A high-order wideband direct solver for electromagnetic scattering from bodies of revolution
This provides a high-order solver for a specific class of geometries (bodies of revolution) in computational electromagnetics, addressing a known bottleneck in accuracy for such problems.
The authors developed the first high-order accurate solver for electromagnetic scattering from bodies of revolution using the generalized Debye source representation, achieving well-conditioned second-kind integral equations stable in the static limit. Numerical examples demonstrate accuracy and speed.
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 $ω\to 0$ 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 Nyström 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.