The improved ultra-wide band characteristic basis function method (IUCBFM) is an efficient approach to analyze the wide-band scattering problems because the improved ultra-wide characteristic basis functions (IUCBFs) can be reused for any frequency sample in the range of interest. However, the number of the IUCBFs constructed at the highest frequency point is excessive, and the computational complexity will be increased when applying the same number of IUCBFs at the lower frequency points. To mitigate this problem, an adaptive IUCBFs construction method is presented which can decrease the computational complexity at the lower frequency points. In the proposed method, the given frequency band is adaptively divided into multiple sub-bands in consideration of the number of the IUCBFs. The adaptive IUCBFs are obtained at the highest frequency point in each sub-band, which leads to smaller number of IUCBFs and significant reduction of solver time at lower frequency band. The numerical results have demonstrated the accuracy and efficiency of the proposed method.
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