Envelope-tracking integral equation methods for band-pass transient scattering analysis
This dissertation presents envelope-tracking (ET) integral equation methods to efficiently analyze band-pass scattering problems. Unlike the traditional time-domain marching-on-in-time (TD-MOT) schemes, ET-MOT schemes solve for space-time samples of not the current density but its complex envelope. The time step size used in ET-MOT schemes is inversely proportional to the bandwidth of the fields of interest and not their maximum frequency content; thus, ET-MOT schemes can use (much) larger time step sizes for band-pass analysis: the smaller the bandwidth of the fields compared to their maximum frequency content, the larger the time step size in ET-MOT solutions compared to those in the TD-MOT solutions. Despite the reduction in the number of time steps, ET-MOT schemes suffer from high computational costs that also affect time- and frequency-domain integral equation methods. This dissertation presents an FFT-based algorithm, the ET adaptive integral method (ET-AIM), to reduce the computational complexity of ET-MOT schemes. ET-AIM is both theoretically and empirically compared to its time-domain and frequency-domain counterparts, TD-AIM and FD-AIM, respectively. Because the performance of the envelope-tracking methods is a complex function of the bandwidth of interest and because each method has different accuracy-efficiency tradeoff, only limited deductions can be made from theoretical comparison of the methods. Thus, in addition to theoretical comparisons, an empirical approach for comparing the different methods is presented: To perform a fair, meaningful, and generalizable comparison, benchmark problems are identified, an appropriate error norm is defined, and the key parameters of the methods are optimized subject to a constraint on the error norm. Computational costs are measured and compared for all three methods for solving progressively larger benchmark scattering problems for varying frequency bandwidths. This dissertation also proposes an out-of-core algorithm to ameliorate the high memory requirement of FFT-accelerated time-marching methods. The proposed algorithm exchanges the core memory requirement with external storage space requirement without significantly increasing the simulation time. The performance of the proposed methods is demonstrated by solving surface- and volume-integral equations pertinent to scattering problems that involve good conductors and inhomogeneous volumes with complex dielectric properties. For example, numerical results obtained using ET-AIM are presented for analysis of scattering of radar pulses from a PEC missile, a generic aircraft, etc. and antenna radiation near anatomically realistic human body model.