Multilevel Fast Multipole Accelerating Condition And Application Research

With the development of electronic communication, higher requirements are needed for accurate and efficient analysis of electrically large complex targets scattering characteristics, which also has been enduring computational electromagnetic research hotspot and difficulty.This thesis is based on the method of moment (MoM) which can be used for arbitrary objects with high precision and has been widely used in the analysis of the electromagnetic scattering problems. However, the MoM costs a lot of memory and time for electrically large object. It is too difficult to solve the large dense linear systems fast and accurately, which formed by the integral equations. It is too hard to calculate the scattering of large-scale electromagnetic objects because of the computation limit. Later, Fast Multipole Method(FMM) and Multilevel Fast Multipole Algorithm (MLFMA) can greatly save the computational time and resource.Although MLFMA can accelerate the matrix-vector product operation, the number of iterations does not reduce at all in the iterative solution. Therefore, the preconditioning technology becomes more and more popular for the complex targets. The Physical Optics(PO)currents preconditioning and Local Multilevel Fast Multipole Algorithm (LMLFMA),which are based on MLFMA, is introduced to effectively reduce the numbers of iterations, further accelerate the matrix-vector product operation,and reduce overall computation time. Moreover, a hybrid algorithm, based on the PO currents and LMLFMA,is created to further improve the efficiency of iteration and has a better efficiency than any one.At last, MLFMA is applied to calculation of the Vlasov radiator in this paper. On the premise of keeping precision we improve the Vlasov radiator computation efficiency of the distribution of near field. EFIE is applied to calculation of near field of the Vlasov radiator, and MLFMA is applied to its speed.