基于多步高阶差分格式求解时域Maxwell方程

计算物理 ›› 2008, Vol. 25 ›› Issue (3): 263-268.

基于多步高阶差分格式求解时域Maxwell方程

黄志祥, 沙威, 吴先良, 陈明生

安徽大学计算智能与信号处理教育部重点实验室, 安徽合肥 230039

收稿日期:2006-11-29 修回日期:2007-07-06 出版日期:2008-05-25 发布日期:2008-05-25
作者简介:黄志祥(1979-),male,Anhui,Ph.D,research on numerical technique in electromagnetics and symplectic schemes.
基金资助:
Supported by "National Natural Science Foundation of China(60671051)","Research Fundfor Doctoral Programof Higher Education (20060357004)" and Key Project of Education Department of Anhui Province(KJ2008A100).

Multi-step High-order Finite Difference Schemes for Time Domain Maxwell's Equations

HUANG Zhixiang, SHA Wei, WU Xianliang, CHEN Mingsheng

Key Laboratory of Intelligent Computing & Signal Processing, Anhui University, Hefei 230039, China

Received:2006-11-29 Revised:2007-07-06 Online:2008-05-25 Published:2008-05-25
Supported by:
Supported by "National Natural Science Foundation of China(60671051)","Research Fundfor Doctoral Programof Higher Education (20060357004)" and Key Project of Education Department of Anhui Province(KJ2008A100).

摘要/Abstract

摘要： 提出基于无穷维哈密尔顿系统及分裂算子理论的多步高阶差分格式,求解时域Maxwell方程.在时间方向上,针对Maxwell方程采用不同阶数的辛算法进行差分离散;在空间方向上,采用四阶差分格式进行差分离散.探讨多步高阶差分格式的稳定性及数值色散性,最后给出数值计算结果.结果表明,五级四阶格式为最有效的多步高阶差分格式,具有高精度、占用较少的计算机资源等优点,适用于长时间的数值模拟.

关键词: 多步高阶差分格式, 无穷维哈密尔顿系统, 分裂算子, Maxwell方程

Abstract: Multi-step high-order finite difference schemes for infinite dimensional Hamiltonian systems with split operators are proposed to solve time domain Maxwell's equations. Maxwell's equations are discretized in time direction and in spatial direction with different order of sympleetie schemes and fourth-order finite difference approximations, respectively. Stability analysis and numerical results are presented. A five-stage fourth-order multi-step high-order finite difference scheme proves accurate and efficient, and applicable to long time simulations.

Key words: multi-step high-order finite difference, infinite dimensional Hamiltonian system, split operators, Maxwell's equations

中图分类号:

黄志祥, 沙威, 吴先良, 陈明生. 基于多步高阶差分格式求解时域Maxwell方程[J]. 计算物理, 2008, 25(3): 263-268.

HUANG Zhixiang, SHA Wei, WU Xianliang, CHEN Mingsheng. Multi-step High-order Finite Difference Schemes for Time Domain Maxwell's Equations[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2008, 25(3): 263-268.

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