Numerical Stability and Dispersion Analysis of the Precise-Integration Time-Domain Method in Lossy Media

In this paper, both the numerical stability condition and dispersion relation of the precise-integration time-domain (PITD) method in lossy media are presented. It is found that the time step size of the PITD method is limited by both the spatial step size of the PITD method and the ratio of permittivity to conductivity. In numerical dispersion investigations, it is shown that: the numerical loss error of the PITD method is always positive; the numerical phase error of the PITD method can be positive or negative; the numerical loss and phase errors can be made nearly independent of the time step size; and as the spatial step size decreases, the amplitudes of the numerical loss and phase errors decrease. In good conductors, the numerical phase velocity of the PITD method is closer to the physical value as compared with the finite-difference time-domain method. The numerical phase anisotropy of the PITD method can be positive or negative. The numerical anisotropies of the PITD method in the 3-D case are usually larger than those in the 2-D case. There is a conductivity giving zero numerical phase anisotropy. These theoretical observations are confirmed by numerical experiments.