An Adaptive Marching-on-in-Order Method With FFT-Based Blocking Scheme

An adaptive marching-on-in-order (MOO) method with FFT-based blocking scheme is proposed to solve the time-domain electric field integral equation (TD-EFIE) for conductive objects, with the temporal basis of Laguerre polynomials (LP) employed. In contrast to most MOO approaches that utilize a priori fixed order of weighted LP for the temporal variation, we choose suitable polynomial order by computing the relative error of the weighted LP expansions. Thus, the accuracy of the MOO scheme is guaranteed. A general principle for choosing the optimal scaling factor of LP is presented, which is crucial for efficiently predicting scattering information of objects. The fast Fourier transform (FFT)-based blocking scheme is also implemented to reduce the computational complexity to O(N_S² N_o log² (No))Numerical results that demonstrate the accuracy and efficiency of this methodology are presented.