# 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
The researchers observed that the boundary-condition error (BCE) induced by the RWG and rooftops basic functions are of the same order for the cases of comparable numbers of basic functions and that the BCE induced by the RWG is certainly not more than that of rooftops despite the nonzero values of the current normal to the patch edges. The triangular discretized RWG simulation results of electromagnetic waves scattering from two-dimensional perfectly conducting random and rough surfaces showed a good agreement when compared with those obtained by the sparse-matrix/canonical-grid approach [254] and the wavelets-based MoM and EFIE results [255]. RWG functions were used, for example, in solving the problem of attaching a thin wire monopole to a ground plane [256]. FEM and MoM were used with the help of RWG to analyze a waveguide radiator with a peripheral choke, a conical and a rectangular horn antenna [257]. In order to analyze dielectric resonator antennas of arbitrary shapes, RWG functions were used with MoM [258; 259], with FDTD [260], and with E-PMCHW [261]. RWG basis functions were effectively used to simulate patch antennas of various kinds [262]. The examples are the double [263], the E-shaped [264], and the slot-loaded trapezoidal [265] patch antennas, and the conformal array [266]. In addition, they were used in the analysis of substrate integrated waveguide slot-based antennas [267]. RWG functions even proved their efficiency in the analysis of arbitrary [268] and densely packed [269] and large-scale [270] microstrip interconnects due to their modeling flexibility. Moreover, RWG functions and wavelet expansions were used to predict shielding effectiveness of electronic equipment enclosures with multiple apertures [271]. They were also used in the analysis of a realistic multilayer printed circuit boards [272; 273]. Over the past decades, in addition to classical electromagnetic problems, RWG functions were applied in other issues, for example in modeling plasmonic nanostructures [274], analyzing transcranial magnetic stimulation [275], human detection problems in forest environments [276], in electromagnetic scattering by 3D buried objects [277; 278], and others. In addition, several modifications of the RWG basis functions have been proposed. For instance, in [279], the authors proposed high order vector basis functions that improve the convergence properties of the solution. Moreover, an explicit form of high order mixed RWG functions based on a combination of triangular and quadrilateral elements was presented in [280]. While in [281], the features of RWG implementation on curvilinear elements were considered in detail, which made it possible to more accurately approximate the surfaces of the simulated objects. In [282], an algorithm was proposed that adapts MoM with RWG basis functions for parallel computing on GPU platforms. In spite of these and other studies to this day, the classical form of RWG functions with flat triangular elementsis still most widely used. Even more, they were extended to triangular-quadrilateral (Mix-RWG) current basis function [283] and showed more simplicity and advantages than RWG. They were further modernized in [280]. In [284], the researchers gave a correction to a magnetic field (MFIE) factor to achieve accurate results comparing to EFIE for small sharp-edged objects. They also proposed some improvements in the MFIE [285,286], and the combined field (CFIE) [287,288], and in the combined source IE (CSIE) [289] with the use of RWG functions through the analysis. Moreover, other modified RWG functions were developed in [290] to enable their use in analyzing periodic structures where the electric or magnetic surface current must be allowed to flow across unit cell boundaries. In [291], the authors used the multibranch RWGs (MB-RWG) [292] with the electric and magnetic current combined field integral equations (JMCFIE), to solve the problem of electromagnetic scattering from dielectric objects.