Thin Layer Models For Electromagnetism

Marc Duruflé (1, 2) , Victor Péron (1, 3) , Clair Poignard (2, 4)

1 Magique 3D - Advanced 3D Numerical Modeling in Geophysics
2 IMB - Institut de Mathématiques de Bordeaux
3 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
4 MC2 - Modélisation, contrôle et calcul

We present a review on the accuracy of asymptotic models for the scattering problem of electromagnetic waves in domains with thin layer. These models appear as first order approximations of the electromagnetic field. They are obtained thanks to a multiscale expansion of the exact solution with respect to the thickness of the thin layer, that makes possible to replace the thin layer by approximate conditions. We present the advantages and the drawbacks of several approximations together with numerical validations and simulations. The main motivation of this work concerns the computation of electromagnetic field in biological cells. The main difficulty to compute the local electric field lies in the thinness of the membrane and in the high contrast between the electrical conductivities of the cytoplasm and of the membrane, which provides a specific behavior of the electromagnetic field at low frequencies.

Keywords: asymptotics; time-harmonic Maxwell's equations; Finite Element Method; Edge Elements

Domains: Analysis of PDEs [math.AP]

Marc Duruflé, Victor Péron, Clair Poignard. Thin Layer Models For Electromagnetism. Communications in Computational Physics, 2014, 16, pp.213-238. ⟨10.4208/cicp.120813.100114a⟩. ⟨hal-00918634⟩