Conference Presentation (After Call)

FZJ-2023-03328

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Interior transmission eigenvalue trajectories

Kleefeld, A. (Corresponding author)FZJ* ; Pieronek, L. (Collaboration author)

2023

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Please use a persistent id in citations: doi:10.34734/FZJ-2023-03328

Abstract: Complex-valued eigenvalue trajectories parametrized by a constant index of refractionare investigated for the interior transmission problem. Several properties are derived forthe unit disk such as that the only intersection points with the real axis are Dirichleteigenvalues of the Laplacian. For general sufficiently smooth scatterers in two dimensionsthe only trajectorial limit points are shown to be Dirichlet eigenvalues of the Laplacian asthe refractive index tends to infinity. Additionally, numerical results for several scatterersare presented which give rise to an underlying one-to-one correspondence between thesetwo eigenvalue families which is finally stated as a conjecture.

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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 2023

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