摘要
数值求解三维时域Maxwell方程的过程中,保持方程的内在结构显得尤为重要.利用Hamilton函数的变分形式,将Maxwell方程表述为Hamilton正则方程形式.在时域方向,利用辛传播子技术对方程进行离散以保持方程的内在结构;在空域方向,采用时域多分辨率方法对三维旋度算符进行差分离散,建立了求解Maxwell方程的辛时域多分辨率(S-MRTD)方法.对S-MRTD方法的稳定性及数值色散性进行了系统的探讨,数值结果表明该方法的正确性及高精度性.
It is especially important to preserve some characters of the original system while numerical simulating three-di- mensional time domain Maxwell' s Equations. The Maxwell' s equations are written as normal Hamilton equations using functional variation method. We discretize Maxwell' s equations in the time direction using sympletic propagation technique and then evaluate the equations in the spatial direction with high-order nature of spatial multi-resolution approximations to construct symplectic Mtdti- Resolution Time Domain (S-MRTD) scheme. The stability and numerical dispersion analysis are also included. Numerical results are given to show the high efficiency and accuracy of the S-MRTD scheme.
出处
《电子学报》
EI
CAS
CSCD
北大核心
2012年第5期1034-1038,共5页
Acta Electronica Sinica
基金
国家自然科学基金(No.60931002
61101064)
安徽省高校自然科学基金(No.KJ2011A002)
安徽省杰出青年基金(No.1108085J01)
安徽大学‘211工程’学术创新团队基金(No.KJTD007A)
关键词
传播子技术
辛时域多分辨率
稳定性
数值色散性
propagation technique
symplectic multi-resolution time domain
stability
numerical dispersion