# On Modeling Antennas Using MoM-Based Algorithms: Wire-Grid versus Surface Triangulation
## 2 Materials and Methods
### Wire-Grid
#### 2.2.1 Wire-Grid: Overview
However, the researcher proved that the wire-grid model can give acceptable results despite the fact that there is no unique way to quantify the difference of the self-capacitive term between the wire-grid model and the corresponding closed structure, since this depends, for example, on the problem geometry. The sensitivity of the wire-grid surface model results to the wire diameter was discussed in [157] on the example of a special case of a canonical problem of scattering (or radiation) from an infinite circular cylinder. This work showed that the best accuracy is obtained when the wire satisfies the \"same surface area\" rule of thumb to calculate the radii of wire-grid models. Moreover, this work discussed the effect of some other aspects, like the wire thickness, the wire spacing, and the boundary value match between wires. By comparing the results of wire-grid with the exact solutions of the true problem, the work indicated that five wires per wavelength generally provide accurate results, although more wires are better and reduce the sensitivity of the error to the wire size. All these results were also confirmed later in [158] on the same problem. In addition, the researchers detailed the facts obtained earlier. Regarding the same surface area rule, it is optimal for the far field, internal field, and the near field in the immediate vicinity of the wire grid; with [PERSON]'s uniform surface current model, the largest errors appeared almost exactly between the wires; for plane wave illumination the largest errors appeared somewhere inside the cylinder, hence, one should not associate near field errors with being too close to the grid. Regarding the boundary value match between the wires, they confirmed that it is not a good error check for the uniform current and also for plane wave incidence, but for different reasons. The reason behind that is that the accuracy of the field between the wires is not a reliable error indicator because a good match when the wire-grid cylinder and the true cylinder have an equal radii does not guarantee an accurate field elsewhere in the case of plane wave incidence. Moreover, they found that for plane wave incidence, the wire radius that gives the best internal field also gives the best external field, and the field inside the cylinder is most sensitive to wire radius, so it is the best error indicator. The adequacy of the \"same surface area\" rule, also known as the \"equal area rule\" (EAR), and in some cases as the \"twice surface area\", was discussed in [159]. The authors showed numerically and experimentally, that the EAR appears to be less accurate in reproducing the electromagnetic field scattered by metallic bodies when using other polygons (such as triangles) than a simple rectangular mesh in order to get a complex body-fitted mesh. Moreover, they provided a general formula to calculate the parameters for arbitrary grids and proved its efficiency. Furthermore, later, the authors of [160] provided a physical interpretation of the EAR and proposed a new EAR to calculate the radii for an arbitrarily meshed surface, the results of which were able to predict a smaller electric field inside a closed metallic surface, which is known to be identical to zero, in the considered frequency range. The EAR is relatively easy to apply as it depends only on segment lengths, but it fails in reproducing the very fine details of the geometry, which has a negative impact on near field results. The new EAR is more difficult to apply as it depends on the angle of source polarization, and its results may not observe the rules of NEC's general geometry construction guidelines, since the radius must be individually calculated for segment groups as a function of several parameters, including the angle of polarization. Both the well-known EAR and the new one were tested experimentally in [161] on the example of the electric field distribution inside a transvers electro-magnetic cell. The compared results showed reasonable agreement for models featuring rectangular meshes.