Based On The Fast Multipole Method For Efficient Iterative Method And Its Engineering Applications

With the development of the stealth and anti-stealth of the military targets, the radar system design and the radar recognition technology, the electromagnetic scattering property of the complex targets needs to be solved accurately and efficiently. The fast multipole method (FMM) and the Multilevel fast multipole algorithm (MLFMA) based on the method of moment (MOM) are the efficient algorithm for solving integral equation. For its high accuracy, it meets the analysis of the EM scattering property of the complex targets. The MLFMA must be further optimized to cope with the complex engineering. Firstly, the differential equation methods, the integral equation methods and the hybrid methods used for analysis of scattering are reviewed. As the basis of FMM, the key techniques of MOM such as geometry modeling and the choice of basis/weight functions are discussed. The FMM and the MLFMA are studied in detail. Secondly, the key points for RCS accuracy in MLFMA have been summarized. Including geometry modeling, electromagnetic modeling, the selection of integral equation, detailed technical requirement is provided to assure the accuracy. The challenges raise from the application are present, and advice for the optimization of the algorithm are list. At last, several highly efficient iterative algorithms based on MLFMA are extensively studied. Such as use preconditioned conjugate gradient (PCG) algorithm to reduce the iterative steps, use modified multipole numbers method to reduce the computation of each step. All numerical results in the paper agree well with the results in the references and those computed by confirmed numerical programs. It proves well their high efficiency and accuracy. The research work in this paper provides a useful means for fast analysis of scattering from complex 3D targets with large electrical size and gives strong support to engineering.