高阶精度无条件稳定SS-FDTD算法研究

近年来随着通信行业的飞速发展，通信器件和设备也趋于小型化，而无条件稳定FDTD算法使时间步长的选取不再受CFL条件的限制，减少了计算时间，提高了计算效率。因此，成为近年来计算电磁学领域的一个研究热点。但是，无条件稳定FDTD算法在计算精度、数值色散及复杂结构中的应用方面仍然存在许多呈待解决的课题。本项目研究高阶精度无条件稳定SS-FDTD算法。具体研究包括新型高阶精度无条件稳定SS-FDTD算法及其数值特性分析；具有低色散特性的无条件稳定SS-FDTD算法；与边界条件相结合的高阶精度SS-FDTD算法；引入集总模型的扩展高阶精度SS-FDTD算法；最终将算法应用于天线、波导、微波电路和电磁兼容等问题中。对于进一步完善无条件稳定FDTD算法，扩大无条件稳定FDTD算法的应用具有重大的意义。

Recently, due to the great development of communication industry, components with characteristics of miniaturization are required. To resolve the limitation of the Courant-Friedrichs-Lewy (CFL) condition on the time step size of the finite-difference time-domain (FDTD) method, an unconditionally-stable FDTD method has been developed, which can reduce the CPU time and improve the computational efficiency. Therefore, it plays an important role in the computational electromagnetics. However, it has some challenge in computaitional accuracy, numerical dispersion and application of the complex structures. Then, the unconditionally-stable split-step (SS)-FDTD methods with high-order accuracy will be researched in this project. Specially, the detailed research is shown as follows, the novel high-order unconditionally-stable SS-FDTD methods and numerical analysis, the unconditionally-stable SS-FDTD methods with low numerical dispersion, the high-order SS-FDTD methods with absorbing boundary conditions, and the high-order SS-FDTD methods with lumped elements. Finally, the proposed methods will be applied into antenna, waveguide, microwave circuits and EMC problems. In addition, the research will have an important significancy for the perfectness and application of the expanded unconditionally-stable FDTD methods.