Exact Spectral Analysis of Traditional and Single-Source Integral Equations for a Penetrable Sphere

Behaviour of the numerical discretization schemes of the integral equations (IEs) such as the Method of Moments, the Locally Corrected Nystrom method and others largely depends on the spectral properties of the continuous integro-differential operators forming such equations. This includes susceptibility of these numerical schemes to various breakdowns including low-frequency breakdown, oversampling breakdown, spurious resonances, and topological breakdown. Revealing the spectra of the pertinent integro-differential operators is difficult but can be done analytically for a few canonical geometric shapes including the sphere. In this work we study spectra of traditional and single-source electromagnetic integral equation formulations for the case of a dielectric sphere. These formulations include traditional two-source equations such as the Electric Field IE (EFIE), Magnetic Field IE (MFIE), Combined Field IE (CFIE), Poggio-Muller-Chu-Harrington-Wu-Tsai (PMCHWT) IE, and Muller IE as well as single-source integral equations such as the Differential Surface Admittance EFIE (DSA-EFIE) and the Surface-Volume-Surface EFIE (SVS-EFIE). The exact MoM solutions of the traditional and single-source IEs accompanying their spectral analysis are validated against the Mie series solution of a dielectric sphere.
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