Fast Wideband Scattering Analysis Based on Taylor Expansion and Higher-Order Hierarchical Vector Basis Functions

A fast wideband electromagnetic scattering analysis method based on Taylor expansion and higher order hierarchical vector basis functions is proposed. By extracting a phase term from the green function, the remaining exponent term can be approximated by its Taylor expansion. After that, some computationally intensive matrices related to the geometry of the object can be computed in advance. During the frequency sweeping process, the impedance matrix is generated efficiently by combining the precomputed matrices and some frequency dependent terms. By using higher order hierarchical vector basis functions, only one coarse mesh corresponding to the lowest frequency of the given frequency band is generated. The order of the basis functions increases with the rising of frequency. Moreover, only the precomputed matrices corresponding to the highest order basis need to be computed. All impedance matrices at different frequencies can be generated by these precomputed matrices due to the hierarchical property of the basis functions. The proposed method is implemented in the platform of the multilevel fast multipole algorithm (MLFMA). Numerical results show that the proposed method can efficiently accelerate the wide-band scattering analysis.