Journal Article

FZJ-2020-02436

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Analysis and computation of the transmission eigenvalues with a conductive boundary condition

Harris, I. (Corresponding author) ; Kleefeld, A.FZJ*

2022

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Please use a persistent id in citations: http://hdl.handle.net/2128/31107  doi:10.1080/00036811.2020.1789598

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

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Contributing Institute(s):

1. Jülich Supercomputing Center (JSC)

Research Program(s):

1. 5112 - Cross-Domain Algorithms, Tools, Methods Labs (ATMLs) and Research Groups (POF4-511) (POF4-511)

Appears in the scientific report 2022

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Database coverage:
; SCOPUS

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