High-order accurate thin layer approximations for time-domain electromagnetics. Part I: General metal backed coatings

We present a family of high-order accurate thin layer approximations for time-domain electromagnetics. The thin layer approximations are valid for metal backed coatings of general isotropic materials and certain classes of anisotropic materials on smooth curvilinear backgrounds. Both dielectric and magnetic materials can be considered. These models are non-trivial and we discuss their properties and implementation in the context of discontinuous Galerkin methods which are particularly well suited for these models. The range of validity, accuracy, and stability of the resulting schemes is demonstrated through one- and two-dimensional examples.