基于多步高阶差分格式求解时域Maxwell方程(英文)

Multi-step High-order Finite Difference Schemes for Time Domain Maxwell's Equations

提出基于无穷维哈密尔顿系统及分裂算子理论的多步高阶差分格式,求解时域Maxwell方程.在时间方向上,针对Maxwell方程采用不同阶数的辛算法进行差分离散;在空间方向上,采用四阶差分格式进行差分离散.探讨多步高阶差分格式的稳定性及数值色散性,最后给出数值计算结果.结果表明,五级四阶格式为最有效的多步高阶差分格式,具有高精度、占用较少的计算机资源等优点,适用于长时间的数值模拟.

Multi-step high-order finite difference schemes for infinite dimensional Hamiltonian systems with split operators are proposed to solve time domain Maxwell＇s equations. Maxwell＇s equations are discretized in time direction and in spatial direction with different order of sympleetie schemes and fourth-order finite difference approximations, respectively. Stability analysis and numerical results are presented. A five-stage fourth-order multi-step high-order finite difference scheme proves accurate and efficient, and applicable to long time simulations.