This title appears in the Scientific Report :
2023
Please use the identifier:
http://hdl.handle.net/2128/34077 in citations.
Interior transmission eigenvalue trajectories
Interior transmission eigenvalue trajectories
Properties of complex-valued eigenvalue trajectories for the interior transmission problem parametrized by a constant index of refraction are investigated. At first, the unit disk is considered and several properties are derived such as that the only intersection points with the real axis are Dirich...
Saved in:
Personal Name(s): | Kleefeld, Andreas (Corresponding author) |
---|---|
Pieronek, Lukas | |
Contributing Institute: |
Jülich Supercomputing Center; JSC |
Imprint: |
2023
|
Conference: | SIAM Conference on Computational Science and Engineering, Amsterdam (Netherlands), 2023-02-27 - 2023-03-03 |
Document Type: |
Conference Presentation |
Research Program: |
Cross-Domain Algorithms, Tools, Methods Labs (ATMLs) and Research Groups |
Link: |
OpenAccess |
Publikationsportal JuSER |
Properties of complex-valued eigenvalue trajectories for the interior transmission problem parametrized by a constant index of refraction are investigated. At first, the unit disk is considered and several properties are derived such as that the only intersection points with the real axis are Dirichlet eigenvalues of the Laplacian. Then, for general sufficiently smooth scatterers also the only trajectorial limit points are shown to be Dirichlet eigenvalues of the Laplacian as the refractive index tends to infinity. Numerical results for several scatterers are presented which even give rise to an underlying one-to-one correspondence. Finally, a conjecture on the link between these two eigenvalue families is given. |