Approximate conditions replacing thin layers

Clair Poignard (1) , Patrick Dular (2) , Ronan Perrussel (3) , Laurent Krähenbühl (3) , Laurent Nicolas (3) , Michelle Schatzman (4)

1 CMAP - Centre de Mathématiques Appliquées
2 Institut Montefiore - Department of Electrical Engineering and Computer Science
3 AMPERE - Ampère
4 ICJ - Institut Camille Jordan

We provide a rigorous asymptotic method to build approximate conditions equivalent to a thin layer. With these conditions the electromagnetic field may be computed in domains such as a biological cell, without meshing the membrane. The influence of the membrane is replaced by an appropriate condition on the inner domain, while in the thin layer, the approximate field is explicitly known. We give error estimates, which validate our asymptotic method, and we present a few numerical results performed with the finite element method.

Mots clés: finite element method; Asymptotic methods; thin layers; finite element method.

Domaines: Modélisation et simulation; Electromagnétisme

Clair Poignard, Patrick Dular, Ronan Perrussel, Laurent Krähenbühl, Laurent Nicolas, et al.. Approximate conditions replacing thin layers. IEEE Transactions on Magnetics, 2008, 44 (6), pp.1154 -- 1157. ⟨10.1109/TMAG.2007.916154⟩. ⟨hal-00165049v2⟩