Finite-difference time-domain method for three-dimensional grid of hexagonal prisms

The finite-difference time-domain (FDTD) method was applied in a grid of hexagonal prisms, having as objective to yield less numerical anisotropy of phase velocity than the Yee FDTD method (with hexahedral cells). Comparisons of wave propagation are made between the FDTD method with grid of hexagonal prisms and the Yee FDTD method. The theoretical analyses of the numerical anisotropy, dispersion and stability condition are obtained using the Fourier analysis in the FDTD method with grid of hexagonal prisms. Measurements of numerical anisotropy are also accomplished in this FDTD method, and then ones are compared with the results of the Fourier analysis. As a result, the grid of hexagonal prisms yielded somewhat less numerical anisotropy and dispersion than the Yee grid. Additionally, a simplification in compensation of numerical dispersion in the grid of hexagonal prisms may improve on the accuracy and density of mesh for indoor buildings that are large, mainly in the xy-plane.