【作者】 傅平；

【导师】 凌国平；

【作者基本信息】 苏州大学 ， 计算数学， 2005， 硕士

【摘要】 传统的时域有限差分法(Finite Difference Time-Domain, FDTD),即Yee 格式,在时间空间导数离散上都采用二阶中心差分格式,格式精度较低,色散耗散误差较大。对电大问题作电磁波传播长期响应分析时,由于误差的积累,往往造成波形的严重失真,这是传统的FDTD 方法的固有缺陷。针对这些问题,本文采用时间辛算法与空间紧致格式相结合的方法,构造出时间、空间均达到四阶精度的FDTD 格式。新格式理论上不产生耗散误差,相比其他一些典型高精度格式有更低的色散误差,和更好的稳定性。在具体格式分析过程中,讨论了紧致格式的色散误差及其各向异性特性;介绍了Hamilton 系统及其辛性质、辛格式的主要构造方法;介绍了辛算法在Maxwell 方程中的应用,和辛FDTD 格式的构造,给出了辛紧致FDTD 格式结合的行为分析:包括稳定性,色散分析,以及同一误差限制下的存储量与计算量估计。数值实例中证实了本文提出的辛紧致FDTD 格式对长期响应分析的有效性。另外还将辛格式应用到电磁目标的散射计算中,得到了与解析解相吻合的结果。更多还原

【Abstract】 The standard finite difference time-domain method of Maxwell equation, i.e. the Yee scheme, which uses the second-order center difference scheme in both time and space, is a low-order explicit scheme, with greater dispersion and dissipation errors. For electrically large domains and late-time analysis, it would result in the waveform distortion due to the accumulation of numerical errors. It is the intrinsic limitation for Yee scheme. In this paper, a temporal symplectic integrator propagator and a spatial compact difference scheme are combined into a new method, which is fourth-order accurate in both space and time, with no dissipation error, lower dispersive error and larger stability compared with other classic high-order difference schemes. First, dispersive error of compact difference scheme is discussed; Then, we introduce the application of symplectic method into Maxwell equation, and give the construction of symplectic FDTD scheme; later, we show the behavioral analysis for the symplectic compact FDTD method. At last, Numerical examples demonstrate the superior performance in late-time analysis of the method, and the electromagnetic scatting field calculation is agreed well with the analysis result.更多还原