Approximate Transmission Conditions through a rough thin layer. The case of the periodic roughness

Ionel Ciuperca (1) , Mohammed Jai (1) , Clair Poignard (2, 3)

1 ICJ - Institut Camille Jordan
2 MC2 - Modélisation, contrôle et calcul
3 IMB - Institut de Mathématiques de Bordeaux

We study the behavior of the steady-state voltage potentials in a material composed by a bidimensional medium surrounded by a rough thin layer and embedded in an ambient medium. The roughness of the layer is supposed to be $\eps$--periodic, $\eps$ beeing the small thickness of the layer. We build approximate transmission conditions in order to replace the rough thin layer by these conditions on the boundary of the interior material. This paper extends previous works of the third author, in which the layer had constant or weakly oscillating thickness.

Domaines: Equations aux dérivées partielles [math.AP]; Modélisation et simulation

Ionel Ciuperca, Mohammed Jai, Clair Poignard. Approximate Transmission Conditions through a rough thin layer. The case of the periodic roughness. European Journal of Applied Mathematics, 2010, 21 (1), pp.51-75. ⟨10.1017/S095679250999012X⟩. ⟨inria-00356124v2⟩