## 5 Numerical Results
Since CST-MWS cannot simulate the infinite holed resistive plane, it has been approximated with a zero-thickness resistive annular ring of internal radius \(a\) and external radius \(a\). The amplitude of the surface current density on the disk along the direction \(\theta=90^{\circ}\) and \(\phi=0^{\circ},180^{\circ}\), for \(a=\lambda/2\), \(R_{i}=100\)\(\Omega\), \(R_{e}=1\) k\(\Omega\), and normal incidence of the plane wave (\(\theta_{0}=0^{\circ}\)) with incident electric field along the direction \(\theta=90^{\circ}\) and \(\phi=90^{\circ},270^{\circ}\), is compared with the behavior obtained by using the integral equation solver of CST-MWS for two values of the external radius, \(a=4a,8a\). As expected, the CST-MWS solution tends to the one provided by the proposed method as the external radius increases, and a quite good agreement can be observed for \(a=8a\). However, the proposed method requires 9 expansion functions and 2 azimuthal harmonics (for \(n=\pm 1\)), which results in 648 matrix coefficients, to achieve a truncation error less than \(10^{-3}\) with a computation time of 2.5 s, whereas CST-MWS needs more than 5 million mesh-cells with a computation time of about 10 min to reconstruct the solution for \(a=8a\). It is obvious to conclude that the proposed method drastically outperforms CST-MWS in terms of both computation time and storage requirements. Figure 2: (**a**) Truncation error, (**b**) amplitude of the effective surface current density on the disk, and (**c**) BRCS for \(a=2\lambda\), \(R_{e}=1\,\mathrm{k}\Omega\), and \(R_{i}=10\,\Omega,100\,\Omega,500\,\,\Omega\), when a TE polarized plane wave impinges onto the structure with \(\theta_{0}=30^{\circ}\) and \(\phi_{0}=0^{\circ}\). \(N=15\) for all the cases examined. Figure 3: (**a**) Truncation error, (**b**) amplitude of the effective surface current density on the disk, and (**c**) BRCS for \(R_{i}=100\)\(\Omega\), \(R_{e}=1\)\(\mathrm{k}\Omega\), and \(a=\lambda,\ 2\lambda,\ 4\lambda\), when a TM polarized plane wave impinges onto the structure with \(\theta_{0}=30^{\circ}\) and \(\phi_{0}=0^{\circ}\). \(N=11,\ 15,\ 23\) for \(a=\lambda,\ 2\lambda,\ 4\lambda\), respectively. To conclude, in Figure 5, the near diffracted and total electric fields in the plane \(\phi=0^{\circ}\), \(180^{\circ}\) are plotted for \(a=2\lambda\), \(R_{i}=100\)\(\Omega\), \(R_{e}=1\) k\(\Omega\), and TE incidence of the plane wave with \(\theta_{0}=30^{\circ}\) and \(\phi_{0}=0^{\circ}\). In this figure, the symmetric behavior of the diffracted electric field with respect to the structure with a maximum in the specular with respect to the incidence direction and the forward direction can be appreciated. Moreover, observing the total electric field behavior, it is clear that the interference between the incident and reflected waves, on one hand, and the transmitted wave, on the other hand, are perturbed by the diffraction due to the discontinuity between the two involved resistive media. Figure 4: Amplitude of the effective surface current density on the disk, for \(a=\lambda/2\), \(R_{i}=100\)\(\Omega\), \(R_{e}=1\) k\(\Omega\), and normal incidence of the plane wave (\(\theta_{0}=0^{\circ}\)) with the incident electric field along the direction \(\theta=90^{\circ}\) and \(\phi=90^{\circ}\), \(270^{\circ}\), reconstructed by means of the presented method, and using CST-MWS by approximating the holed resistive plane with a zero-thickness resistive annular ring of internal radius \(a\) and external radius \(a=4a,8a\). Figure 5: _Cont._