Wentzel--Kramers--Brillouin Expansions and Generalized Impedance Transmission Conditions for Thin-Layer Problems in Electromagnetism with Application to Biological Cells

TL;DR

This paper develops WKB expansions and second-order asymptotic models with curvature-dependent impedance conditions for electromagnetic problems involving thin layers, facilitating efficient simulations in biological cell applications.

Contribution

It introduces new curvature-dependent impedance transmission conditions derived from WKB expansions for thin-layer electromagnetism problems.

Findings

Derived WKB expansions for Maxwell equations in thin layers

Developed second-order asymptotic models with generalized impedance conditions

Applied models to electromagnetic field computation in biological cells

Abstract

In this work we derive a WKB expansion for the electromagnetic fields solution of the time-harmonic Maxwell equations set in a domain with a thin layer. As a by-product of this expansion we obtain new second order asymptotic models with generalized impedance transmission conditions that turn out to depend on the mean curvature of the boundary of the subdomain surrounded by the thin layer. We show that these models can be easily integrated in finite element methods by developing mixed variational formulations. One application of this work concerns the computation of the electromagnetic field in biological cells.