Skip to Main content Skip to Navigation
Journal articles

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.
Document type :
Journal articles
Complete list of metadata

Cited literature [10 references]  Display  Hide  Download

https://hal.inria.fr/inria-00334771
Contributor : Clair Poignard <>
Submitted on : Monday, October 27, 2008 - 7:33:58 PM
Last modification on : Thursday, March 5, 2020 - 6:21:39 PM
Long-term archiving on: : Monday, June 7, 2010 - 6:57:49 PM

File

GIBC-18pp.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

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⟩

Share

Metrics

Record views

396

Files downloads

367