A high-order wideband direct solver for electromagnetic scattering from bodies of revolution

The generalized Debye source representation of time-harmonic electromagnetic fields yields well-conditioned second-kind integral equations for a variety of boundary value problems, including the problems of scattering from perfect electric conductors and dielectric bodies. Furthermore, these representations, and resulting integral equations, are fully stable in the static limit as $\omega \to 0$ in multiply connected geometries. In this paper, we present the first high-order accurate solver based on this representation for bodies of revolution. The resulting solver uses a Nystr"om discretization of a one-dimensional generating curve and high-order integral equation methods for applying and inverting surface differentials. The accuracy and speed of the solvers are demonstrated in several numerical examples.