Homogenization of Helmholtz equation in a periodic layer to study Faraday cage-like shielding effects
Résumé
The work is motivated by the Faraday cage effect. We consider the Helmholtz equation over a 3Ddomain containing a thin heterogeneous interface of thickness δ 1. The layer has a δ−periodic structure in the in-plane directions and is cylindrical in the third direction. The periodic layer has one connected component and a collection of isolated regions. The isolated region in the thin layer represents air or liquid, and the connected component represents a solid metal grid with a δ thickness. The main issue is created by the contrast of the coefficients in the air and in the grid and that the zero-order term has a complexvalued coefficient in the connected faze while a real-valued in the complement. An asymptotic analysis with respect to δ → 0 is provided, and the limit Helmholtz problem is obtained with the Dirichlet condition on the interface. The periodic unfolding method is used to find the limit.
Domaines
Analyse numérique [math.NA]
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