Optimal Coefficients of the Spatial Finite Difference Operator for the Complex Nonstandard Finite Difference Time-Domain Method

Optimal coefficients of the spatial finite difference (FD) operator for the complex nonstandard finite difference time-domain (CNS-FDTD) method are presented. To derive the optimal coefficients that minimize the dispersion error, we employ a semianalytical method based on the FD Laplacian. The propagation constant is a complex number in lossy media, therefore, the derivation of the coefficients is more complicated than the derivation for the NS-FDTD method. It is confirmed by numerical tests using the numerical dispersion equation that our coefficients give the CNS-FDTD method a higher accuracy than the standard FDTD method. The coefficients are used for the reflection analysis of a grid ferrite electromagnetic wave absorber, and the validity of the coefficients is shown. The calculation time to derive the coefficients is negligible compared with that for the CNS-FDTD calculations themselves.