Time-harmonic Maxwell equations in biological cells — the differential form formalism to treat the thin layer

Duruflé, Marc; Péron, Victor; Poignard, Claire

Confluentes Mathematici, Tome 3 (2011) no. 2, pp. 325-357.

We study the behavior of the electromagnetic field in a biological cell modeled by a medium surrounded by a thin layer and embedded in an ambient medium. We derive approximate transmission conditions in order to replace the membrane by these conditions on the boundary of the interior domain. Our approach is essentially geometric and based on a suitable change of variables in the thin layer. Few notions of differential calculus are given in order to obtain the first-order conditions in a simple way, and numerical simulations validate the theoretical results. Asymptotic transmission conditions at any order are given in the last section of the paper. This paper extends to the time-harmonic Maxwell equations the previous works presented in [30, 33, 31, 6].

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