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An accurate discretization scheme for the numerical solution of time domain integral equations

Time-domain integral equation (TDIE) methods for the solution of electromagnetic scattering problems have steadily increased in popularity over the past few years. Despite the advances, accuracy enhancements for TDIE-based methods remain largely unstudied. While higher-order spatial discretizations can be accomplished with techniques designed for the frequency-domain method of moments (MoM), no basis has yet been reported for precision temporal modeling. Worse yet, because the stability properties of marching-on-in-time (MOT) schemes are not well understood, any accuracy gains made by purportedly high-order temporal bases are likely to be eradicated by incipient instability. To solve these problems, this study introduces a new band-limited interpolation function (BLIF) basis for temporal modeling, based on the Knab (1979) approximate prolate series. Because the highly noncausal nature of these functions precludes the application of standard MOT schemes, the approach used here is "fully-implicit", that is, the current on the entire scatterer for all times under consideration is solved at once. This method of moments time-domain (MoM-TD) approach also eliminates the stability question entirely. Higher-order spatial discretization is accomplished with the geometric mappings and divergence-conforming basis of Graglia et al. (1997).