# On Modeling Antennas Using MoM-Based Algorithms: Wire-Grid versus Surface Triangulation
## 3 Results
### Horn Antenna
The normalized electric field intensity was calculated in the \(E\) plane. The obtained antenna RPs were compared at the frequencies of 8 GHz in Figure 31. Then, they were compared at the same frequency but using \(\lambda/15\) as a segment length in Wire-Grid (Figure 32). As can be observed, the results for both codes results illustrated a good agreement with the measured ones. Figure 30: Isometric view of the horn antenna (**a**), and its constructed grid in Triangle-Grid (**b**) and in Wire-Grid (the red wire is the excitation source) (**c**). Table 12 summarizes the characteristics of the horn antenna models and their computational costs like the required memory, the simulation time spent, \(N\) and the cond of the SLAE matrix \(\mathbf{Z}\), and the percentage of the relative difference between those obtained using Wire-Grid and those obtained using Triangle-Grid code. In general, Wire-Grid surpasses Triangle-Grid in the computational costs consumed. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Code** & **Memory (GB)** & **Time (ms)** & \(N\) & **Cond (Z)** \\ \hline Wire-Grid (\(\lambda/40\)) & * \(\approx\)29.90 & 466,309 & 25,760 & 1.44 \(\times\) 10\({}^{6}\) \\ \hline Wire-Grid (\(\lambda/15\)) & \(\approx\)6.13 & 68,233 & 11,483 & 3.30 \(\times\) 10\({}^{5}\) \\ \hline Triangle-Grid (\(\lambda/15\)) & \(\approx\)3.63 & 232,867 & 15,148 & 2.03 \(\times\) 10\({}^{17}\) \\ \hline RD (\%) & \(-\)69 & 71 & 24 & \\ \hline \hline \end{tabular}  
* (\(\approx\)) denotes that the value is approximately equal to these numbers. (\(-\)) indicates by what percent the value is bigger than the reference one (here Triangle-Grid values).  
\end{table} 
Table 12: The characteristics of the horn antenna models and their computational costs. Figure 31: RPs of the horn antenna at a frequency of 8 GHz in the \(E\) (**a**) and \(H\) (**b**) planes: Triangle-grid (**–**), Wire-grid (\(\lambda/40\)) (—), measurements [347] (—) and -3 dB level (**–** -**). Figure 32: RPs of the horn antenna at a frequency of 8 GHz in the \(E\) (**a**) and \(H\) (**b**) planes: Triangle-grid (**–**), Wire-grid (\(\lambda/15\)) (—), measurements [347] (—) and -3 dB level (**–** -**). In order to verify the proposed algorithms validity, the horn antenna was simulated using the Monte Carlo methodology as in [350]. Table 13 contains the nominal values and the acceptable variation ranges of the geometrical parameters of the antenna internal dimensions. These ranges were determined by the manufacturer of the antenna prototype. On its base, a sample set of 11 different geometrical parameter values were generated and summarized in Table 14.  
Then, these samples were used to create 11 different geometrical models of the horn antenna. For each one of them, we calculated the RP and performed a statistical analysis of the obtained data. Tables 15 and 16 present the statistical characteristics (mathematical expectation (ME), dispersion, standard deviation, and confidence interval) for the maximum side-lobe level (\(\mathrm{SL}_{\mathrm{max}}\)) and beamwidth (BW) for both Wire-Grid and Triangle-Grid codes. The results showed that variations in the input parameters did not affect the BW in either code. However, the side-lobe level varied and the its standard deviation for Wire-Grid was 0.65%, while for Triangle-Grid it was 2.01%. One can say that the sensitivity of wire-grid to the input parameters variations is lower than its level for Triangle-Grid. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter** & **ME** & **Dispersion** & **Standard Deviation** & **Standard Deviation, \%** & **Confidence Interval** \\ \hline BW (\({}^{\circ}\)), \(E\) plane & 25 & 0.0 & 0.0 & 0.0 & 0.0 \\ \hline BW (\({}^{\circ}\)), \(H\) plane & 35 & 0.0 & 0.0 & 0.0 & 0.0 \\ \hline \(\mathrm{SL}_{\mathrm{max}}\) (dB) & \(-12.64\) & 0.0078 & 0.0082 & 0.65 & 0.049 \\ \hline \hline \end{tabular}
\end{table} 
Table 15: Statistical characteristics of horn antenna parameters in Wire-Grid.