摘要
引入一种新的数值计算方法—辛算法求解M axw e ll方程,即在时间上用不同阶数的辛差分格式离散,空间分别采用二阶及四阶精度的差分格式离散,建立了求解二维M axw e ll方程的各阶辛算法,探讨了各阶辛算法的稳定性及数值色散性.通过理论上的分析及数值计算表明,在空间采用相同的二阶精度的中心差分离散格式时,一阶、二阶辛算法(T 1S2、T 2S2)的稳定性及数值色散性与时域有限差分(FDTD)法一致,高阶辛算法的稳定性与FDTD法相当;四阶辛算法结合四阶精度的空间差分格式(T 4S4)较FDTD法具有更为优越的数值色散性.对二维TM z波的数值计算结果表明,高阶辛算法较FDTD法有着更大的计算优势.
A new scheme for approximating the solution of 2D Maxwell＇s equations using the symplectic scheme is introduced. The scheme is obtained by discretizing the Maxwell＇s equations in the time direction based on symplectic scheme with different orders, and then evaluated the equation in the spatial direction with a second or fourth order finite difference approximation. The stability condition and numerical dispersion of the schemes with different orders are de- rived. The results are demonstrated by theoretical analysis and numerical simulation, the stability and numerical dispersion of the scheme with first and second order symplectic scheme （T1S2,T2S2） are identical to FDTD with a second order approximation in spatial direction. Although the high order schemes have almost the same stability as the FDTD, the fourth order scheme with a fourth order approximation in spatial direction（T4S4） has the superior numerical disper- sion--isotropic properties of the scheme. Numerical results show that high order symplectic scheme is superior compared with FDTD for solving two-dimensional TMz case.
出处
《电子学报》
EI
CAS
CSCD
北大核心
2006年第3期535-538,共4页
Acta Electronica Sinica
基金
国家自然科学基金(NO.60371041)
