WHEN EVALUATING PROBLEMS like the radar cross section (RCS) of an object, the system response must often be calculated at multiple frequencies. If traditional frequency-domain numerical methods are used to accomplish this task, a dense matrix equation must be solved at each frequency. Several approaches can alleviate this time-consuming computational burden. To further speed processing, a model-order reduction algorithm for the volume electric-field-integral-equation (EFIE) formulation has been presented by Patrick Bradley, Conor Brennan, and Marissa Condon from Dublin City University's School of Electronic Engineering. This algorithm vows to achieve fast and accurate frequency sweep calculations of electromagnetic (EM) wave scattering.
Specifically, the researchers use an efficient and mathematically stable, projection-based algorithm for model-order reduction called the well-conditioned asymptotic waveform evaluation (WCAWE). They then apply that algorithm to the volume EFIE formulation. The algorithm produces a well-conditioned and higher-order approximation from a single expansion point with a significantly wider bandwidth than that obtained from model order reduction techniques like Pad via Lanczos (PVL) via AWE and its variants. It overcomes the loss of accuracy as the order increases due to the explicit momentmatching process and the ill-conditioned Pad coefficient matrix.
In their work, the researchers investigate the variation of the dielectric properties of the ceramic BaxLA4Ti2 + xO12 + 3x in the sub-1-GHz range for various values of x in a frequency sweep analysis. Next, they apply the WCAWE method to circumvent the computational complexity associated with the numerical solution of such formulations. The researchers also demonstrate a multipoint, automatic WCAWE method that can produce an accurate solution over a much broader bandwidth. Several numerical examples are provided to illustrate the accuracy and robustness of the proposed methods. For varying contrast profiles, a significant reduction in system size can be achieved. See "Efficient Wideband Electromagnetic Scattering Computation for Frequency Dependent Lossy Dielectrics Using WCAWE," IEEE Transactions On Antennas And Propagation, October 2009, p. 3274.