| Autor: |
Aiyappan, S., Griso, Georges, Orlik, Julia |
| Předmět: |
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| Zdroj: |
Complex Variables & Elliptic Equations; Apr2024, Vol. 69 Issue 4, p607-625, 19p |
| Abstrakt: |
The work is motivated by the Faraday cage effect. We consider the Helmholtz equation over a 3D domain containing a thin heterogeneous interface of thickness $ \delta \ll 1 $ 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 complex-valued coefficient in the connected faze while a real-valued in the complement. An asymptotic analysis with respect to $ \delta \to 0 $ 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. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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