On the choice of optimal basis functions for MoM/SIE, MoM/VIE, FEM and hybrid methods

Analysis of composite metallic and dielectrics structures placed in a time-harmonic electromagnetic field is usually based on the MoM (Method of Moments), or FEM (Finite Element Method). Particularly, if MoM is applied to SIE (Surface Integral Equation), the method is termed as MoM/SIE, and if MoM is applied to VIE (Volume Integral Equation) the method is termed as MoM/VIE. Besides that, all these methods can be mutually combined giving different types of hybrid methods. Efficiency of all these methods depends greatly on the choice of basis functions. A variety of basis functions is used by different authors. Sometimes it seems that basis functions written in one notation and used by one method are completely different from and without any connection with basis functions written in another notation and used by another method. In addition, it seems that some of the used basis functions are not optimally adopted. The first goal of this paper is to show that practically all basis functions used in MoM/SIE, MoM/VIE and FEM belong to a few general classes of basis functions. The second goal is to establish the set of desired properties of basis functions used in each of the methods. Finally, the third goal is to compare different classes of basis functions starting from the set of desired properties, and choose the optimal classes of basis functions.