一种强鲁棒性的时域非连续伽略金可穿透薄层算法

杨谦; 魏兵; 李林茜; 邓浩川

doi:10.7498/aps.72.20222230

摘要

本文研究了时域非连续伽略金算法(discontinuous Galerkin time-domain, DGTD)中的可穿透薄层问题, 薄层问题属于多尺度问题, 精确建模资源消耗太高难以实施, 可采用近似方案. 研究发现采用等效表面电流激励易产生发散, 为提高计算方案鲁棒性, 研究了电磁场修正方案, 这一方案允许采用参数很大的薄层(高介电系数), 其计算方法简便易行. 此外, 还给出了多层介质薄层的仿真方案, 并对相关数值算例进行验证, 结果说明了本文算法的精确性和有效性, 本文方案可用于复杂薄层电磁问题的快速求解.

关键词:

Abstract

The thin layer problem is common in some engineering cases, such as a coating target or dielectric radome. If the skin depth of the medium behind the thin layer is much smaller than the medium scale, the transmission line impedance boundary can be used to solve the thin layer problem . When both sides of the thin layer are free space or the skin depth of the medium behind the thin layer is greater than or comparable to the scale of the medium, the transmission line impedance boundary condition is not applicable. Such problems need incident and reflected wave data and are also known as penetrable thin-layer problems.When dealing with penetrable thin-layer problems, we need to give the electromagnetic wave data on both sides. In addition, the thin layer problem can belong with multi-scale problems. The EM simulation is difficult to implement because of the high resource consumption of accurate modeling.The accurate modeling is a very expensive algorithm, and the mesh-size difference between the thin layer region and the surrounding ordinary region is too large, thus seriously affecting the quality of the elements (tetrahedrons). So, it is difficult to solve the problem of thin layer quickly by using the time-domain discontinuous Galerkin method or even by using local time steps or other optimization methods. To acquire a fast solution, the approximate boundary condition can be used to describe the thin layer. The DGTD has also the advantage of the geometric fitting property. If a thin layer model is curved, we can build a conformal geometric model to deal with the thin layer, thus avoiding the complicated interpolation correction scheme.In this work, A robust DGTD method for penetrable thin layers is proposed. In our study, we find that the current excitation scheme is prone to divergence when large dielectric coefficients are dealt with and its robustness is poor. To solve this problem, we use the electromagnetic field correction scheme in DGTD to deal with the thin layer problems. In addition, engineering problems may encounter multiple thin layers. In this work, a simulation scheme for multiple thin layers is presented and relevant numerical examples are given to verify it. The results illustrate the accuracy and effectiveness of the method in this work, and the method presented in this work can be used for the fast calculation of complex thin layer problems.

Keywords:

penetrable thin layers /
multi-scale problems /
discontinuous Galerkin time domain method

作者及机构信息

1.
西安电子科技大学物理学院, 西安　710071

2.
电磁散射重点实验室, 北京　110000

通信作者: 杨谦, qyang@xidian.edu.cn

基金项目: 国家自然科学基金(批准号: 61901324, 62001345)、中国博士后科学基金(批准号: 2019M653548, 2019M663928XB)、电波环境特性及模化技术国防科技重点实验室基金 (批准号: 201903002)、电磁散射重点实验室基金(批准号: 61424090111)和中央高校基本科研业务费(批准号: XJS200501, XJS200507, JB200501)资助的课题.

Authors and contacts

1.
School of Physics, Xidian University, Xi’an 710071, China

2.
The Science and Technology on Electromagnetic Scattering Laboratory, Beijing 110000, China

Corresponding author: Yang Qian, qyang@xidian.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61901324, 62001345), the China Postdoctoral Science Foundation (Grant Nos. 2019M653548, 2019M663928XB), the Foundation of National Key Laboratory of Electromagnetic Environment, China (Grant No. 201903002), the Science and Technology on Electromagnetic Scattering Laboratory, China (Grant No. 61424090111), and the Fundamental Research Funds for the Central Universities of China (Grant Nos. XJS200501, XJS200507, JB200501).

文章全文 : translate this paragraph

参考文献

[1]	Feliziani M 2011 IEEE Trans. Electromagn. Compat. 54 299 Google Scholar
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[8]	Van den Berghe S, Olyslager F, De Zutter D 1998 IEEE Microw. Guided Wave Lett. 8 75 Google Scholar
[9]	Schild S, Chavannes N, Kuster N 2007 IEEE Trans. Antennas Propag. 55 3587 Google Scholar
[10]	Wang Y, Langdon S 2014 IEEE Antennas and Propagation Society International Symposium (APSURSI) Memphis, July 6–July 11, 2014 pp504–505
[11]	Karlsson A 2009 IEEE Trans. Antennas Propag. 57 144 Google Scholar
[12]	Nayyeri V, Soleimani M, Ramahi O M 2013 IEEE Trans. Electromagn. Compat. 56 385 Google Scholar
[13]	Mi J, Ren Q, Su D 2020 IEEE Trans. Antennas Propag. 69 2230 Google Scholar
[14]	Yang Q, Wei B, Li L, Ge D 2020 IEEE Trans. Antennas Propag. 69 3371 Google Scholar
[15]	Ban Z G, Shi Y, Wang P 2021 IEEE Trans. Antennas Propag. 70 3916 Google Scholar
[16]	Zhang T, Bao H, Gu P, Ding D, Werner D H, Chen R 2021 IEEE Trans. Antennas Propag. 70 526 Google Scholar
[17]	Mitzner K 1968 IEEE Trans. Antennas Propag. 16 706 Google Scholar
[18]	Li P, Shi Y, Jiang L J, Bağcι H 2015 IEEE Trans. Antennas Propag. 63 5686 Google Scholar
[19]	Li P, Jiang L J, Bağcι H 2015 IEEE Trans. Antennas Propag. 63 3065 Google Scholar
[20]	Li P, Jiang L J, Bağcı H 2018 IEEE Trans. Antennas Propag. 66 3590 Google Scholar

施引文献

图 1 薄涂层示意图

Fig. 1. Plane wave incident on a thin layer.

下载: 全尺寸图片幻灯片

图 2 一维DGTD反射透射结果

Fig. 2. The reflection and transmission coefficients (1D-DGTD).

下载: 全尺寸图片幻灯片

图 3 薄层-四面体示意图 (DGTD)

Fig. 3. Thin layer-tetrahedrons schematic (DGTD).

下载: 全尺寸图片幻灯片

图 4 多薄层-四面体示意图(DGTD)

Fig. 4. Thin layers-tetrahedrons schematic (DGTD).

下载: 全尺寸图片幻灯片

图 5 一维DGTD反射透射结果

Fig. 5. The reflection and transmission coefficients (1D-DGTD).

下载: 全尺寸图片幻灯片

图 6 一维DGTD反射透射结果

Fig. 6. The reflection and transmission coefficients (1D-DGTD).

下载: 全尺寸图片幻灯片

图 7 一维模型示意图

Fig. 7. One-dimensional model schematic.

下载: 全尺寸图片幻灯片

图 8 一维DGTD反射透射结果

Fig. 8. The reflection and transmission coefficients (1D-DGTD)

下载: 全尺寸图片幻灯片

图 9 双薄层示意图

Fig. 9. Thin layers schematic.

下载: 全尺寸图片幻灯片

图 10 一维DGTD反射透射结果

Fig. 10. The reflection and transmission coefficients (1D-DGTD).

下载: 全尺寸图片幻灯片

图 11 双薄层示意图(一侧为介质层)

Fig. 11. Thin layers with thick layer schematic.

下载: 全尺寸图片幻灯片

图 12 一维DGTD反射透射结果

Fig. 12. The reflection and transmission coefficients (1D-DGTD).

下载: 全尺寸图片幻灯片

图 13 球形薄层

Fig. 13. Spherical thin layer.

下载: 全尺寸图片幻灯片

图 15 涂覆球

Fig. 15. Spherical thin layer.

下载: 全尺寸图片幻灯片

图 14 球形薄层单站RCS结果

Fig. 14. Monostatic RCS of the spherical thin layer.

下载: 全尺寸图片幻灯片

图 16 涂覆球单站RCS结果

Fig. 16. Monostatic RCS of the coated sphere.

下载: 全尺寸图片幻灯片

图 17 涂覆球(双层涂覆)

Fig. 17. Coated sphere (double thin layers).

下载: 全尺寸图片幻灯片

图 18 涂覆双层球单站RCS结果

Fig. 18. Monostatic RCS of the coated sphere (double layers)

下载: 全尺寸图片幻灯片

map

[1]	Feliziani M 2011 IEEE Trans. Electromagn. Compat. 54 299 Google Scholar
[2]	Hanson G W 2008 J. Appl. Phys. 103 064302 Google Scholar
[3]	Shapoval O V, Gomez-Diaz J S, Perruisseau-Carrier J, Mosig J R, Nosich A I 2013 IEEE Trans. Terahertz Sci. Technol. 3 666 Google Scholar
[4]	Maloney J G, Smith G S 1992 IEEE Trans. Antennas Propag. 40 323 Google Scholar
[5]	Richmond J 1965 IEEE Trans. Antennas Propag. 13 334 Google Scholar
[6]	Harrington R, Mautz J 1975 IEEE Trans. Antennas Propag. 23 531 Google Scholar
[7]	Luebbers R J, Kunz K 1992 IEEE Trans. Antennas Propag. 40 349 Google Scholar
[8]	Van den Berghe S, Olyslager F, De Zutter D 1998 IEEE Microw. Guided Wave Lett. 8 75 Google Scholar
[9]	Schild S, Chavannes N, Kuster N 2007 IEEE Trans. Antennas Propag. 55 3587 Google Scholar
[10]	Wang Y, Langdon S 2014 IEEE Antennas and Propagation Society International Symposium (APSURSI) Memphis, July 6–July 11, 2014 pp504–505
[11]	Karlsson A 2009 IEEE Trans. Antennas Propag. 57 144 Google Scholar
[12]	Nayyeri V, Soleimani M, Ramahi O M 2013 IEEE Trans. Electromagn. Compat. 56 385 Google Scholar
[13]	Mi J, Ren Q, Su D 2020 IEEE Trans. Antennas Propag. 69 2230 Google Scholar
[14]	Yang Q, Wei B, Li L, Ge D 2020 IEEE Trans. Antennas Propag. 69 3371 Google Scholar
[15]	Ban Z G, Shi Y, Wang P 2021 IEEE Trans. Antennas Propag. 70 3916 Google Scholar
[16]	Zhang T, Bao H, Gu P, Ding D, Werner D H, Chen R 2021 IEEE Trans. Antennas Propag. 70 526 Google Scholar
[17]	Mitzner K 1968 IEEE Trans. Antennas Propag. 16 706 Google Scholar
[18]	Li P, Shi Y, Jiang L J, Bağcι H 2015 IEEE Trans. Antennas Propag. 63 5686 Google Scholar
[19]	Li P, Jiang L J, Bağcι H 2015 IEEE Trans. Antennas Propag. 63 3065 Google Scholar
[20]	Li P, Jiang L J, Bağcı H 2018 IEEE Trans. Antennas Propag. 66 3590 Google Scholar

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一种强鲁棒性的时域非连续伽略金可穿透薄层算法