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

TL;DR

This paper introduces a high-order accurate, efficient solver for electromagnetic scattering from bodies of revolution using the generalized Debye source representation, suitable for static and dynamic regimes.

Contribution

It presents the first high-order solver based on this representation specifically for bodies of revolution, combining Nyström discretization with integral equation methods.

Findings

Demonstrates high accuracy in numerical examples

Shows stability in static limit as frequency approaches zero

Achieves efficient computation for complex geometries

Abstract

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.