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The pre-corrected fast Fourier transform (PFFT)/adaptive integral method (AIM) is combined with the asymptotic waveform evaluation (AWE) technique to present fast RCS calculation for arbitrarily shaped three-dimensional PEC objects over a frequency band. The electric field integral equation (EFIE) is used to formulate the problem and the method of moments (MoM) is employed to solve the integral equation. By using the AWE method, the unknown equivalent current is expanded into a Taylor series around a frequency in the desired frequency band. Then, instead of solving the equivalent current at each frequency point, it is only necessary to solve for the coefficients of the Taylor series (called ldquomomentsrdquo) at each expansion point. Since the number of the expansion points is usually much smaller than that of the frequency points, the AWE can achieve fast frequency sweeping. To facilitate the analysis of large problems, in this paper, all the full matrices are stored in a sparse form and the PFFT/AIM method is employed to accelerate all the matrix-vector products on both sides of the matrix equation for the moments. Further, the incomplete LU preconditioner is used at each expansion point to improve the convergence behaviour of the matrix equation for the moments. The present method can deal with much larger problems than the conventional MoM-AWE method since the PFFT/AIM achieves considerable reduction in memory requirement and computation time. Numerical results will be presented to show the efficiency and capability of the method.