In this paper, a hierarchical ultra-wideband characteristic basis function method (HUCBFM) is presented for high-precision analysis of wideband scattering problems. Unlike existing improved ultra-wideband characteristics basis function method (IUCBFM), HUCBFM reduces the number of characteristic basis functions (CBFs) necessary to express a current distribution. This reduction is achieved by combining primary CBFs (PCBFs) with the secondary level CBFs (SCBFs) to form a single hierarchical ultra-wideband characteristic basis function (HUCBF). As HUCBF incorporates the effects of PCBFs and SCBFs, the accuracy does not change significantly compared to that obtained by IUCBFM. Furthermore, the efficiencies of constructing the CBFs and filling the reduced matrix are improved. Numerical examples verify and demonstrate that the proposed method is credible both in terms of accuracy and efficiency.
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