高阶LOD-FDTD方法的数值特性研究

该文分析并证明了高阶局部1维时域有限差分(LOD-FDTD)方法的数值特性，即：稳定性、数值色散及高阶收敛性。文中首次推导出3维各阶LOD-FDTD方法的增长因子和数值色散关系的一致形式，解析证明了这类方法均是无条件稳定的。基于此一致性关系，首次分析了这类方法的数值色散误差随阶数的收敛情况，并给出收敛性条件。在用此类方法计算谐振腔本征模频率的实验中，数值结果显示高阶方法可达到更优的计算精度，同时不显著增加计算时间。

Study for the Numerical Properties of the Higher-Order LOD-FDTD Methods

In this paper, the numerical properties of higher-order Locally One Dimensionally Finite-Difference Time-Domain (LOD-FDTD) are investigated, i.e. stability, numerical dispersion, and convergence. The universal formulas of the amplitude factor and the numerical dispersion relationship are derived for 3D varying-order LOD-FDTD, and their unconditional stability is analytically proved. Based on this universal formula, the numerical convergence of this class of methods is discussed, and the convergence condition is presented for the first time. Numerical results in calculating the resonant frequency show that, higher-order methods can achieve better performance while not dramatically increasing computational time.