Conference Presentation (After Call)

FZJ-2026-02914

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Transmission eigenvalues for biharmonic plate scattering: Existence, discreteness, far-field recovery, and numerical computations

Kleefeld, A. (Corresponding author)FZJ*

2026

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Please use a persistent id in citations: doi:10.34734/FZJ-2026-02914

Abstract: A novel transmission eigenvalue problem defined in all of $\mathbb{R}^2$ isconsidered. This problem arises in the context of scattering by aclamped cavity within a thin elastic material. The existence anddiscreteness of an infinite number of positive real transmissioneigenvalues are established. Furthermore, a numerical method based onboundary integral equations is developed and discretized with theboundary element collocation method. A variety of numerical results ispresented for a range of scatterers thereby complementing thetheoretical findings. Finally, several open questions, including theexistence of complex-valued transmission eigenvalues, monotonicity, andan interlacing property are illustrated. This research was conducted incollaboration with Isaac Harris and Heejin Lee.

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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 2026

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