2019/10/02 by Isaac Harris, Harris, Isaac
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1910.01009
openalex publication_date 2019/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we present a Spectral-Galerkin Method to approximate the\nzero-index transmission eigenvalues with a conductive boundary condition. This\nis a new eigenvalue problem derived from the scalar inverse scattering problem\nfor an isotropic media with a conductive boundary condition. In our analysis,\nwe will consider the equivalent fourth-order eigenvalue problem where we\nestablish the convergence when the approximation space is the span of finitely\nmany Dirichlet eigenfunctions for the Laplacian. We establish the convergence\nrate of the spectral approximation by appealing to Weyl's law. Numerical\nexamples for computing the eigenvalues and eigenfunctions for the unit disk and\nunit square are presented. Lastly, we provide a method for estimating the\nrefractive index assuming the conductivity parameter is either sufficiently\nlarge or small but otherwise unknown.\n