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Construction of 3D FDTD schemes with frequency-dependent operator coefficients

Aiming at the minimization of numerical dispersion effects in finite-difference time-domain (FDTD) simulations, we investigate the potential of introducing frequency-dependent coefficients in the approximations of differential operators. The proposed methodology exploits some previous results on optimized finite-differences, but initially avoids the necessity for selecting a specific optimization point. Herein, the operators' coefficient formulae are approximated by a low-order polynomial, which is transformed into a finite-difference counterpart using the Helmholtz equation. This modifies the initial spatial stencil and improves performance over all frequencies, which can be further controlled with the least-squares method, leading to various new FDTD schemes of augmented reliability.