The Factorization Method for a Mixed Scattering Problem from a Bounded Obstacle and an Open Arc (Journal of Computational Mathematics, 2019)
In this paper, we consider the scattering problem of time-harmonic electromagneticwaves from an infinite cylinder having an open arc $Γ$ and a bounded domain $D$ in $\mathbb{R}$2 as crosssection. We focus on the inverse scattering problem, that is, to reconstruct the shape of $Γ$ and $D$ from the far-field pattern by using the factorization method. Through establishing amixed reciprocity relation, we prove that the scatters $Γ$ and $D$ can be uniquely determinedby the far-field pattern. Furthermore, the mathematical basis is given to explain that thefactorization method is feasible to our problem. At the end of this paper, we give somenumerical examples to show the efficaciousness of the algorithms.
Keywords: Factorization method; Inverse scattering problem; Mixed scattering; Time-harmonic electromagnetic wave.