Coefficients of Finite Difference Operator for Rectangular Cell NS-FDTD Method

The nonstandard finite difference time domain (NS-FDTD) method is a dispersion error reduction technique for the FDTD method. High accuracy is achieved by the optimal selection of the coefficients used for the finite difference (FD) operators in the NS-FDTD method. However, the previously published method of obtaining the coefficients for rectangular cells, using a full numerical technique, takes an enormous amount of computing time. To solve this difficulty, we propose a semi-analytical method to obtain the optimal coefficients with a far higher computational efficiency. It is shown, by numerical tests, that the optimal coefficients need six significant digits for accurate NS-FDTD solutions. Consequently our new method can reduce the computing time to obtain the optimal coefficients from an estimated 42 × 10⁴ minutes by the previous method to about 7 seconds for three dimensional rectangular cells.