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A Generalized Method of Moments based discretization of the Müller integral formulation

Rao-Wilton-Glisson(RWG) basis functions [1] have become the de-facto standard for the discretization of surface integral equations, and for good reason; these basis functions have been shown to be highly effective in a wide variety of problems. RWG functions are designed to maintain continuity of certain components across patch boundaries and have spawned of higher order [2] and singular variants that satisfy similar constraints. While the satisfaction of these continuity constraints have significant advantages, this also means that the definition of the basis function is tightly coupled to the tessellation of the geometry. Recently a generalization of this scheme has been proposed, called the Generalized Method of Moments (GMM), where the basis function definition has been decoupled from the tessellation of the geometry [3]. The scheme detailed in [3] employs a partition of unity on overlapping patches and thereby, provides means for the mixing of arbitrary functions in the basis space. Results on several classes of conducting bodies have been presented in [3] and the method has also been observed to be low frequency stable.