Low-Dispersion Leapfrog WCS-FDTD with Artificial Anisotropy Parameters and Simulation of Hollow Dielectric Resonator Antenna Array

An optimized three-dimensional one-step leapfrog finite-difference time-domain (FDTD) method has been investigated, which is with a weakly conditional stability (WCS) to reduce numerical dispersion further. By introducing the artificial anisotropy parameters in a cross-correspondence manner, the phase velocity error is effectively limited without additional computational time and memory cost. An auxiliary field variable is adopted to simplify the iterative formulae with few additional processes; and the same stability has been validated between methods of conventional leapfrog WCS-FDTD and ourselves. Moreover, much lower numerical dispersion is shown to withstand larger Courant-Friedrich-Levy number under the same error condition. To verify our method efficiently, a newly designed hollow dielectric resonator antenna (DRA), instead of a solid one, is conducted effective calculation. Furtherly, two forms of four-elements arrays have been developed with the DRA element above; and a T-shaped power divider are designed as a fed-network and subjected to calculations and experimental analyses. Reflection coefficients and radiation patterns are shown the effectiveness of both DRA and arrays. The most noteworthy aspect is that our low-dispersion WCS-FDTD scheme can be effectively simulated the hollow DRA and arrays, and with excellent performance in terms of memory occupation, calculation accuracy, and efficiency.