Generalized method of moments: a framework for analyzing scattering from homogeneous dielectric bodies

In this paper, we present a novel framework for discretizing integral equations--specifically, those used for analyzing scattering from dielectric bodies. The candidate integral equations chosen for the analysis are the well-known Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) and the Müller equations. Discrete solutions to these equations are typically obtained by representing the spatial variation of the currents using the Rao-Wilton-Glisson (RWG) basis functions or their higher order equivalents. In this paper, we propose a framework for defining basis functions that departs significantly from those of RWG functions in that approximation functions can be chosen independent of continuity constraints. We will show that using this framework together with a quasi-Helmholtz type representation has a number of benefits. Namely, (i) it shows excellent convergence, (ii) it permits inclusion of different orders of polynomials or different functions as basis functions without imposition of additional constraints, (iii) the method can easily handle nonconformal meshes, and (iv) the method is well conditioned at all frequencies. These features will be demonstrated via a number of numerical experiments.