电导率不为零的麦克斯韦方程的分裂时域有限差分方法

Splitting Finite-difference Time-domain Methods for Maxwell's Equations with Non-zero Electrical Conductivity in Two Dimensions

考虑带有非零电导率的二维麦克斯韦方程的分裂时域有限差分方法,利用分裂技巧,给出了一般分裂有限差分格式(S-FDTDI)和修正格式(S-FDTDII),推导出局部截断误差和格式的计算步骤。误差表达式表明格式I关于时间是一阶的,校正后的格式II是二阶的。数值试验验证了理论分析,计算结果表明这两种格式都是无条件稳定的,且在模拟一类波导问题时,格式II比格式I更精确。同时给出S-FDTDII与ADI-FDTD的比较,发现前者比后者更好,计算时间短,精度高。

Splitting finite-difference time-domain methods of two dimensional Maxwell＇ s equations with electrical conductivity is considered. Two kinds of schemes, S-FDTDI and S-FDTDII are proposed by using non-zero splitting technique and correcting techniques. Truncation error of the two schemes is derived and show that S-FDTDI is first order accurate and S-FDTDII is second order accurate in time. Numerical experiments are carried out and computational results show that S-FDTDII is more accurate than S-FDTDI for simulating the two schemes are unconditionally stable and that S-FDTDII is more accurate Maxwell＇ s equations with non-zero electrical conductivity. a wave guide problem that both of than ADI-FDTDI for approximating