CONSTRUCTION AND ANALYSIS OF WEIGHTED SEQUENTIAL SPLITTING FDTD METHODS FOR THE 3D MAXWELL’S EQUATIONS
CONSTRUCTION AND ANALYSIS OF WEIGHTED SEQUENTIAL SPLITTING FDTD METHODS FOR THE 3D MAXWELL’S EQUATIONS
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3D麦克斯韦方程组加权序贯分裂FDTD方法的构造与分析
DOI：
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
V. Bokil
中科院分区：
文献类型：
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作者：
V. Bokil
本文提出了求解三维Maxwell方程的单参数族全离散加权序列分裂(WSS)-时域有限差分(FDTD)方法。在一个时间步长内，Maxwell WSS-FDTD格式由两个子阶段组成，每个子阶段涉及几个一维离散Maxwell方程组的解。在时间步长结束时，我们取子阶段解的加权平均，权参数为θ，0，≤θ≤1。与YEE-FDTD方法类似，Maxwell WSS-FDTD格式在离散网格中交错空间电场和磁场。然而，在我们的分裂格式中，所有一维Maxwell系统的时间离散化都使用了Crank-Nicolson方法。我们证明了对于所有的θ值，Maxwell WSS-FDTD格式是无条件稳定的，并且当θ6=0.5时精度是一阶的，当θ=0.5时精度是二阶的。Maxwell WSS-FDTD格式对于θ的所有值在空间上都具有二阶精度。我们证明了Maxwell WSS-FDTD方法对权参数θ的所有取值都是收敛的，并给出了误差估计。我们还分析了Maxwell WSS-FDTD格式对所有θ值的解的离散散度，证明了当θ6=0.5时，电场和磁场解的离散散度近似为一阶，而当θ=0.5时，我们得到了精确散度的三阶近似。文中给出了数值实验和算例，验证了我们的理论结果。
In this paper, we present a one parameter family of fully discrete Weighted Sequential Splitting (WSS)-finite difference time-domain (FDTD) methods for Maxwell’s equations in three dimensions. In one time step, the Maxwell WSS-FDTD schemes consist of two substages each involving the solution of several 1D discrete Maxwell systems. At the end of a time step we take a weighted average of solutions of the substages with a weight parameter θ, 0 ≤ θ ≤ 1. Similar to the Yee-FDTD method, the Maxwell WSS-FDTD schemes stagger the electric and magnetic fields in space in the discrete mesh. However, the Crank-Nicolson method is used for the time discretization of all 1D Maxwell systems in our splitting schemes. We prove that for all values of θ, the Maxwell WSS-FDTD schemes are unconditionally stable, and the order of accuracy is of first order in time when θ 6= 0.5, and of second order when θ = 0.5. The Maxwell WSS-FDTD schemes are of second order accuracy in space for all values of θ. We prove the convergence of the Maxwell WSS-FDTD methods for all values of the weight parameter θ and provide error estimates. We also analyze the discrete divergence of solutions to the Maxwell WSS-FDTD schemes for all values of θ and prove that for θ 6= 0.5 the discrete divergence of electric and magnetic field solutions is approximated to first order, while for θ = 0.5 we obtain a third order approximation to the exact divergence. Numerical experiments and examples are given that illustrate our theoretical results.
影响因子：
2.5
作者：
V. Bokil;Yingda Cheng;Yan Jiang;Fengyan Li;Puttha Sakkaplangkul
通讯作者：
V. Bokil;Yingda Cheng;Yan Jiang;Fengyan Li;Puttha Sakkaplangkul