ABSTRACT

We provide a new analytical and computational study of the transmission eigenvalues with a conductive boundary condition. These eigenvalues are derived from the scalar inverse scattering problem for an inhomogeneous material with a conductive boundary condition. The goal is to study how these eigenvalues depend on the material parameters in order to estimate the refractive index. The analytical questions we study are: deriving Faber–Krahn type lower bounds, the discreteness and limiting behavior of the transmission eigenvalues as the conductivity tends to infinity for a sign changing contrast. We also provide a numerical study of a new boundary integral equation for computing the eigenvalues. Lastly, using the limiting behavior we will numerically estimate the refractive index from the eigenvalues provided the conductivity is sufficiently large but unknown.

摘要

我们对具有导电边界条件的传输特征值进行了新的分析和计算研究。这些特征值源自具有导电边界条件的非均匀材料的标量逆散射问题。目标是研究这些特征值如何依赖于材料参数以估计折射率。我们研究的分析问题是：导出 Faber-Krahn 型下界、传输特征值的离散性和限制行为，因为电导率趋于无穷大，符号变化的对比度。我们还提供了一个用于计算特征值的新边界积分方程的数值研究。最后，