On spectral enclosures for Maxwell’s equations with the Drude–Lorentz model

Abstract

In this paper, we compare two approaches to derive spectral enclosures for Maxwell’s equations with the Drude–Lorentz model in possibly unbounded domains. The enclosures can be computed in the infinite-dimensional case as well as for the matrix-valued function obtained after a discretization. The enclosures are minimal given only the numerical ranges of the operator coefficients and we compare in the case of purely imaginary poles the derived enclosures with enclosures from the literature.