A Wideband Electromagnetic Scattering Analysis Using MLFMA With Higher Order Hierarchical Vector Basis Functions

A method of the multilevel fast multipole algorithm (MLFMA) with the higher order hierarchical vector basis functions is introduced to solve the wideband electromagnetic scattering problems in frequency domain. Instead of employing different meshing grids at different frequencies, this new method requires only one coarse mesh generated at the lowest frequency of the given bandwidth. The scattering at other higher frequency sample points can be calculated simply by adjusting the order of the bases. This approach saves much work in geometrical modeling and leads to less unknowns than using the traditional bases for wideband scattering problem. Some important parameters in the numerical calculation (for example, the patch size, the order of the basis, and the cube size in the finest layer of MLFMA, etc.) and their coordination related to this new method are also discussed in detail. An improved interpolation method is introduced to get scattering results without the direct calculation at the points beyond the frequency samples. Some numerical examples are presented in this paper to show the advantages of the method in the wideband scattering analysis.