TY  - JOUR
A1  - Pieronek, Lukas
A1  - Kleefeld, Andreas
T1  - On trajectories of complex-valued interior transmission eigenvalues
JF  - Inverse problems and imaging : IPI
N2  - 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.
KW  - Interior transmission problem
KW  - Eigenvalue trajectories
KW  - Complex-valued eigenvalues
Y1  - 2024
U6  - https://doi.org/10.3934/ipi.2023041
SN  - 1930-8337 (Print)
SN  - 1930-8345 (Online)
VL  - 18
IS  - 2
SP  - 480
EP  - 516
PB  - AIMS
CY  - Springfield, Mo
ER  - 
TY  - CHAP
A1  - Pieronek, Lukas
A1  - Kleefeld, Andreas
ED  - Constanda, Christian
ED  - Harris, Paul
T1  - The Method of Fundamental Solutions for Computing Interior Transmission Eigenvalues of Inhomogeneous Media
T2  - Integral Methods in Science and Engineering: Analytic Treatment and Numerical Approximations
N2  - The method of fundamental solutions is applied to the approximate computation of interior transmission eigenvalues for a special class of inhomogeneous media in two dimensions. We give a short approximation analysis accompanied with numerical results that clearly prove practical convenience of our alternative approach.
Y1  - 2019
SN  - 978-3-030-16077-7
U6  - https://doi.org/10.1007/978-3-030-16077-7_28
SP  - 353
EP  - 365
PB  - Birkhäuser
CY  - Cham
ER  -