A CN-RK Discontinuous Galerkin Time-Domain Method Without the Stability Restriction Due to Material Loss

XIANG Ru; MA Xi-kui; MA Liang; CHI Ming-jun; WANG Jia-wei

doi:10.12263/DZXB.20241004

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A CN-RK Discontinuous Galerkin Time-Domain Method Without the Stability Restriction Due to Material Loss

PAPERS | 更新时间：2025-12-27

- A CN-RK Discontinuous Galerkin Time-Domain Method Without the Stability Restriction Due to Material Loss
- ACTA ELECTRONICA SINICA Vol. 53, Issue 8, Pages: 2649-2657(2025)
- 作者机构：
  
  西安交通大学电气工程学院，陕西西安 710049
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China(52207014)
- DOI：10.12263/DZXB.20241004
  CLC： TM15;TN011
- Received：06 November 2024，
  
  Accepted：15 July 2025，
  
  Published：25 August 2025
- 稿件说明：
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向汝, 马西奎, 马亮, 等. 一种稳定性不受媒质损耗影响的CN-RK时域间断伽辽金方法[J]. 电子学报, 2025, 53(08): 2649-2657.

XIANG Ru, MA Xi-kui, MA Liang, et al. A CN-RK Discontinuous Galerkin Time-Domain Method Without the Stability Restriction Due to Material Loss[J]. Acta Electronica Sinica, 2025, 53(08): 2649-2657.
向汝, 马西奎, 马亮, 等. 一种稳定性不受媒质损耗影响的CN-RK时域间断伽辽金方法[J]. 电子学报, 2025, 53(08): 2649-2657. DOI：10.12263/DZXB.20241004

XIANG Ru, MA Xi-kui, MA Liang, et al. A CN-RK Discontinuous Galerkin Time-Domain Method Without the Stability Restriction Due to Material Loss[J]. Acta Electronica Sinica, 2025, 53(08): 2649-2657. DOI：10.12263/DZXB.20241004

摘要

采用显式龙格-库塔（Runge-Kutta，RK）时间积分格式的时域间断伽辽金（Discontinuous Galerkin Time-Domain，DGTD）方法求解涉及有耗媒质的电磁问题时，时间步长会受到电导率或导磁率的严格限制.虽然已经有研究通过数值试验验证了有耗媒质对稳定性的影响，但缺乏严格的理论依据.因此，本文基于理论推导建立了有耗媒质中显式RK-DGTD方法的稳定性条件，得到时间步长上限的估计值，并对其准确性进行了数值验证.此外，为了提高计算效率，本文提出了一种适用于DGTD方法的隐式-显式时间离散格式，采用隐式Crank-Nicolson（CN）格式对损耗项进行离散，而对其余项采用显式RK格式，从理论上证明了该方法的时间稳定性不受媒质损耗的影响，并通过数值算例验证了其可靠性与效率.

Abstract

When discontinuous Galerkin time-domain (DGTD) methods with explicit runge-kutta (RK) schemes are applied to the analysis of electromagnetic (EM) problems involving lossy media

the time-step size is strictly limited by electric and magnetic conductivity. Although the influence of lossy media on stability has been verified by numerical experiments

it lacks strict theoretical support. Therefore

the stability condition of the explicit RK-DGTD methods in lossy media is established based on theoretical derivation. The upper limit of time-step size is estimated

and numerical results demonstrate its accuracy. In addition

to improve computational efficiency

an implicit-explicit time integration scheme is proposed for DGTD methods. The lossy terms are discretized using an implicit crank-nicolson (CN) scheme

while the remaining terms are discretized using an explicit RK scheme. The time stability of the proposed method is theoretically proven to be unaffected by material loss

and numerical experiments validate its reliability and efficiency.

关键词

Keywords

references

杨谦 , 魏兵 , 李林茜 , 等 . 一种强鲁棒性的时域非连续伽略金可穿透薄层算法 [J ] . 物理学报 , 2023 , 72 ( 8 ): 17 - 26 .

YANG Q , WEI B , LI L Q , et al . A robust discontinuous Galerkin time domain algorithm for penetrable thin layers [J ] . Acta Physica Sinica , 2023 , 72 ( 8 ): 17 - 26 . (in Chinese)

JIA Z L , ZHANG H H , DING D Z , et al . Time-domain shielding effectiveness analysis based on DGTD method accelerated by local time-stepping and parallel techniques [J ] . IEEE Transactions on Electromagnetic Compatibility , 2023 , 65 ( 3 ): 900 - 911 .

ZHANG X , LI P , LI X C , et al . A hybridizable discontinuous Galerkin time-domain method with robin transmission condition for transient thermal analysis of 3-D integrated circuits [J ] . IEEE Transactions on Components, Packaging and Manufacturing Technology , 2022 , 12 ( 9 ): 1474 - 1483 .

LI X , XU L , YANG Z H , et al . A new explicit-implicit hybridizable discontinuous Galerkin time-domain method for electromagnetics [J ] . IEEE Microwave and Wireless Components Letters , 2022 , 32 ( 11 ): 1263 - 1266 .

LIU Q Q , ZHAO W S , WANG H , et al . 3-D domain decomposition method with nonconformal meshes for thermoelastic modeling [J ] . IEEE Geoscience and Remote Sensing Letters , 2024 , 21 : 7502105 .

LEE J F , LEE R , CANGELLARIS A . Time-domain finite-element methods [J ] . IEEE Transactions on Antennas and Propagation , 1997 , 45 ( 3 ): 430 - 442 .

文腾 , 崔翔 , 李学宝 , 等 . 考虑介质介电驰豫影响时瞬态电场计算的时域有限元法 [J ] . 电工技术学报 , 2022 , 37 ( 7 ): 1735 - 1745 .

WEN T , CUI X , LI X B , et al . Time-domain finite element method for calculation of transient electric field in combined insulating structures considering the influence of dielectric relaxation [J ] . Transactions of China Electrotechnical Society , 2022 , 37 ( 7 ): 1735 - 1745 . (in Chinese)

张黎 , 童美松 . 基于双区域增强体-面积分方程的有损互连结构的低频分析 [J ] . 电子学报 , 2025 , 53 ( 6 ): 1874 - 1884 .

ZHANG L , TONG M S . Low-frequency analysis of lossy interconnect structures based on two-region augmented volume-surface integral equations [J ] . Acta Electronica Sinica , 2025 , 53 ( 6 ): 1874 - 1884 . (in Chinese)

张金颢 , 周恒 , 张守龙 , 等 . 基于仿真及神经网络的大型电磁脉冲模拟器近区场计算 [J ] . 电子学报 , 2023 , 51 ( 3 ): 712 - 719 .

ZHANG J H , ZHOU H , ZHANG S L , et al . Calculation of near-field of large-scale electromagnetic pulse simulator based on simulation and neural network [J ] . Acta Electronica Sinica , 2023 , 51 ( 3 ): 712 - 719 . (in Chinese)

ÖZAKIN M B , CHEN L , AHMED S , et al . Stability analysis of discontinuous Galerkin time-domain method for conductive media [C ] // 2021 International Applied Computational Electromagnetics Society Symposium (ACES) . Piscataway : IEEE , 2021 : 1 - 3 .

CATELLA A , DOLEAN V , LANTERI S . An unconditionally stable discontinuous Galerkin method for solving the 2-D time-domain Maxwell equations on unstructured triangular meshes [J ] . IEEE Transactions on Magnetics , 2008 , 44 ( 6 ): 1250 - 1253 .

WANG J W , CHEN F , MA X K , et al . A Krylov-subspace-based exponential time integration scheme for discontinuous Galerkin time-domain methods [J ] . IEEE Transactions on Magnetics , 2019 , 55 ( 6 ): 7204605 .

CHEN J F , TOBON L E , CHAI M , et al . Efficient implicit-explicit time stepping scheme with domain decomposition for multiscale modeling of layered structures [J ] . IEEE Transactions on Components, Packaging and Manufacturing Technology , 2011 , 1 ( 9 ): 1438 - 1446 .

XIANG R , MA X K , MA L , et al . A stable discontinuous Galerkin time-domain method with implicit-explicit time-marching for lossy media [J ] . IEEE Transactions on Magnetics , 2024 , 60 ( 12 ): 7001804 .

HESTHAVEN J S , WARBURTON T . Nodal Discontinuous Galerkin Methods [M ] . New York : Springer New York , 2008 .

葛德彪 , 魏兵 . 电磁波时域不连续伽略金方法 [M ] . 北京 : 科学出版社 , 2019 .

GE D B , WEI B . Discontinuous Galerkin Time-Domain Method for Electromagnetic Waves [M ] . Beijing : Science Press , 2019 . (in Chinese)

张志勇 , 程曦 . 色散有损介质土壤对电磁回波影响的不确定性分析研究 [J ] . 电子学报 , 2021 , 49 ( 3 ): 614 - 618 .

ZHANG Z Y , CHENG X . Uncertainty analysis of the influence of dispersive and lossy soil on electromagnetic wave propagation [J ] . Acta Electronica Sinica , 2021 , 49 ( 3 ): 614 - 618 . (in Chinese)

XIE G D , FENG N X , FANG M , et al . A stability extensible symplectic FDTD(4, 4) method and its application in subgrid technique for arbitrary grid ratios [J ] . IEEE Transactions on Antennas and Propagation , 2023 , 71 ( 11 ): 9124 - 9129 .

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