A Chebyshev-based High-order-accurate Integral Equation Solver for Maxwell's Equations

07/29/2020

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by   Jin Hu, et al.

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This paper 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 Nyström-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 Magnetic Field Integral Equation (MFIE) and the N-Müller 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.