An explicit finite difference time domain method with high order accuracy in time for Maxwell's equations

Time discretization is an important research topic, concerning with stability,convergence, accuracy and computational complexity. In this paper, a new explicit time marching methodwith any high accuracy and ease of combining with spatial discretization methods is proposed. By this method andcentral difference methods an explicit finite difference time domain method (called HAIT-FDTD) for three dimensionalMaxwell's equations is proposed and shown to be second order accurate in space and M-th order in time, where M is polynomial degree and can be chosen to be any integer greater than three. By Fourier method it is proved that HAIT-FDTD is stable, and independent of the CFL number when M is large enough, and that the numerical dispersion relation of HAIT-FDTD converges to the one in theory. Numerical experiments to compute amplification factors and numerical dispersion error, and to solve a wave guide problem are carried out. Experimental results confirm the analysis in theory and show that HAIT-FDTD has the following advantages: (i) numerical dispersion error is less than that of Yee scheme and ADI-FDTD; (ii) it is approximately energy conserving and divergence free; (iii) it has the merits of Yee scheme and ADI-FDTD such as easy implementation and taking relatively large step size; (iv) it is efficient in a long time computation and it saves much CPU time than ADI-FDTD.