麦克斯韦方程的修正分裂时域有限差分方法

MODIFIED SPLITTING FDTD METHOD FOR MAXWELL'S EQUATIONS

在分裂麦克斯韦方程的基础上,利用摄动项减少分裂误差,提出了二维麦克斯韦方程的一种新的分裂时域有限差分方法(MS-FDTD),利用能量方法,推导出了该方法的数值能量恒等式,证明了MS-FDTD在离散L2和H1范数意义下是稳定和二阶收敛.数值实验证实了这种方法的有效性及对稳定性和收敛性的分析.

In this paper,based on splitting of equations we propose a modified splitting finite difference time domain method （MS-FDTD） for 2-D Maxwell’s equations by the technique of reducing splitting error by perturbation terms.Then,by the energy method,the numerical energy identities of MS-FDTD are derived,and the stability and convergence of this method in the discrete L2 and H1 norms are proved.Numerical experiments to confirm the efficiency and the analysis of MS-FDTD on stability and convergence are provided.