等离子体模型ADI-FDTD格式的最大模误差估计及外推

在周期边界条件下,首先提出了求解二维等离子体麦克斯韦方程组的交替方向隐式时域有限差分(alternating direction implicit finite-difference time-domain, ADI-FDTD)格式,然后利用离散能量法,给出了该格式的先验估计,并由此证明了该格式在最大模意义下具有时空二阶收敛性。在此基础上,为了提高数值结果的精度,利用截断误差的渐近展开式对所提出的ADI-FDTD格式做Richardson外推,得到了时空四阶精度的算法。最后通过数值实验验证了理论结果。

Maximum norm error estimate and extrapolation of the ADI-FDTD scheme for plasma model

The ADI-FDTD scheme for solving the two-dimensional Maxwells equations in plasma media is proposed under periodical boundary conditions. A prior estimate of the proposed scheme is given by using the discrete energy method, and it is proved that the scheme is of second-order accuracy both in time and space in the sense of the maximum norm. In order to improve the accuracy of the numerical results, Richardson extrapolation is applied to the proposed ADI-FDTD scheme by using the asymptotic expansion of the truncation error, and we obtain the algorithm having fourth-order accuracy both in time and space. Finally, the theoretical results are verified by numerical experiments.