用于电磁波多尺度问题求解的高效FDTD-PITD混合算法  

An Efficient Hybrid FDTD-PITD Formulation for Solving Multiscale Electromagnetic Wave Problems

作　　者：康祯 杨方 张瑞祥[1] 刘俊峰[1] 姚尧 KANG Zhen;YANG Fang;ZHANG Rui-xiang;LIU Jun-feng;YAO Yao(Department of Nuclear Power Technology,Xi'an Thermal Power Research Institute Co.,Ltd,Xi'an 710054,China;College of Electrical arid Control Engineering,Xi'an University of Science and Technology,Xi'an 710054,China)

机构地区：[1]西安热工研究院有限公司核电技术部,西安710054 [2]西安科技大学电气与控制学院,西安710054

出　　处：《微波学报》2022年第3期46-52,共7页Journal of Microwaves

基　　金：中国博士后科学基金(2021M693880);陕西省自然科学基础研究计划(2019JQ-792)。

摘　　要：针对电磁波多尺度问题的高效仿真需求,提出了基于亚网格技术的时域有限差分(FDTD)方法与时域精细积分(PITD)方法的混合数值算法。该混合算法的基本思想是采用局部亚网格技术分别对精细结构区域以及其他区域进行剖分,并应用FDTD方法和PITD方法分别对粗网格区域与细网格区域进行求解,同时构建信息交互策略交换细网格区域与粗网格区域的计算信息。一方面该方法减少了电磁波多尺度问题的网格剖分数目,显著降低了内存需求;另一方面由于应用于细网格区域的PITD方法不受Courant-Friedrich-Levy(CFL)数值稳定性条件的限制,该混合方法能够采用较大的时间步长进行仿真,减少了迭代步数以及CPU执行时间。数值计算结果验证了混合算法的稳定性、可行性以及高效性。A novel hybrid sub-gridding algorithm based on both the finite-difference time-domain(FDTD)method and the precise-integration time-domain(PITD)method is proposed for efficient numerical simulations of the multiscale electromagnetic wave problems.The fundamental idea of the proposed hybrid method consists of discretizing the computational domain by the local refined sub-grids containing the fine structures and the coarse grids for other domain,solving the field components on the coarse grids and the sub-grids by FDTD method and PITD method,respectively.Meanwhile,a stable interpolation strategy is proposed to exchange the computational information through the interface between the coarse and fine grids.This method can reduce the number of meshes for electromagnetic multiscale problems and significantly reduce the memory requirements.On the other hand,because the PITD method can break through the limit of the Courant-Friedrich-Levy(CFL)numerical stability condition,the proposed hybrid method can use a larger time step depending on the coarse grid to finish the simulation.The numerical results demonstrate the stability,feasibility and high efficiency of the proposed hybrid algorithm.

关 键 词：时域有限差分方法 时域精细积分方法 混合算法 多尺度仿真 亚网格技术 

分 类 号：O441.4[理学—电磁学]