The construction of low-dispersive FDTD on hexagon

Based on the sampling theorem with arbitrary geometry, the spatial discretization can be carried out on hexagonal lattices (grids) instead of rectangular lattices in the two-dimensional case. With the concept of the directional derivative in aid, a new finite-difference time-domain (FDTD) method based on hexagonal lattices (H-FDTD) is introduced. The coefficients of the H-FDTD method are chosen with aim to obtain the low numerical dispersion. Final numerical experiment shows that the numerical anisotropy of the H-FDTD method is lower than that of the conventional Yee-FDTD method based on rectangular lattices (R-FDTD). In addition, some numerical examples are provided to verify its good performance on the low numerical anisotropy.