%0 Conference Paper
%A Kleefeld, Andreas
%T Non-scattering wave numbers versus transmission eigenvalues
%M FZJ-2025-01834
%D 2025
%X 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.
%B Conference on Mathematics of Wave Phenomena
%C 24 Feb 2025 - 28 Feb 2025, Karlsruhe (Germany)
Y2 24 Feb 2025 - 28 Feb 2025
M2 Karlsruhe, Germany
%F PUB:(DE-HGF)6
%9 Conference Presentation
%R 10.34734/FZJ-2025-01834
%U https://juser.fz-juelich.de/record/1040320