Journal Article

FZJ-2024-03155

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png On trajectories of complex-valued interior transmission eigenvalues

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

2024
AIMS Springfield, Mo.

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Please use a persistent id in citations: doi:10.3934/ipi.2023041

Abstract: This paper investigates the interior transmission problem for homogeneous media via eigenvalue trajectories parameterized by the magnitude of the refractive index. In the case that the scatterer is the unit disk, we prove that there is a one-to-one correspondence between complex-valued interior transmission eigenvalue trajectories and Dirichlet eigenvalues of the Laplacian which turn out to be exactly the trajectorial limit points as the refractive index tends to infinity. For general simply-connected scatterers in two or three dimensions, a corresponding relation is still open, but further theoretical results and numerical studies indicate a similar connection.

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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 2024

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Database coverage:
; Clarivate Analytics Master Journal List ; Current Contents - Physical, Chemical and Earth Sciences ; Essential Science Indicators ; IF < 5 ; JCR ; SCOPUS ; Science Citation Index Expanded ; Web of Science Core Collection

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