2020/01/20 by Isaac Harris, Andreas Kleefeld, Harris, Isaac +1 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Electromagnetic Scattering and Analysis #FOS: Mathematics #Microwave Imaging and Scattering Analysis #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2001.07188
openalex publication_date 2020/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We provide a new analytical and computational study of the transmission\neigenvalues with a conductive boundary condition. These eigenvalues are derived\nfrom the scalar inverse scattering problem for an inhomogeneous material with a\nconductive boundary condition. The goal is to study how these eigenvalues\ndepend on the material parameters in order to estimate the refractive index.\nThe analytical questions we study are: deriving Faber-Krahn type lower bounds,\nthe discreteness and limiting behavior of the transmission eigenvalues as the\nconductivity tends to infinity for a sign changing contrast. We also provide a\nnumerical study of a new boundary integral equation for computing the\neigenvalues. Lastly, using the limiting behavior we will numerically estimate\nthe refractive index from the eigenvalues provided the conductivity is\nsufficiently large but unknown.\n