Generalized Impedance Boundary Condition At High Frequency For A Domain With Thin Layer: The Circular Case

Abstract : Consider a disk surrounded by a thin conducting layer submitted to an electric field at the pulsation ω . The conductivity of the layer σm grows as ω 1-γ , for γ in [0,2/3), as the pulsation ω tends to infinity. Using a pseudodifferential approach on the torus, we build an equivalent boundary condition with the help of an appropriate factorization of Helmholtz operator in the layer. This generalized impedance condition approximates the thin membrane as ω tends to infinity and the thickness of the layer tends to zero. Error estimates are given and we illustrate our results with numerical simulations. This work extends, in the circular geometry, previous works of Lafitte and Lebeau, in which γ identically equals zero.
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Applicable Analysis, Taylor & Francis, 2007, 86 (12), pp.1549-1568. 〈10.1080/00036810701714172〉
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Clair Poignard. Generalized Impedance Boundary Condition At High Frequency For A Domain With Thin Layer: The Circular Case. Applicable Analysis, Taylor & Francis, 2007, 86 (12), pp.1549-1568. 〈10.1080/00036810701714172〉. 〈inria-00334771〉

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