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 truncated 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 pre-computed 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 pre-computed matrices corresponding to the highest order basis need to be computed. All impedance matrices at different frequencies can be generated by these pre-computed matrices due to the hierarchical property of the basis functions. Numerical results show that the proposed method can greatly accelerate the wide-band scattering analysis.