Mardi 17 septembre 2024 à 11h00 / Amphithéâtre François Canac, LMA
In this talk we consider the following eigenvalue problem, arising from time-harmonic Maxwell’s equations in the context of perfectly conducting cavities:
(1/ε) curl (1/μ) curl E = λE, in Ω,
div εE = 0, in Ω,
ν × E = 0, on ∂Ω.
Here the cavity is represented by a bounded domain Ω of R3, with ν being its outer unit normal. The matrix-fieldsε and μ represent the electric permittivity and the magnetic permeability of the medium filling Ω, respectively. This problem admits a discrete spectrum composed of isolated eigenvalues of finite multiplicity.
The study of electromagnetic cavities is quite important in applications, for example in designing cavity resonators or shielding structures for electronic circuits.
We analyze the dependence of the eigenvalues λ with respect to the variation of the geometry of Ω, and we discuss possible applications towards shape optimization challenges.