A Chebyshev-Based High-Order-Accurate Integral Equation Solver for Maxwell's Equations

This article introduces a new method for discretizing and solving integral equation formulations of Maxwell's equations, which achieves spectral accuracy for smooth surfaces. The approach is based on a hybrid Nystrom-collocation method using Chebyshev polynomials to expand the unknown current densities over curvilinear quadrilateral surface patches. As an example, the proposed strategy is applied to the magnetic field integral equation (MFIE) and the N-Muller formulation for scattering from metallic and dielectric objects, respectively. The convergence is studied for several different geometries, including spheres, cubes, and complex NURBS geometries imported from CAD software, and the results are compared against a commercial Method-of-Moments solver using RWG basis functions.