# On Modeling Antennas Using MoM-Based Algorithms: Wire-Grid versus Surface Triangulation
## 2 Materials and Methods
### Triangle-Grid
#### 2.3.1 Surface Patch Approach: Overview
This combination increased the flexibility of mesh generation, which is attractive for multiscale dielectric models with the same iterative convergence comparing to the conventional JMCFIE. MB-RWG were also used in developing a quasi-Helmholtz decomposition analysis with loop-star basis functions for electromagnetic scattering problems on an object with multiple surfaces [293]. The use of half RWG was also common in several works. For example, in [294] to an efficient radar cross section computation technology by the analyze of electromagnetic scattering from 3-D medium-coated targets with varying geometrical shapes. Several works have been devoted to the use of RWG functions with other methods and approaches. For example, in [295,296], frequency-selective surfaces were analyzed using RWG functions. In addition, they were used with the fast multipole method (FMM) to solve EM radiation of electrically very large problems. This was achieved by the virtue of FMM, since it enables the solution of such problems with existing computational resources by reducing computational complexity and memory requirements for the solution iterative scheme without sacrificing the accuracy [297]. RWGs were also used with the comp1 ex image method (CIM) to eliminate the modeling flexibility limits in describing the geometry of the unit cell. These limits arise when enforcing a uniform discretization that allows FFTs to be employed in constructing matrix elements efficiently. Such discretization is used to alleviate the difficulties faced when analyzing planar periodic structures with MoM. This analysis in turn requires summing tens of thousands of Floquet's modes to achieve convergence, which is very difficult [298]. Since the CG-FFT is an iterative solver for solving the MOM matrix equation, and it is efficient only with uniform rectangular grids, to model an arbitrary geometry accurately, one has to use triangular elements. However, they do not allow the application of FFT to speed up matrix-vector multiplication. Therefore, the adaptive integral method (AIM) was used to overcome this problem by discretizing arbitrarily shaped microstrips with RWGs at first and then translate them onto a rectangular grid to enable the utilization of FFT to carry out matrix-vector multiplication. Then, the required spatial Green's functions are computed efficiently using the discrete (DCIM) [299]. In addition, the combined generalized scattering matrix (GSM) moment method was used with the help of RWGs to design a waveguide component including structures of more universal shape like a waffle-iron filter with round teeth [300]. RWGs have also been used in the time domain analysis like in [301, 302, 303]. Moreover, the authors of [304] proved that not only the spatial RWGs but also the transient RWG can be used in marching-on-in-time based EFIE solvers to evaluate the time domain fields. Even more, they were also used with marching-on-in-degree [305]. The RWGs and Schaubert-Wilton-Glisson convolutional integrals were evaluated by a fast convergent quadrature method in [306], and then they were used in [307,308] to efficiently analyze of lossy interconnect structures based on two-region augmented volume-surface integral equations. Moreover, several solutions of volume-surface integral equations were proposed with the help of RWGs like in [309]. RWGs were also combined with other basic functions like the accurate subentire-domain [310] and the simplified prism vector basis functions [311]. In addition, a surface integral equation (SIE) method with RWG was developed to analyze electromagnetic scattering by objects with generalized soft-and-hard (GSH) [312] and soft-and-hard / DB [313], as well as mixed impedance [314] boundary conditions. RWGs were also used by the equivalence principle (EP) to solve EM scattering problems [315], by EP and the addition theorem [316], and by the random auxiliary sources method to solve general EM problems [317]. However, there are a number of issues when solving electromagnetic problems using the MoM and RWG basis functions.