as the union of a bounded impenetrable obstacle and a penetrable inhomogeneous medium with compact support. Having established the well-posedness of the direct problem by a variational method, we study the factorization method for recovering the location and shape of the mixed-type scatterer. Some numerical experiments are presented to demonstrate its feasibility and effectiveness. One by-product of the factorization method is that it provides an explicit proof of uniqueness of the inverse scattering problem under certain assumptions.