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.Th...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.展开更多
基金the Investments for the Future Programme IdEx Bordeaux CPU(ANR-10-IDEX-03-02).C.P.is partly funded by ANR projects INTCELL(ANR 2010-BLAN-916)MEMOVE(ANR 2011 BS0100601)。
文摘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.
