混合散射体的分解方法

Factorization Method of Mixed Scatterers

考虑混合散射体在时谐声波散射下的反散射问题,该散射体是由具有导电传输边界的可穿透非齐次介质和具有阻抗边界的不可穿透障碍物组成。首先利用变分方法证明正问题解的适定性,然后基于远场数据利用分解方法同时反演混合散射体的位置和形状,最后给出数值算例来验证提出的反演算法的有效性。

We consider the problem of inverse scattering of time-harmonic acoustic waves by a mixed scatterer.The inverse problem is composed of a penetrable inhomogeneous medium with a conducting transmission boundary and an impenetrable obstacle with an impedance boundary.We first prove the well-posedness of the direct scattering problem by using a variational approach.Subsequently,the factorization method is applied to simultaneously locate and recover the mixed scatterer from the far-field data.Several numerical examples are given to demonstrate the effectiveness of the inverse algorithm.