The Fast Multipole Method In Electromagnetic Field Research

The fast multipole method (FMM) and the multilevel fast multipole algorithm(MLFMA) are new efficient methods for analysis problems of electrically large objects. It become possible to solving large-scale problems of EM scattering on a small computer even a personal computer by the approach. The methods have very practical value and foreground of the applied. There have important realistic significance to study the methods.Firstly, in this paper, the theory of FMM and MLFMA is summarized ; Immediately, the foundation of FMM and MLFMA is introduced. It includes: moment method, triangular patch model and vector triangular basis function(RWG), solving electric field integral equation (EFIE) by MM, numerical integration technique and conjugate gradient (CG) for solving liner equations. Then, as the example , we analyze the RCS of the conductor cylinder (2D). At the same time, the steps of FMM, computational complexity and memory requirement are presented. Again we analyze RCS of the conductor sphere (3D) , and some techniques in the application of FMM are presented. So the algorithm has been optimized.Lastly, a kind of deformed FMM-The thin-stratified medium fast multipolealgorithm (TSM-FMA) is presented for solving problems of thin stratified structures.TSM-FMM reduces computational complexity to o(NlogN) for sparse structures and to o(N) for dense structures, from o(N3) for the Gaussian elimination method and o(N2) per iteration for the CG method. The memory requirement for TSM-FMM isalso o(NlogN) for sparse structures and o(N) for dense structures.As the total, we research primarily and verify FMM and MLFMA in this paper, and analysis of the microstrip structures by TSM-FMA. All those have formed a good base for the further.