## 4 Conclusions  
The work presented in this document describes the development of a numerical analysis technique focused on complex radomes covering arbitrary antennas, by means of the separation of both domains (antenna and radome) and an iterative approach using macro-basis functions in order to ease the computational burden imposed by this kind of problem. We have found that this method performs efficiently compared with conventional alternatives with as few as three iterations between domains, offering good accuracy and convergence properties.  
The results presented in this work validate the analysis technique proposed for the simulation of complex radomes using CBFM-MLFMA and a domain decomposition ap  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Approach** & **Pre-Processing Time 1 (s)** & **Iteration Time (s)** & **Total CPU-Time (s)** \\ \hline MoM-MLFMA (newFASANT) & 13,586 & 27,964 & 41,550 \\ Proposed approach, 1 iteration & 17,670 & 4655 & 22,325 \\ Proposed approach, 2 iterations & 17,672 & 6650 & 24,320 \\ Proposed approach, 3 iterations & 17,672 & 9392 & 27,062 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison of the CPU-time required by the proposed approach with one, two, and three iterations between domains, and MoM-MLFMA.  
Figure 8: (a) Radiation pattern results considering the radome with the antenna and compared with the antenna alone; (b) frequency sweep around the resonant frequency considering the radome with the antenna and the antenna alone, showing the frequency filtering characteristics of the embedded FSS.  
proach. The agreement is good compared with the conventional MoM-MLFMA results, obtaining a noticeable efficiency improvement in the solution process. In this and many other cases analyzed by the authors, three iterations between domains offer a very good compromise between accuracy and computational efficiency. Future research may include the study of techniques that may offer a further efficiency improvement, such as adaptively limiting the distance within which the CBFs are coupled. In this regard, it seems that self-coupling CBFs do not provide accurate results and neighboring coupling CBFs offer better results, although still not comparable to the base algorithm proposed.  
An additional result from the work presented in this document was a fully parallelized computer tool for the analysis of radomes covering arbitrary antennas, which makes use of both shared and distributed memory paradigms (hybrid MPI/OpenMP approach) and can be executed on conventional computers, workstations, or large computing clusters.  
Conceptualization, C.D. and F.C.; Data curation, F.C.; Formal analysis, C.D.; Funding acquisition, C.D. and F.C.; Investigation, C.D.; Methodology, E.G.; Project administration, F.C.; Resources, F.C.; Software, C.D. and E.G.; Supervision, E.G.; Validation, E.G., and F.C.; Visualization, C.D.; Writing--original draft, C.D.; Writing--review & editing, C.D. All authors have read and agreed to the published version of the manuscript.  
This work was supported in part by the Junta de Comunidad de Castilla-La Mancha (Project Ref. SBPLY/17/180501/000433); by the Universidad de Alcala, project number CCG20/IA-063; and contracts ART.83 from Altair Inc. numbers REF.180/2019, 181/2019, and 183/2019.  
The authors declare no conflict of interest.