Fast And Efficient Algorithm Based On The Multilevel Fast Multipole Method

To realize efficient solution of electromagnetic (EM)?scattering from complex target has very practical value for the design of radar system and identify of radar targets. Nowadays, more and more engineering projects need faster and more efficient methods to solve such problems. Even though two most attractive solvers—fast multipole method (FMM) and multilevel fast multipole algorithm (MLFMA) are used, they are still time consuming in solving the scattering problems of large objects. Based on MLFMA, this paper uses several approximate methods, and implement some highly efficient and fast methods to analyse EM scattering of complex 3D targets. Compared with the traditional algorithms, they can work much faster still with a reasonable accuracy. This characteristic makes them suitably to be implemented into engineering projects. This paper gives numerical results to compare with those of MLFMA , which prove the efficiency of the algorithms.Firstly, the integral equation methods used for analysis of scattering are reviewed. As the basis of fast multipole method, the key techniques of moment of method such as target modeling and the choice of basis/test functions are discussed.Secondly, the fast multipole method (FMM) and the multilevel fast multipole algorithm (MLFMA) are studied in detail. After expatiating their principles and numerical computing process, the paper gives some results to affirm their correctness.At last, several highly effcient algorithms based on MLFMA are extensively studied, such as adaptive ray-propagation MLFMA (ARP-MLFMA) , fast far-field approximation MLFMA (FAFFA-MLFMA) and fast far-field approximation partial coupling MLFMA (FAFFA-PC-MLFMA). Using physical principle of scattering, these methods divide the groups in the coarsest level into different regions, and simplify the translator of MLFMA. Hence, the computational cost is reduced greatly, especially when the number of unknowns is very large.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 more and more engineering projects.