Electromagnetic solution for dielectric objects with multilevel fast multipole algorithm and singular value decomposition

The efficient calculation of the electromagnetic interactions with dielectric objects is always a challenge to CEM (computational electromagnetics). Among the numerical exact methods, the method of moment (MoM) is considered to be more preferable than finite element method (FEM) and finite difference method (FDTD) for its high precision and discretization on the geometry model instead of the field space. However, MoM generates a dense matrix, which handicaps its applications in electrically large problems. One way to improve the efficiency of MoM is to speed up the matrix-vector multiplication and reduce the memory requirement. For this purpose, a number of effective fast algorithms had been developed, such as the multilevel fast multipole algorithm (MLFMA), the fast Fourier transform (FFT) techniques, and the adaptive integral method (AIM), etc.