## 3 Numerical Results  
This section provides a test case considering a complex scenario in order to validate the accuracy and computational efficiency of the method described in the previous sections. The simulations with which the approach presented in this work has been compared using the conventional MoM-MLFMA and named as such in several plots contained in this section were carried out using the commercial software Altair newFASANT, which has been extensively validated in the past. The scenario, shown in Figure 4, contains a Cassegrain reflector antenna fed by a conical horn, and this radiating system is covered by a hemispherical dome composed by two radomes: one at the top containing two dielectric layers with an FSS embedded within the inner interface (closest to the antenna), and a second radome at the bottom containing a single layer of dielectric. Both radomes are aligned, creating a perfectly smooth outer surface. Figure 4: Geometrical model of (**a**) antenna, containing a conical horn and a Cassegrain Reflector; (**b**) the full scenario, containing the antenna covered by a hemispherical dome built using a two-layered radome with a cross-shaped FSS embedded within the inner interface at the top, and a single layer radome at the bottom. The diameter of the parabolic reflector is 200 mm and that of the hyperbolic sub-reflector is 67.2 mm. The working frequency is 14 GHz. The aperture of the conical horn is centered at the origin of coordinates and lays on the \(z=0\) plane. The vertex of the sub-reflector is located at \(z=70\) mm. There are four strips modeling supporting struts. The external diameter of the dome structure is 242 mm. The first radome extends from the tip of the dome at \(z=121\) mm down to \(z=69.18\) mm, and is composed of an inner layer of dielectric with a thickness of 1 mm, \(\varepsilon_{r}=1.12\), and tan \(\delta=0.002\), and an outer layer with a thickness of 0.6 mm and \(\varepsilon_{r}\)= 4.3. The second radome extends from \(z=69.18\) mm down to \(z=0\) and contains a single layer of dielectric material matching the outer layer of the first radome, which makes the external surface of the dome structure continuous. There is an FSS on the inner interface of the first radome. This FSS was designed using the unit cell shown in Figure 5 on a planar layout and then projected onto the curved interface of the radome. The same figure shows the reflection and transmission coefficients of this FSS using the infinite periodic Green's function for a plane wave impinging in the \(-z\) direction and a frequency sweep ranging from 4 GHz to 24 GHz. After mapping the FSS elements on a curved surface, the electromagnetic behavior of the structure can differ from that computed over an infinite planar layout. However, such a layout is a good starting point, allowing very fast simulations to design the unit cell. After projecting the FSS onto the curved interface, the resonance frequency may shift, which could require adjustments on the planar design (like cell scaling and so on). In many cases, such as that presented in this work, the curved design retains the frequential behavior originally desired and no further modifications are required. The aforementioned test case was simulated using the conventional MoM-MLFMA approach as well as the technique proposed in this document, considering one, two, and three interactions between the antenna and radome domains following the iterative approach described in the previous section. The total number of NURBS surfaces used to model the scenario was 623. The number of low-level basis functions (rootfops) was 883,013. The number of blocks was 652 and the total number of CBFs was 153,899. The simulations were performed using a workstation containing two Intel Xeon E5-2690 processors with 128 GB of RAM and considering the electric field integral equation (EFIE) formulation.