# On Modeling Antennas Using MoM-Based Algorithms: Wire-Grid versus Surface Triangulation
## 2 Materials and Methods
### Wire-Grid
#### 2.2.1 Wire-Grid: Overview
The use of equivalent wire-grid array instead of a solid conducting object was also investigated and proved, for example in [116]. It was shown that if a sufficiently big number of wires is used, the scattering pattern of a solid conducting cylinder of the same cross-section shape is the same as the wire-grid array pattern. Similar conclusions were made for plane, circular, semicircular, and square arrays. In general, the wire-grid analysis was used mostly with MoM [117]. The ease of MoM enables researchers to develop several approaches and solutions to analyze wire-grid, like in [118; 119; 120] where MoM was hybridized with the geometrical theory of diffraction. Also, in [121] where a banded matrix iterative solution method was applied for linear simultaneous equations arising from thin wire moments problems. In addition, to speed up the matrix fill process in wavelet-based MoM codes when solving the thin-wire EFIE by the multiresolution wavelet expansion method, the researchers in [122], appropriately replaced the triangular scaling functions of a nonorthogonal piecewise liner wavelet at the finest spatial resolution by sinusoidal dipoles for which mutual impedances are available in closed-form analytical expressions. Then, they exploited the fast wavelet bases transform to effectively transfer the resultant matrix equation to multiresolution wavelet domain. All these studies form the base of a considerable number of wire-grid-MoM-based applications and investigations. One example is the use of wire-grid structures as bistatic calibration reference in the studies related to the bistatic polarimetric radars for synthetic-aperture radar (SAR) applications [123]. In the area of backscattering, wire-grid MoM based approach also was used to calculate the radar cross section (RCS) of PEC wire-grid canonical models of objects in the resonance domain using the pulse basis functions and point matching [124]. Optimization methods have been wildly used with this approach on several problems like in designing a microstrip-patch antenna [125] and a trapezoidal-tooth log-periodic antenna [126]. Moreover, several studies have been devoted to the development of this approach in regards to the image theory [127], characteristic modes theory [128; 129], microwave theory [130], modeling dielectric bodies [131; 132], using different types of meshes [133], and even investigating its properties not only in the frequency domain but also in the time domain [134; 135; 136; 137]. The seeds of the question of validating the results of using wire-grid model of a structure were sowed since the work of [PERSON] [138; 139; 140; 141] and [PERSON] [142] that used wire-grid codes. The researchers presented so many works devoted to the validation of such codes. For example, the results of the MoM-based NEC code [143] were compared with those obtained via other methods like the FDTD [144]. The results of other wire-grid models have also been compared with those obtained via other programs like the MESHES, FNDRAD and CHECK codes [145; 146], and yet with other techniques like the point matching one [147]. NEC itself has been used in modeling and solving electromagnetic problems [148] in different applications and proved its capability [149; 150]. Thus, it is still today in use for designing and fabricating wire-grid antennas [151]. Alternatively, researchers have also developed their own wire-grid codes with the same capabilities and applications [152; 153; 154; 155]. Wire-grid is a promising approach, despite its limitations, which have been discussed in several works. For example, the results of modeling a conducting closed surface were compared with those of wire-grid model for the same surface using the direct, the formal, and the circuit approaches [156]. The differences of the wire-grid model from these approaches were shown.