Three types of higher-order MoM basis functions automatically satisfying current continuity conditions

This paper presents our investigations aimed at improving the orthogonality properties of polynomial higher-order hierarchical basis functions leading to better conditioned MoM matrices and more stable solutions, in both volume integral equation (VIE) modeling and surface integral equation (SIE) modeling. Three different types of polynomial basis functions are implemented in the large-domain Galerkin SIE method, enabling cross-validation of the results and comparison of numerical properties of the three sets of basis functions. We show that by combining the simple 2D power functions of parametric coordinates in accordance to ultraspherical and Chebyshev polynomials, and modifying them so that the current-continuity condition across the quadrilateral edges is automatically satisfied, higher-order polynomial MoM basis functions are obtained that have much better orthogonality properties.