The electromagnetic properties of conductive, anisotropic materials are described by Maxwell's equations with non-trivial conductivity. In the time-harmonic formulation, the underlying operator is non-selfadjoint; therefore, spectral approximations (such as the Galerkin approximations or the domain truncation method) might be prone to spectral pollution.
First, I will present a new non-convex enclosure for the spectrum of the Maxwell system in a possibly unbounded domain of the three-dimensional Euclidean space, with weak assumptions on the geometry and none on the behaviour of the coefficients at infinity.
For asymptotically constant coefficients, I will describe the essential spectrum and show that spectral pollution may occur only in a subset of the real line. Further, spectral exactness of the domain truncation method outside a `singular set' is achieved.
Time permitting, I will describe further developments in the spectral analysis of Maxwell's equations in conductive media with `anisotropy at infinity'.
Based on joint works with S. Bögli, M. Marletta, and C. Tretter.