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The spectral order of accuracy: A unified ool for designing excitation-adaptive wave equation FDTD schemes

The spectral order of accuracy (SOoA), defined herein, is a general property of a given FDTD scheme that is shown to encompass the traditionally defined order of accuracy (OoA) as well as the numerical dispersion relationship. Using the SOoA, it becomes possible to design schemes tailored to a given excitation spectrum in order to reduce the overall error. While the conventional OoA is related to a special case of the SOoA, defined about the origin of the dispersion curve, the general definition of the SOoA applies to cases where the OoA is undefined. Since the OoA becomes irrelevant for a pulse whose spectrum does not have a DC component, it can be traded for higher accuracy in terms of numerical dispersion errors. The SOoA concept consolidates and simplifies the methodology reported in [1] and [2]. This methodology is shown to encompass both existing [3] and new schemes. Numerical examples demonstrate the improvement in long term errors for a modulated pulse.