An efficient algorithm combining the fast multipole method (FMM) and the characteristic basis function method (CBFM) for analysis of scattering from microstrip antennas over a wide band is introduced in this paper. In the hybrid algorithm, the characteristic basis function method is used to construct the currents on microstrip antennas by using characteristic basis functions (CBFs) which are constructed from the solution vectors at several samples using the singular value decomposition (SVD), thus obviating the need to repeatedly compute using a computational electromagnetic code and repeatedly solve a large method of moments matrix system at each point within the wide band of interest. The fast multipole method is used to obtain the solution vectors at these samples and speed up the matrix-vector product in the characteristic basis function method (CBFM). The resultant hybrid algorithm (FMM-CBFM) eliminates the need to generate and store the usual square impedance matrix and repeatedly use an iterative solver at each point and thus leads to a significant reduction in memory requirement and computational cost. Numerical examples are given to illustrate the accuracy and robustness of this method.
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