电工技术学报2025，Vol.40Issue(5)：1333-1343,11.DOI:10.19595/j.cnki.1000-6753.tces.240355
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
摘要
Abstract
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 fine grids with that for coarse grids.Meanwhile,1-D simulation can greatly reduce the memory requirement of PITD.Compared with PITD(2),PITD(4)has higher accuracy without additional memory burden.Therefore,the high-order hybrid FDTD-PITD method is proposed to model the embedded thin conductive layer,which is a synergetic combination of FDTD and 1-D PITD(4).FDTD is adopted for coarse grids outside the thin conductive layer,while 1-D PITD(4)is used for fine grids inside the thin conductive layer. Conventional FDTD is used to update the EM fields outside the thin conductive layer,and the magnetic fields adjacent to the boundaries of the thin conductive layer need to be specially treated by using the boundary electric fields obtained by 1-D PITD(4)inside the thin conductive layer.For the PITD domain,the transition region is introduced between the high-order region and the interface of different grids.The fourth-order spatial central difference is used for the high-order region and the second-order for the transition region.The thickness of the transition region is selected following the principle that all unknowns used to solve the high-order region are located inside the thin conductive layer.The tangential electric field components at the interface are updated by using effective permittivity and conductivity,thereby connecting coarse and fine grids.Finally,the numerical stability and numerical reflection of the hybrid method are analyzed,and several canonical numerical examples are presented to verify the effectiveness and accuracy of the proposed method.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Key words
Finite-difference time-domain method/fourth-order precise-integration time-domain method/subgridding technology/matrix exponential分类
信息技术与安全科学引用本文复制引用
马亮,马西奎,迟明珺,向汝,朱晓杰..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[J].电工技术学报,2025,40(5):1333-1343,11.基金项目
国家自然科学基金资助项目(52177008). （52177008）
