FDTD Schemes With Minimal Numerical Dispersion

A novel formulation of hybrid finite-difference time-domain (FDTD) methods is presented. Significant reduction of numerical dispersion is achieved by the proposed FDTD methods that combine the second-order and higher-order finite-differences. Also, the proposed FDTD methods exhibit significantly higher solution accuracy than the accuracy of standard FDTD schemes as a result of partial mutual cancellation of numerical errors provided by the developed FDTD update procedure. The residual numerical error of the phase velocity remains low even for sampling of a few points per wavelength. Also, the FDTD schemes based on the proposed approach are faster and more accurate than the corresponding purely higher-order FDTD schemes with the same mesh. Test examples are provided for validation purposes.