Multiscale Modeling &Simulation, Volume 19, Issue 2, Page 846-885, January 2021.
We consider the scattering of time-harmonic electromagnetic waves by a penetrable thin tubular scattering object in three-dimensional free space. We establish an asymptotic representation formula for the scattered wave away from the thin tubular scatterer as the radius of its cross-section tends to zero. The shape, the relative electric permittivity, and the relative magnetic permeability of the scattering object enter this asymptotic representation formula by means of the center curve of the thin tubular scatterer and two electric and magnetic polarization tensors. We give an explicit characterization of these two three-dimensional polarization tensors in terms of the center curve and of the two two-dimensional polarization tensors for the cross-section of the scattering object. As an application we demonstrate how this formula may be used to approximate the residual and the shape derivative in an iterative reconstruction algorithm for an inverse scattering problem with thin tubular scattering objects. We present numerical results to illustrate our theoretical findings.

中文翻译：

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细管结构散射的渐近表示公式及其在逆散射中的应用

多尺度建模与仿真，第 19 卷，第 2 期，第 846-885 页，2021 年 1 月。
我们考虑了三维自由空间中可穿透的细管状散射物体对时谐电磁波的散射。我们建立了远离细管状散射体的散射波在其横截面半径趋于零时的渐近表示公式。散射物体的形状、相对介电常数和相对磁导率通过细管状散射体的中心曲线和两个电、磁极化张量进入这个渐近表示公式。我们根据中心曲线和散射物体横截面的两个二维偏振张量给出了这两个三维偏振张量的明确表征。作为一个应用程序，我们演示了如何使用此公式来近似迭代重建算法中的残差和形状导数，以解决具有薄管状散射对象的逆散射问题。我们提供数值结果来说明我们的理论发现。