As the fastest integral equation solver to date, the multilevel fast multipole algorithm （MLFMA） has been applied successfully to solve electromagnetic scattering and radiation from 3D electrically large objects. But for very large-scale problems, the storage and CPU time required in MLFMA are still expensive. Fast 3D electromagnetic scattering and radiation solvers are introduced based on MLFMA. A brief review of MLFMA is first given. Then, four fast methods including higher-order MLFMA （HO-MLFMA）, fast far field approximation combined with adaptive ray propagation MLFMA （FAFFA-ARP-MLFMA）, local MLFMA and parallel MLFMA are introduced. Some typical numerical results demonstrate the efficiency of these fast methods.
Hu Jun Nie Zaiping Lei Lin Hu Jie Gong Xiaodong Zhao Huapeng
This paper introduces the research work on the extension of multilevel fast multipole algorithm （MLFMA） to 3D complex structures including coating object, thin dielectric sheet, composite dielectric and conductor, cavity. The impedance boundary condition is used for scattering from the object coated by thin lossy material. Instead of volume integral equation, surface integral equation is applied in case of thin dielectric sheet through resistive sheet boundary condition. To realize the fast computation of scattering from composite homogeneous dielectric and conductor, the surface integral equation based on equivalence principle is used. Compared with the traditional volume integral equation, the surface integral equation reduces greatly the number of unknowns. To computc conducting cavity with electrically large aperture, an electric field integral equation is applied. Some numerical results are given to demonstrate the validity and accuracy of the present methods.
