A flexible framework for the solution to surface scattering problems using integral equations

Abstract

Most method of moment solutions to integral equations in electromagnetics use the Rao Wilton Glisson (RWG) basis functions. These functions, which are constructed on a triangulation of the geometry are limited by their inherent need to satisfy continuity conditions. Recent developments by the authors have resulted in a new basis function scheme for integral equations called the Generalized Method of Moments (GMM). This scheme permits a wide variety of basis functions and their arbitrary mixtures. These functions are described on a locally smooth representation of the underlying surface. However, it is not possible to provide such a locally smooth representation in the presence of geometric singularities such as edges and corners. In this work, we address this problem by hybridizing the GMM patch construction and basis function definitions with RWG basis functions and piecewise flat triangulations. We will describe a scheme to automatically choose and mix GMM and RWG patch definitions, and basis functions. This hybridization can also be extended to other basis function types (and corresponding geometry descriptions). Preliminary results are presented that validate the method.