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Approximate transmission conditions through a rough thin layer: The case of periodic roughness

Published online by Cambridge University Press:  23 November 2009

I. S. CIUPERCA ,
M. JAI  and
C. POIGNARD
I. S. CIUPERCA
Affiliation:
Université de Lyon, Université Lyon 1, CNRS, UMR 5208, Institut Camille Jordan, 43 boulevard du 11 novembre 1918, F-69622 Villeurbanne Cedex, France email: Ciuperca@math.univ-lyon1.fr
M. JAI
Affiliation:
ICJ CNRS-UMR 5208, INSA de Lyon, 20 avenue A. Einstein, F-69621 Villeurbanne Cedex, France email: Mohammed.jai@insa-lyon.fr
C. POIGNARD
Affiliation:
INRIA Bordeaux-Sud-Ouest, Institut de Mathématiques de Bordeaux, CNRS UMR 5251 & Université de Bordeaux1, 351 cours de la Libération, F-33405 Talence Cedex, France email: clair.poignard@inria.fr
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Abstract

We study the behaviour of the steady-state voltage potentials in a material composed of a two-dimensional object surrounded by a rough thin layer and embedded in an ambient medium. The roughness of the layer is supposed to be ϵ-periodic, ϵ being the magnitude of the mean thickness of the layer. For ϵ tending to zero, we determine approximate transmission conditions in order to replace the rough thin layer by these conditions on the boundary of the interior material. This paper extends the previous works (Poignard, 2009, Math. Meth. Appl. Sci., vol. 32, pp. 435–453; Poignard et al., 2008, IEEE Trans. Magnet., vol. 44, no. 6, pp. 1154–1157) of the third author, which deal with smooth thin layers.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 21 , Issue 1 , February 2010 , pp. 51 - 75
Copyright
Copyright © Cambridge University Press 2009

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