Grid-Dispersion Error Reduction for Broadband Electromagnetic Simulations

摘要

We introduce a generic procedure to reduce numeric (grid) dispersion error in finite-difference time-domain (FDTD) simulations. Dispersion error functionals are expanded in a Taylor series that, for a broadband signal, indicates larger dispersion errors for high frequency components. By a change of basis, modified FDTD update coefficients are obtained instead in order to minimize the dispersion error over some pre-assigned frequency band. Moreover, desirable properties such as a local dispersion error that decreases within a frequency band can be attained. In particular, Butterworth (maximally flat) or Chebyshev expansions are considered along with their application to tile optimization of two high order FDTD schemes.