I. Introduction
In both the finite element method (FEM) [1], [2] and the method of moments (MoM) [3], [4], for solutions of general electromagnetic (EM) problems in the frequency domain, unknown EM quantities are expanded in terms of basis functions. After testing, they give rise to a system of linear equations, which is generally sparse for the FEM and dense for the MoM. Either way, a larger system of equations requires more computational recourses and more time to be solved. Because of this, higher order basis functions recently attract much attention [5], [6]. In comparison with low-order basis functions, they yield much better accuracy for the same number of unknowns or, similarly, fewer unknowns for the same accuracy [6], especially when they are div- or curl-conforming. Unfortunately, div- and curl-conforming higher order basis functions usually possess significant linear dependence, which leads to ill-conditioned system matrices, thus limiting the maximal order of basis functions in the mesh [7], and disabling the efficient usage of iterative solvers [8].