In this paper, the Adaptive Modified Characteristic Basis Function Method (AMCBFM) is proposed for quickly simulating electromagnetic scattering from a one-dimensional perfectly electric conductor (PEC) rough surface. Similar to the traditional characteristic basis function method (CBFM), Foldy-Lax multiple scattering equations are applied in order to construct the characteristic basis functions (CBFs). However, the CBFs of the AMCBFM are different from those of the CBFM. In the AMCBFM, the coefficients of the CBFs are first defined. Then, the coefficients and the CBFs are used to structure the total current, which is used to represent the induced current along the rough surface. Moreover, a current criterion is defined to adaptively halt the order of the CBFs. The validity and efficiency of the AMCBFM are assessed by comparing the numerical results of the AMCBFM with the method of moments (MoM). The AMCBFM can effectively reduce the size of the matrix, and it costs less than half the CPU time used by the MoM. Moreover, by comparing it with the traditional CBFM, the AMCBFM can guarantee the accuracy, reduce the number of iterations, and achieve better convergence performance than the CBFM does. The second order of the CBFs is set in the CBFM. Additionally, the first order of the CBFs of the AMCBFM alone is sufficient for this result.
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