# Iterative MLFMA-MADBT Technique for Analysis of Antenna Mounted on Large Platforms
## 1 Introduction  
The analysis of the antennas mounted on large complex platforms is of growing importance in the area of computational electromagnetics (CEM). For analysis of large electromagnetic problems in frequency domain, there are two main kinds of method: the low-frequency numerical method and the high-frequency asymptotic method. Among the low-frequency methods, the method of moments (MoM) [1], the multi-level fast multiple algorithm (MLFMA) [2, 3], the precorrected-FFT (P-FFT) [4] and the adaptive integral method (AIM) [5] are developed to provide reliable accuracy. However, the expensive computational resources cost of the low-frequency methods makes them unsuitable for the analysis of the radiation problem including large platforms. In the high-frequency asymptotic area, the physical optics (PO) and the iterative PO based on ray tracing (RT) has been widely used in the analysis of electromagnetic scattering and radiation. The shouting and bouncing ray (SBR) technique [6] is one of the most efficient ways to predict the scattering field of electrically large and complex targets with great accuracy and efficiency. The divergence problem in the RT leads to the beam tracing method (BT) in which the ray tube is replaced by the adaptive division beam [7, 8]. A promising approach to solve this problem is to combine the fast but approximate high-frequency asymptotic method and the slow but accurate low-frequency method to produce a hybrid technique. The method of moments-physical optics (MoM-PO) [9, 10, 11, 12] and the multi-level fast multipole algorithm-physical optics(MLFMA-PO) [13] are the mostclassic hybrid technique with high accuracy and high efficiency. The high order MoM-PO [14; 15] method was introduced to decrease the number of unknowns. The method of moments-iterative physical optics (MoM-IPO) method is developed to model the multi-bounce effects outside the MoM region [16]. To consider the interaction between the MoM region and the PO region, the matrix-vector production (MVP) is applied in the iterative MLFMA-PO method [13] at the expense of computation time. In this paper, a modified adaptive division beam tracing (MADBT) is proposed to model the multi-bounce effects outside the MLFMA region. In contrast to the previous work, which only uses the BT to solve the scattering problem under the plane wave [17], we use the BT for analyzing the complex radiation problem. To the best of our knowledge, it is the first time that the beam-based method is used to analyze the antennas mounted on large platforms. A point source in the MLFMA region is used as the original point of the MADBT when considering the coupling from the MLFMA region to BT region. And the radiation pattern of the point source is modeled by the FFAFA-FMLMA [18] after a quantitative estimation of the size of the MLFMA region. Thus, the proposed MLFMA-MADBT hybrid method can also be used to analyze complex antenna structure such as patch antenna array. In detail, the analysis of the antennas mounted on large platforms is solved in several steps: First, the strong coupling problem, namely the connection between the antenna and the platform, is solved and decoupled by partitioning a transition region surrounding the junction. Second, the coupling interaction between the MLFMA region and the BT region is calculated with the induced field from one region to another region. The field from the MLFMA region acts as the incident field of the initial beams launched toward the BT region, while the PO field from the BT region impacts on the MLFMA region as an additional excitation voltage vector. Third, by applying the MADBT method, the multi-bounce effects within the platform can be obtained. The MADBT method is based on beams rather than the PO current, which means the MVP can be avoided and memory usage can be greatly reduced. Furthermore, the BT process of the MADBT method only depends on the geometry of the platform, so the adaptive division of BT is mesh-independent.