Skip to Main content Skip to Navigation
Journal articles

Two-scale analysis for very rough thin layers. An explicit characterization of the polarization tensor

Ionel Sorin Ciuperca 1 Ronan Perrussel 2 Clair Poignard 3, 4, *
* Corresponding author
3 MC2 - Modélisation, contrôle et calcul
Inria Bordeaux - Sud-Ouest, UB - Université de Bordeaux, CNRS - Centre National de la Recherche Scientifique : UMR5251
Abstract : We study the behaviour of the steady-state voltage potential in a material composed of a two-dimensional object surrounded by a very rough thin layer and embedded in an ambient medium. The roughness of the layer is described by a quasi $\eps$--periodic function, $\eps$ being a small parameter, while the mean thickness of the layer is of magnitude $\eps^\beta$, where $\beta\in(0,1)$. Using the two-scale analysis, we replace the very rough thin layer by appropriate transmission conditions on the boundary of the object, which lead to an explicit characterization of the polarization tensor of Vogelius and Capdeboscq (ESAIM:M2AN. 2003; 37:159-173). This paper extends the previous works Poignard (Math. Meth. App. Sci. 2009; 32:435-453) and Ciuperca \textsl{et al.} (Research report INRIA RR-6812), in which $\beta\geq1$.
Document type :
Journal articles
Complete list of metadata

Cited literature [19 references]  Display  Hide  Download

https://hal.inria.fr/inria-00401835
Contributor : Clair Poignard <>
Submitted on : Monday, July 6, 2009 - 11:08:58 AM
Last modification on : Thursday, February 11, 2021 - 2:54:02 PM
Long-term archiving on: : Tuesday, June 15, 2010 - 7:29:10 PM

File

RR-6975.pdf
Files produced by the author(s)

Identifiers

Citation

Ionel Sorin Ciuperca, Ronan Perrussel, Clair Poignard. Two-scale analysis for very rough thin layers. An explicit characterization of the polarization tensor. Journal de Mathématiques Pures et Appliquées, Elsevier, 2011, 95 (3), pp.227-295. ⟨10.1016/j.matpur.2010.12.001⟩. ⟨inria-00401835⟩

Share

Metrics

Record views

1256

Files downloads

640