TY  - JOUR
A1  - Ayala, Rafael Ceja
A1  - Harris, Isaac
A1  - Kleefeld, Andreas
A1  - Pallikarakis, Nikolaos
T1  - Analysis of the transmission eigenvalue problem with two conductivity parameters
JF  - Applicable Analysis
N2  - In this paper, we provide an analytical study of the transmission eigenvalue problem with two conductivity parameters. We will assume that the underlying physical model is given by the scattering of a plane wave for an isotropic scatterer. In previous studies, this eigenvalue problem was analyzed with one conductive boundary parameter whereas we will consider the case of two parameters. We prove the existence and discreteness of the transmission eigenvalues as well as study the dependence on the physical parameters. We are able to prove monotonicity of the first transmission eigenvalue with respect to the parameters and consider the limiting procedure as the second boundary parameter vanishes. Lastly, we provide extensive numerical experiments to validate the theoretical work.
KW  - Transmission Eigenvalues
KW  - Conductive Boundary Condition
KW  - Inverse Scattering
Y1  - 2023
U6  - https://doi.org/10.1080/00036811.2023.2181167
SN  - 0003-6811
PB  - Taylor & Francis
ER  - 
TY  - JOUR
A1  - Ayala, Rafael Ceja
A1  - Harris, Isaac
A1  - Kleefeld, Andreas
T1  - Direct sampling method via Landweber iteration for an absorbing scatterer with a conductive boundary
JF  - Inverse Problems and Imaging
N2  - In this paper, we consider the inverse shape problem of recovering isotropic scatterers with a conductive boundary condition. Here, we assume that the measured far-field data is known at a fixed wave number. Motivated by recent work, we study a new direct sampling indicator based on the Landweber iteration and the factorization method. Therefore, we prove the connection between these reconstruction methods. The method studied here falls under the category of qualitative reconstruction methods where an imaging function is used to recover the absorbing scatterer. We prove stability of our new imaging function as well as derive a discrepancy principle for recovering the regularization parameter. The theoretical results are verified with numerical examples to show how the reconstruction performs by the new Landweber direct sampling method.
Y1  - 2024
U6  - https://doi.org/10.3934/ipi.2023051
SN  - 1930-8337
SN  - 1930-8345 (eISSN)
VL  - 18
IS  - 3
SP  - 708
EP  - 729
PB  - AIMS
CY  - Springfield
ER  -