Generalized Method of Moments: A Novel Discretization Technique for Integral Equations

Typical method of moments solution of integral equations for electromagnetics relies on defining basis functions that are tightly coupled to the underlying tessellation. This limits the types of functions (or combinations thereof) that can be used for scattering analysis. In this paper, we introduce a framework that permits seamless inclusion of multiple functions within the approximation space. While the proposed scheme can be used in a mesh-less framework, the work presented herein focuses on implementing these ideas in an existing mesh topology. A number of results are presented that demonstrate approximation properties of this method, comparison of scattering data with other numerical and analytical methods and several advantages of the proposed method; including the low frequency stability of the resulting discrete system, its ability to mix different orders and types of basis functions and finally, its applicability to non-conformal tessellations.