A Fully Fourth Order Accurate Energy Stable Finite Difference Method for Maxwell's Equations in Metamaterials
A Fully Fourth Order Accurate Energy Stable Finite Difference Method for Maxwell's Equations in Metamaterials
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DOI：
10.1109/jmmct.2019.2953309
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发表时间：
2019-09
影响因子：
2.3
通讯作者：
Puttha Sakkaplangkul;V. Bokil;C. Carvalho
中科院分区：
文献类型：
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作者：
Puttha Sakkaplangkul;V. Bokil;C. Carvalho
提出了一种新的求解超材料麦克斯韦方程的全四阶时空有限差分方法。我们考虑了材料对入射电磁场响应的Drude超材料模型。我们考虑偏微分方程组的二阶形式，它控制着电场和磁场随时间的演化以及极化和磁化电流密度的演化。我们的离散化使用了不同场分量在空间上的四阶交错和修正的方程方法来获得时间上的四阶精度。利用能量方法，我们导出了连续模型的能量关系，并设计了保持能量关系的离散相似的数值格式。给出了一维和二维情况下的数值模拟，以说明四阶收敛以及与二阶格式的比较。
We present a novel fully fourth order in time and space finite difference method (FDM) for the time domain Maxwell's equations in metamaterials. We consider a Drude metamaterial model for the material response to incident electromagnetic fields. We consider the second-order formulation of the system of partial differential equations that govern the evolution in time of electric and magnetic fields along with the evolution of the polarization and magnetization current densities. Our discretization employs fourth-order staggering in space of different field components and the modified equation approach to obtain fourth-order accuracy in time. Using the energy method, we derive energy relations for the continuous models and design numerical schemes that preserve a discrete analogue of the energy relation. Numerical simulations are provided in one- and two-dimensional settings to illustrate fourth-order convergence as well as to compare with second-order schemes.