Thin Layer Models for Electromagnetism (Communications in Computational Physics, 2014)
We present a review on the accuracy of asymptotic models for the scatteringproblem of electromagnetic waves in domains with thin layer. These models appearas first order approximations of the electromagnetic field. They are obtained thanks toa multiscale expansion of the exact solution with respect to the thickness of the thinlayer, that makes possible to replace the thin layer by approximate conditions. Wepresent the advantages and the drawbacks of several approximations together withnumerical validations and simulations. The main motivation of this work concerns thecomputation of electromagnetic field in biological cells. The main difficulty to computethe local electric field lies in the thinness of the membrane and in the high contrastbetween the electrical conductivities of the cytoplasm and of the membrane, whichprovides a specific behavior of the electromagnetic field at low frequencies.