## 4 Algorithm Validation
### Validation by Numerical Analysis  
Next, the generalized algorithm was validated using FEM-based numerical analysis. The COMSOL Multiphysics(r) (Stockholm, Sweden) RF Module was used for this purpose. In the FEM simulation, a perfect electrical conductor was used as the enclosure material. A hexagonal mesh with adaptive refinement was used to discretize the enclosures. The initial number of cells per wavelength was 45, and the mesh refinement percentage did not exceed 25% of the total number of elements at each step. The SE values were defined as:  
\[\mathrm{SE}=20\log_{10}\frac{\left|E^{0}\right|}{\left|E\right|}, \tag{39}\]  
where; \(E\) and \(E^{0}\) are the electric field strengths (intensities) at the observation point in the presence and absence of the enclosure, respectively. In all the cases considered below, the SE was calculated in the range from 1 MHz to 1 GHz with a resolution of just under 1 MHz, giving frequency dependencies consisting of 1000 points.  
First, using FEM and the proposed algorithm, we calculated the SE for the enclosure of the Ethernet filter (Figure 22a). It has a volume of 440 \(\times\) 42 \(\times\) 197.5 mm\({}^{3}\), a wall thickness of 1 mm, and it has 12 square apertures (16 \(\times\) 16 mm\({}^{2}\)) on the front wall. The analysis was performed without the internal filling of the enclosure, and only the dominant mode excitation was taken into account in the analytical calculation (\(m=1\) and \(n=0\)). When using the generalized algorithm, \(Z_{ap}\) was determined, according to Flowchart 4, based on the combination of Equations (14) and (20). The results are shown in Figure 22b. It can be seen that frequency dependencies of the SE, obtained by FEM and the proposed algorithm, are in good agreement, and \(\left|\Delta\right|=2.9\) dB.  
Figure 21: Frequency dependencies of the SE for enclosures from cases 2 (**a**) and 3 (**b**).  
Figure 20: Frequency dependencies of the SE for the empty enclosure with a squared aperture.  
Next, we analyzed the enclosure of the ABB FOX 515 multiplexer (Figure 23a) with a volume of 445 \(\times\) 270 \(\times\) 278 mm\({}^{3}\), a wall thickness of 1.5 mm, and an array of 108 \(\times\) 15 circular staggered apertures (\(r\) = 1.5 mm) located at the top of the front wall. In the analytical calculation, the \(Z_{ap}\) was determined according to Flowchart 3 using Equations (20) and (21). The equivalent circuit transformation was performed, taking into account the excitation of higher-order modes in the enclosure (mixture of \(TE_{10}\), \(TE_{20}\) and \(TE_{30}\) modes). Figure 23b shows the SE frequency dependencies of the multiplexer enclosure calculated by FEM and the proposed algorithm. A small discrepancy can be seen between the frequency dependencies at low frequencies and in the region of 750 MHz. For the most part, however, the results are in good agreement, and the value of \(\mid\Delta\mid\) is only 1.52 dB.  
Finally, using FEM and the proposed algorithm, we calculated the frequency dependencies of the SE for a cylindrical enclosure with a circular aperture at \(R\) = \(r\) = 150 mm and \(d\) = 300 mm. Moreover, the enclosure under study was completely filled with dielectric material, with \(\varepsilon_{r}\) = 3.7. In the calculation by the proposed algorithm, \(Z_{ap}\) was determined using (13) and (14). The transformation of the equivalent circuit was performed according to Flowchart 7, and \(\lambda_{c\,mn}\) was determined at \(m\) = \(n\) = 1. Figure 24 illustrates that the results obtained by the generalized algorithm and FEM are in agreement. In this case, the value of \(\mid\Delta\mid\) is 3.12 dB.  
Figure 23: Enclosure of the ABB FOX 515 multiplexer (**a**) and frequency dependencies of its SE (**b**).  
Figure 22: Shielding enclosure of the Ethernet filter (**a**) and frequency dependencies of its SE (**b**).