适用于有耗型德拜色散媒质电磁特性仿真的RI-CDI-FDTD方法及程序实现  

RI-CDI-FDTD method and program implementation for electromagnetic characteristics simulation of lossy Debye dispersive medium

作　　者：谢国大 侯桂林 牛凯坤 冯乃星 方明[1,2] 李迎松 黄志祥[1,2] Xie Guo-Da;Hou Gui-Lin;Niu Kai-Kun;Feng Nai-Xing;Fang Ming;Li Ying-Song;Huang Zhi-Xiang(School of Electronic and Engineering,Anhui University,Hefei 230601,China;Key Laboratory of Intelligent Computing and Signal Processing,Ministry of Education,Anhui University,Hefei 230601,China)

机构地区：[1]安徽大学电子信息工程学院,合肥230601 [2]安徽大学,智能计算与信号处理教育部重点实验室,合肥230601

出　　处：《物理学报》2023年第15期1-9,共9页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:62201003,2022YFA1404003,62101002,U20A20164,61901001)资助的课题.

摘　　要：提出了一种新的处理有耗型德拜色散媒质的单步蛙跳遵从发散隐式-时域有限差分(complying divergence implicit FDTD,CDI-FDTD)方法.从频域下的Maxwell方程出发,利用傅里叶变换将电磁场分量从频域转换到时域,并采用递归积分(recursive integration,RI)方法对频域-时域转换过程中存在的积分项进行近似处理.然后应用单步蛙跳隐式格式对时域Maxwell方程和辅助变量进行差分离散,推导出有耗型德拜色散媒质的RI-CDI-FDTD算法的迭代公式.接着利用von Neumann方法验证了基于RI方法的CDI-FDTD算法的无条件稳定特性,最后通过数值算例验证了本文所提方法的正确性和有效性.Dispersive media refer to a class of natural substances,including living organisms,composite materials,plasma and water,with diverse applications in areas such as biomedicine,microwave sensing,electromagnetic protection,and stealth technology.In the pursuit of investigating the electromagnetic properties of these media,time-domain numerical methods,including finite difference in time domain(FDTD),finite element method,and time domain boundary integral equation method,have been widely utilized.Time-domain numerical methods are preferred to their frequency-domain counterparts owing to their ability to handle nonlinear and wideband problems,as well as various material properties.The FDTD method,in particular,is a highly adaptable,robust,and easy-to-use numerical method that directly solves the Maxwell equations while also simulating the reflection,transmission,and scattering of electromagnetic waves in complex dispersion media.Nonetheless,the traditional FDTD method suffers low computational efficiency arising from the Courant-Friedrichs-Lewy(CFL)stability condition.To solve the problem of low computational efficiency,a new method,the complying divergence implicit finite-difference time-domain(CDI-FDTD)method with a one-step leapfrog scheme,is introduced for lossy Debye dispersive media.The Maxwell equations in the frequency domain form a starting point,and the Fourier transform is utilized to transform the electromagnetic field components from the frequency domain to the time domain.To approximate the integral terms arising from the frequency-to-time domain transformation,a recursive integration(RI)method is employed.Subsequently,the time-domain Maxwell equations and auxiliary variables are discretized with a one-step leapfrog implicit scheme.The iterative formula of the RI-CDI-FDTD algorithm for lossy Debye dispersive media is then derived.The RI-CDI-FDTD method does not change the formulas of the traditional CDI-FDTD method while only requiring to add auxiliary variables for updating field components to the dispe

关 键 词：德拜色散媒质 遵从发散隐式-时域有限差分 递归积分 无条件稳定 

分 类 号：O441.4[理学—电磁学] O241.82[理学—物理]