基于向量拟合技术的广义色散媒质模型与高效DGTD算法

祝强强; 胡志明; 王思凡; 吴扬; 申子昂; 贾浩文; 徐若锋; 郭卿超; 赵雷

doi:10.12263/DZXB.20250241

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基于向量拟合技术的广义色散媒质模型与高效DGTD算法

学术论文 | 更新时间：2026-02-10

- 基于向量拟合技术的广义色散媒质模型与高效DGTD算法
- Generalized Dispersive Media Model Based on Vector Fitting Technique and Efficient DGTD Algorithm
- 电子学报 2025年53卷第11期页码：4010-4021
- 作者机构：
  
  1.中国矿业大学，江苏徐州 221000
  2.南京航空航天大学，江苏南京 210000
  3.电磁信息控制与效应全国重点实验室，辽宁沈阳 110035
- 作者简介：
  
  [ "祝强强男，2000年11月出生于山西省朔州市.2025年取得中国矿业大学工科硕士学位.主要研究方向为计算电磁学.E-mail: qqzhunax@163.com" ]
  [ "胡志明男，2000年11月出生于江苏省徐州市.现为中国矿业大学信息与控制工程学院硕士研究生.主要研究方向为计算电磁学.E-mail: zmhu@cumt.edu.cn" ]
  [ "王思凡男，1996年3月出生于江苏省徐州市.现为中国矿业大学信息与控制工程学院博士研究生.主要研究方向为计算电磁学.E-mail: sfwang@cumt.edu.cn" ]
  [ "吴扬男，1998年10月出生于安徽省铜陵市.2025年取得中国矿业大学工科硕士学位.主要研究方向为计算电磁学.E-mail: yangwunax@163.com" ]
  [ "申子昂男，1994年12月出生于河南省济源市.现为南京航空航天大学博士研究生.主要研究方向为电磁场数值方法中的频域、时域及高频近似等算法及其高性能计算.E-mail: shenziang@nuaa.edu.cn" ]
  [ "贾浩文男，1998年3月出生于宁夏回族自治区银川市.现为中国矿业大学博士研究生.主要研究方向为电磁散射建模及合成孔径雷达成像技术.E-mail: jhwxx@foxmail.com" ]
  [ "徐若锋男，1982年3月出生于江苏省徐州市.现任中国矿业大学信息与控制工程学院副教授.主要研究方向为微波毫米波技术及应用、场路联合仿真算法等.E-mail: xuruofeng@cumt.edu.cn" ]
  [ "郭卿超男，1985年11月出生于山西省长治市.现为沈阳飞机设计研究所研究员.主要研究方向为飞机总体设计、电磁散射特性研究.E-mail: gqch985@163.com" ]
  [ "赵雷男，1974年3月出生于江苏省徐州市.现为中国矿业大学信息与控制工程学院教授、博士生导师，ACES Fellow，中国电子学会天线分会委员、中国电子学会高级会员.主要研究方向为计算电磁学、射频与微波器件等，在国内外发表学术论文130余篇.中国电子学会会员编号：E190021907S.E-mail: leizhao@cumt.edu.cn" ]
- 基金信息：
  
  电磁信息控制与效应全国重点实验室基金(20240101);中国矿业大学中央高校基本科研业务费专项资金(2024-10942);江苏省研究生科研与实践创新计划(KYCX24_2767);中国矿业大学研究生创新计划(2024WLKXJ092)
- DOI：10.12263/DZXB.20250241
  中图分类号： TN95;O441.4
- 收稿：2025-03-30，
  
  录用：2025-11-04，
  
  纸质出版：2025-11-25
- 稿件说明：
移动端阅览
祝强强, 胡志明, 王思凡, 等. 基于向量拟合技术的广义色散媒质模型与高效DGTD算法[J]. 电子学报, 2025, 53(11): 4010-4021.

ZHU Qiang-qiang, HU Zhi-ming, WANG Si-fan, et al. Generalized Dispersive Media Model Based on Vector Fitting Technique and Efficient DGTD Algorithm[J]. Acta Electronica Sinica, 2025, 53(11): 4010-4021.
祝强强, 胡志明, 王思凡, 等. 基于向量拟合技术的广义色散媒质模型与高效DGTD算法[J]. 电子学报, 2025, 53(11): 4010-4021. DOI：10.12263/DZXB.20250241

ZHU Qiang-qiang, HU Zhi-ming, WANG Si-fan, et al. Generalized Dispersive Media Model Based on Vector Fitting Technique and Efficient DGTD Algorithm[J]. Acta Electronica Sinica, 2025, 53(11): 4010-4021. DOI：10.12263/DZXB.20250241

摘要

色散媒质的电磁特性在雷达隐身、天线设计等众多工程领域具有关键影响，如何精确高效地建立色散媒质模型一直是计算电磁学研究难点.经典色散模型虽能描述特定色散效应，但在拟合宽频复杂色散响应方面存在局限，难以适用于多频段、多机制耦合的复杂场景.为了实现对色散媒质电磁特性的准确、高效时域分析，本文基于向量拟合技术构建了广义色散媒质（Generalized Dispersive Media，GDM）数学模型，以实现对媒质色散特性精确表征，并结合辅助微分方程法与局部时间步技术（Local Time-Stepping，LTS），发展了一种基于时域间断伽辽金（Discontinuous Galerkin Time-Domain，DGTD）方法的色散媒质高效求解算法.针对给定的色散媒质频域响应数据，本文引入向量拟合技术，在施加物理约束与数学变换的基础上，建立了包含实极点与复共轭极点对的广义色散媒质模型，从而统一描述弛豫型和谐振型色散行为.为克服色散本构关系引入的时域卷积计算复杂度，采用辅助微分方程法构建了适用于该广义色散媒质模型的DGTD求解格式，将卷积运算转化为一组耦合常微分方程组，实现了高效时域步进求解.为进一步提升计算效率，设计了基于低存储龙格-库塔积分方法的局部时间步策略，显著提高了色散媒质问题的求解速度.本文对色散球体、色散材料涂覆弹头的雷达散射截面（Radar Cross Section，RCS）以及频率选择表面（Frequency Selective Surface，FSS）周期单元的反射系数进行了数值求解，结果表明基于向量拟合构建的广义色散媒质模型能够准确描述媒质的频域色散特性，拟合误差始终保持在较低水平；所获得的RCS、反射系数结果与CST商业软件及传统有限差分法的计算结果高度吻合，绝对误差控制在3 dB以内.在保证计算精度的同时，局部时间步技术的引入使整体计算效率提升了超过40.42%.本文所提出的方法为复杂色散媒质的电磁仿真提供了一种兼具通用性、高效性和可靠性的数值分析工具.

Abstract

The electromagnetic properties of dispersive media play a critical role in various engineering fields such as radar stealth and antenna design. Accurately and efficiently modeling dispersive media has long been a challenging research focus in computational electromagnetics. Although classical dispersion models can describe specific dispersive effects

they exhibit limitations in fitting complex broadband dispersive responses

making them difficult to apply in multi-band

multi-mechanism coupled complex scenarios. To achieve accurate and efficient time-domain analysis of the electromagnetic characteristics of dispersive media

this paper constructs a generalized dispersive media (GDM) mathematical model based on the vector fitting technique

enabling precise characterization of the dispersive properties of media. Combined with the auxiliary differential equation method and local time-stepping (LTS) technique

an efficient solving algorithm for dispersive media based on the discontinuous Galerkin time-domain (DGTD) method is developed. For given frequency-domain response data of dispersive media

this paper introduces the vector fitting technique and

under physical constraints and mathematical transformations

establishes a generalized dispersive media model that includes real poles and complex conjugate pole pairs

thereby unifying the description of relaxation-type and resonance-type dispersive behaviors. To overcome the computational complexity of time-domain convolution introduced by dispersive constitutive relations

the auxiliary differential equation method is employed to construct a DGTD solving scheme suitable for the generalized dispersive media model. This transforms the convolution operation into a set of coupled ordinary differential equations

enabling efficient time-domain stepping solutions. To further enhance computational efficiency

a local time-stepping strategy based on a low-storage Runge-Kutta integration method is designed

significantly improving the solving speed for dispersive media problems. This paper numerically solves the radar cross section (RCS) of dispersive spheres

dispersive material-coated warheads

and the reflection coefficients of frequency selective surface (FSS) periodic units. The results demonstrate that the generalized dispersive media model constructed via vector fitting accurately describes the frequency-domain dispersive characteristics of the media

with fitting errors consistently maintained at a low level. The obtained RCS and reflection coefficient results are in strong agreement with those from CST commercial software and traditional finite-difference methods

with absolute errors controlled within 3 dB. While ensuring computational accuracy

the introduction of the local time-stepping technique improves overall computational efficiency by over 40.42%. The proposed method provides a numerical analysis tool for electromagnetic simulations of complex dispersive media that combines generality

efficiency

and reliability.

关键词

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