论文标题
薄管结构散射的渐近表示公式，并在反散射中应用
An asymptotic representation formula for scattering by thin tubular structures and an application in inverse scattering
论文作者
论文摘要
我们考虑了三维自由空间中可穿透的薄管散射对象的时间谐波电磁波的散射。我们为散射波远离细管散射器的散射波建立了一个渐近表示公式，因为其横截面的半径趋于零。散射对象的形状，相对电渗透性和相对磁性功能通过薄管散射器的中心曲线以及两个电气和磁极化张量来输入此渐近表示公式。我们根据中心曲线和两个二维极化张量的散射对象的横截面对这两个三维极化张量进行了明确的表征。作为一种应用，我们证明了如何使用该公式来评估具有薄管状散射对象的反向散射问题的有效迭代重建算法中的残差和形状衍生物。我们提出数值结果来说明我们的理论发现。数学主题分类（MSC2010）：35C20，（65N21，78A46）
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 permeability and the relative magnetic permittivity 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 tensor for the cross-section of the scattering object. As an application we demonstrate how this formula may be used to evaluate the residual and the shape derivative in an efficient iterative reconstruction algorithm for an inverse scattering problem with thin tubular scattering objects. We present numerical results to illustrate our theoretical findings. Mathematics subject classifications (MSC2010): 35C20, (65N21, 78A46)
