A comparison of some model order reduction techniques

In this paper, an analysis of some model order reduction (MORe) techniques is presented. More precisely, this paper considers asymptotic waveform evaluation (AWE), Galerkin asymptotic waveform evaluation (GAWE) with a short-term vector recurrence relation, multipoint Galerkin asymptotic waveform evaluation (MGAWE) also using a short-term recurrence, and matrix-Pads via Lanczos (MPVL). These techniques are applied to matrix equations resulting when the finite element method (FEM) is tried to model electromagnetic wave propagation problems. The reduced order model equations can then be solved repeatedly to obtain a wideband frequency simulation with a reduction in total computation tune. The analysis contained herein compares and contrasts the MORe techniques by not only considering the nature of the individual algorithms, but also solving several illustrative numerical examples. These examples show how, for a MORe technique, a radiation and scattering problem might have to be treated very differently. In addition, it is noted that the unknown(s) desired as output(s) from the FEM mesh can influence which MORe technique is more efficient. The solutions obtained through the MORe techniques are compared to an LU decomposition at each frequency point of interest to benchmark their accuracy and efficiency.