Time-dependent electromagnetic scattering from thin layers

The scattering of electromagnetic waves from obstacles with wave-material interaction in thin layers on the surface is described by generalized impedance boundary conditions, which provide effective approximate models. In particular, this includes a thin coating around a perfect conductor and the skin effect of a highly conducting material. The approach taken in this work is to derive, analyse and discretize a system of time-dependent boundary integral equations that determines the tangential traces of the scattered electric and magnetic fields. In a second step the fields are evaluated in the exterior domain by a representation formula, which uses the time-dependent potential operators of Maxwell's equations. A key role in the well-posedness of the time-dependent boundary integral equations and the stability of the numerical discretization is taken by the coercivity of the Calder\'on operator for the time-harmonic Maxwell's equations with frequencies in a complex half-plane. This entails the coercivity of the full boundary operator that includes the impedance operator. The system of time-dependent boundary integral equations is discretized with Runge--Kutta based convolution quadrature in time and Raviart--Thomas boundary elements in space. The full discretization is proved to be stable and convergent, with explicitly given rates in the case of sufficient regularity. The theoretical results are illustrated by numerical experiments.