Aix-Marseille Université
Institut de Mathématiques de Marseille (I2M) - UMR 7373
3 place Victor Hugo
Case 19
13331 Marseille Cedex 3


Shape sensitivity of time-harmonic Maxwell’s equations in bounded domains

Michele Zaccaron
Institut Fresnel (Marseille)

Date(s) : 25/06/2024   iCal
11h00 - 12h00

In this talk we consider the following eigenvalue problem, arising from time-harmonic
Maxwell’s equations in the context of perfectly conducting cavities:

ε^{-1} curl μ^{-1} 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-valued functions ε 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

FRUMAM, St Charles (2ème étage)


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