CONVERGENCE ANALYSIS OF YEE-FDTD SCHEMES FOR 3D MAXWELL’S EQUATIONS IN LINEAR DISPERSIVE MEDIA
CONVERGENCE ANALYSIS OF YEE-FDTD SCHEMES FOR 3D MAXWELL’S EQUATIONS IN LINEAR DISPERSIVE MEDIA
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发表时间：
2021
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通讯作者：
P. Bokil
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作者：
P. Bokil
本文建立并分析了三种不同类型线性色散介质（德拜、洛伦兹和冷等离子体）下三维麦克斯韦方程组的时域有限差分方法。这些方法是将时域有限差分（FDTD）方法扩展到线性色散材料。用能量法分析了时域有限差分格式的稳定性判据。基于连续模型的能量恒等式，导出了三种色散模型的时域有限差分格式的离散能量估计。在完美的导电边界条件下证明了FDTD格式的收敛性，说明了该方法在时间和空间上的二阶精度。研究了时域有限差分格式的离散无散度条件。最后，通过数值算例验证了本文的研究结果。
In this paper, we develop and analyze finite difference methods for the 3D Maxwell’s equations in the time domain in three different types of linear dispersive media described as Debye, Lorentz and cold plasma. These methods are constructed by extending the Yee-Finite Difference Time Domain (FDTD) method to linear dispersive materials. We analyze the stability criterion for the FDTD schemes by using the energy method. Based on energy identities for the continuous models, we derive discrete energy estimates for the FDTD schemes for the three dispersive models. We also prove the convergence of the FDTD schemes with perfect electric conducting boundary conditions, which describes the second order accuracy of the methods in both time and space. The discrete divergence-free conditions of the FDTD schemes are studied. Lastly, numerical examples are given to demonstrate and confirm our results.