Conference Presentation (After Call)

FZJ-2025-01834

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Non-scattering wave numbers versus transmission eigenvalues

Kleefeld, A. (Corresponding author)FZJ*

2025

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Please use a persistent id in citations: doi:10.34734/FZJ-2025-01834

Abstract: An important question arising in inverse problems for wave scattering is whether for a given inhomogeneous bounded obstacle in two dimensions there is an incident wave that does not scatter. Closely connected to this question is the solution of the interior transmission problem.Therefore, let $A$ be the discrete set of non-scattering wave numbers and $B$ be the discrete set of transmission eigenvalues.It is well-known that $A=B\neq \emptyset$ holds for a disk and $B\supsetneq A=\emptyset$ holds for a square. The questions remains whether there is a bounded obstacle for which $A\subsetneq B$ with $A\neq \emptyset$. To address this question, the problem at hand is recasted as a constrained optimization problem using Fourier-Besselfunctions and then finally solved numerically. Some numerical results are presented and interesting observations are made both of which merit further investigation.

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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 2025

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