一种适用于嵌入式导电薄层的高阶电磁波混合时域有限差分-时程精细积分法  

A High-Order Hybrid FDTD-PITD Method of Electromagnetic Waves for Embedded Thin Conductive Layers

作　　者：马亮[1] 马西奎[1] 迟明珺 向汝 朱晓杰 Ma Liang;Ma Xikui;Chi Mingjun;Xiang Ru;Zhu Xiaojie(State Key Laboratory of Electrical Insulation and Power Equipment,Xi’an Jiaotong University,Xi’an,710049,China;Dipartimento di Elettronica Informazione e Bioingegneria,Politecnico di Milano,Milan,20133,Italy)

机构地区：[1]电工材料电气绝缘全国重点实验室(西安交通大学),西安710049 [2]电子信息与生物工程系(米兰理工大学),米兰20133

出　　处：《电工技术学报》2025年第5期1333-1343,共11页Transactions of China Electrotechnical Society

基　　金：国家自然科学基金资助项目(52177008)。

摘　　要：应用单一时域数值方法,在面对嵌入式导电薄层一类多尺度问题时,都面临着建模极为困难的挑战。该文提出了一种基于时域有限差分(FDTD)法和高阶时程精细积分(PITD)法的电磁波混合数值方法。该方法对导电薄层外部进行粗网格剖分并应用FDTD法,而对薄层内部进行一维细网格剖分并应用四阶PITD法,以实现不同网格尺度的同步时间推进。为了实现粗细网格之间的信息交换,在PITD域中引入过渡区域并应用二阶PITD法,通过等效本构参数来更新交界面处的切向电场。分析了该混合算法的数值稳定性和数值反射,并通过典型数值算例验证了所提方法的有效性和准确性。For wideband characteristic analysis,frequency-domain numerical methods need to calculate complicated equations at each frequency point repeatedly.However,time-domain numerical methods only need to perform the Fourier transform on time-domain results of one calculation to obtain the wideband frequency-domain information.The finite-difference time-domain(FDTD)method is the most widely used time-domain method,but its time step size is limited by the Courant-Friedrichs-Lewy(CFL)stability condition.To overcome this shortcoming,the precise-integration time-domain(PITD)method is proposed to be free from the CFL restriction by discretizing the spatial derivatives with difference and solving the ordinary differential equations about time by using the precise integration technique,designated as the second-order PITD[PITD(2)].For the improvement of the numerical dispersion characteristics,the fourth-order PITD[PITD(4)]method is proposed by using the fourth-order spatial central difference scheme.The difference in memory requirements between PITD(2)and PITD(4),merely reflected in the size and sparsity of the matrix exponential,is not significant.Thin conductive layers,as typical multiscale problems,exist widely in electromagnetic(EM)systems for shielding,posing challenges to any single numerical algorithm.For such problems,the cell size of FDTD must be sufficiently small to capture the thickness and skin effect of the thin conductive layer,requiring significant resources.To describe their EM properties more effectively,the subgridding technology is introduced to employ high-density sampling only for the local thin layer and coarse-grid divisions for the remaining areas.Since the waves inside the good conductor propagate nearly perpendicular to its surfaces,the thin conductive layer is divided into fine grids only along the vertical direction and its internal EM fields can be found by one-dimensional(1-D)full-wave simulation.To relax the CFL restriction of fine grids,PITD can be used to synchronize the time step size for fin

关 键 词：时域有限差分法 四阶时程精细积分法 亚网格技术 矩阵指数 

分 类 号：TM15[电气工程—电工理论与新技术]