An Unconditionally Stable Precise Integration Time Domain Method for Solving Maxwell’s Equations

ZHAO Xin-tai; MA Xi-kui

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An Unconditionally Stable Precise Integration Time Domain Method for Solving Maxwell’s Equations

更新时间：2025-07-16

- An Unconditionally Stable Precise Integration Time Domain Method for Solving Maxwell’s Equations
- Acta Electronica Sinica Vol. 34, Issue 9, Pages: 1600-1604(2006)
- 作者机构：
  
  西安交通大学电气工程学院,陕西,西安,710049
- 作者简介：
- 基金信息：
- DOI：
  CLC： TM15
- Published Online：25 September 2006，
  
  Published：2006
- 稿件说明：
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ZHAO Xin-tai, MA Xi-kui. An Unconditionally Stable Precise Integration Time Domain Method for Solving Maxwell’s Equations[J]. Acta Electronica Sinica, 2006, 34(9): 1600-1604.
DOI：

ZHAO Xin-tai, MA Xi-kui. An Unconditionally Stable Precise Integration Time Domain Method for Solving Maxwell’s Equations[J]. Acta Electronica Sinica, 2006, 34(9): 1600-1604. DOI：

摘要

本文提出了一种基于精细积分技术求解Maxwell旋度方程的半解析时域方法.由于精细积分技术的引入

该方法不仅摆脱了Courant-Frendrich-Levy稳定性条件对时间步长的限制

而且使得数值色散与时间步长的选取无关.文中分别推导了时域精细积分法在计算区域内和吸收边界处的差分格式

时域递推的计算格式;并提出了时域递推过程涉及的矩阵不可逆问题的解决方案.进行了实例计算

并与解析解和时域有限差分法的结果进行了对比.

Abstract

This paper presents a time domain semi-analysis method based on the precise integration (PI) technique for solving Maxwell’s curl equations.Due to the introduction of the PI technique

the time domain method can not only eliminate the limitation of the stability condition for the time step size t

but also make the numerical dispersion being independent of t .The finite difference schemes of the precise integration time domain (PITD) method are deduced in computational domain and on absorbing boundary

respectively

and the time domain recursion scheme is also deduced.Moreover

the resolving scheme of the invertible matrix problem involving the time domain iteration is presented.Practical calculation is carried out

and the results are compared with the ones of the analysis solution and finite difference time domain method.The results show that the PITD method is free from the restriction of the Courant-Frendrich-Levy stability condition.At the same time

the larger time step size will not deteriorate the numerical dispersion.

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