Unified Analysis of Leap-Frog Methods for Solving Time-Domain Maxwell's Equations in Dispersive Media

Jichun Li

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Unified Analysis of Leap-Frog Methods for Solving Time-Domain Maxwell's Equations in Dispersive Media

机译：求解分散介质中时域麦克斯韦方程组的蛙跳方法统一分析

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In this paper, we consider the time dependent Maxwell's equations resulting from dispersive medium models. First, the stability and Gauss's law are proved for all three most popular dispersive medium models: the isotropic cold plasma, the one-pole Debye medium and the two-pole Lorentz medium. Then leap-frog mixed finite element methods are devel oped for these three models. Optimal error estimates are proved for all three models solved by the lowest-order Raviart-Thomas-Nedelec spaces. Extensions to multiple pole dispersive media are presented also. Numerical results confirming the analysis are presented.

机译：在本文中，我们考虑了由色散介质模型产生的时间相关的麦克斯韦方程。首先，针对三种最流行的色散介质模型（各向同性冷等离子体，一极德拜介质和两极洛伦兹介质）证明了稳定性和高斯定律。然后针对这三个模型开发了蛙跳混合有限元方法。证明了通过最低阶Raviart-Thomas-Nedelec空间求解的所有三个模型的最优误差估计。还介绍了对多极分散介质的扩展。给出了证实分析的数值结果。

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来源
《Journal of Scientific Computing》 |2011年第1期|p.1-26|共26页
作者
Jichun Li;
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作者单位

Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan 411105, China Department of Mathematical Sciences, University of Nevada Las Vegas, Las Vegas, NV 89154-4020,USA;

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正文语种 eng
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关键词
maxwell's equations; dispersive media; leap-frog scheme;

机译：麦克斯韦方程;色散介质;跳蛙法;

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专利

1. Analysis of a time-domain finite element method for 3-D Maxwell's equations in dispersive media [J] . Jichun Li, Yitung Chen Computer Methods in Applied Mechanics and Engineering . 2006,第33a36期

机译：色散介质中3-D Maxwell方程的时域有限元方法分析
2. Convergence of an explicit iterative leap-frog discontinuous Galerkin method for time-domain Maxwell’s equations in anisotropic materials [J] . Adérito Araújo, Sílvia Barbeiro, Maryam Khaksar Ghalati Journal of Mathematics in Industry . 2018,第1期

机译：各向异性材料中时域麦克斯韦方程的显式迭代跳跃不连续伽勒金方法的收敛性
3. An implicit leap-frog discontinuous Galerkin method for the time-domain Maxwell's equations in metamaterials [J] . Jichun Li, Jiajia Wang Waters, Eric A. Machorro Computer Methods in Applied Mechanics and Engineering . 2012,第Juna1期

机译：超材料中时域麦克斯韦方程组的隐式蛙跳不连续伽勒金方法
4. Time-Domain Finite Element Methods for Maxwell's Equationsin Dispersive Media: a Review [C] . Jichun Li, Yitung Chen International Workshop on Computational Sciences and its Education . 2008

机译：Maxwell公式的时域有限元方法分散媒体：综述
5. Development and evaluation of novel finite-difference time-domain methods for solving Maxwell's equations. [D] . Sun, Guilin. 2005

机译：求解麦克斯韦方程组的新型时域有限差分方法的开发和评估。
6. On the immersed interface method for solving time-domain Maxwell’s equations in materials with curved dielectric interfaces [O] . Shaozhong Deng -1

机译：关于在具有弯曲介电界面的材料中求解时域麦克斯韦方程的沉浸界面方法
7. Stability of a Leap-Frog Discontinuous Galerkin Method for Time-Domain Maxwell's Equations in Anisotropic Materials [O] . Araújo, Adérito, Barbeiro, Sílvia, Ghalati, Maryam Khaksar 2017

机译：各向异性材料中时域maxwell方程的Leap-Frog间断Galerkin方法的稳定性
8. High-Order Time-Domain Methods for Maxwells Equations [R] . Gottlieb, D. 2000

机译：麦克斯韦方程组的高阶时域方法

Unified Analysis of Leap-Frog Methods for Solving Time-Domain Maxwell's Equations in Dispersive Media

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