Electromagnetic Scattering Of Fast Multipole Method To Improve The Technology

The high efficiency and the low memory requirement are usually regarded as two dominant characters of the fast algorithms. This dissertation concentrates on how to enhance efficiency and to reduce memory cost of the methods. The contributions of this dissertation are as following.First, the Fourier transform of functions with polygonal support and linear amplitude variation are proposed to replace the Gauss Integral in MLFMA. These transforms can reduce the computational time of integral. Then, it is proposed to expand the k -space representation of the basis functions by spherical harmonics in order to reduce the sampling redundancy introduced by numerical quadrate rules.To efficiently solve large dense complex linear systems arising in the electric field integral equation formulation, the improved electric field integral equation (IEFIE) is developed to achieve fast and accurate solution of electromagnetic scattering from 3-D conducting structures. Then the near-field impedance matrix of EFIE with the principle value term of the magnetic field integral equation (MFIE) operator is used for building ILU(0) preconditioner. Numerical experiments indicate that this incomplete LU (ILU) preconditioner can reduce both the iteration number and computational time substantially.Combined-field integral equation (CFIE) is modified and generalized to formulate the electromagnetic problems of composite geometries involving both open and closed conducting surfaces. These problems are customarily formulated with the electric-field integral equation (EFIE) due to the presence of the open surfaces. With the new definition and application of the CFIE, iterative methods for these problems can converge significantly fast when compared to the EFIE without loss of the accuracy.