A Note on Matrix Decomposition for Synthetic Basis Functions Method in the Analysis of Periodic Structures

Authors

  • Yanlin Xu College of Electronic Science and Technology National University of Defense Technology, Changsha 410073, China
  • Ning Hu Information Engineering University Zhengzhou 450001, China
  • Chenxi Liu College of Electronic Science and Technology National University of Defense Technology, Changsha 410073, China
  • Hao Ding College of Electronic Science and Technology National University of Defense Technology, Changsha 410073, China
  • Jun Li The Second Representative Office of Changsha Area Changsha 410011, China

DOI:

https://doi.org/10.13052/2025.ACES.J.400209

Keywords:

Matrix decomposition, method of moments, periodic structures, surface integral equation, synthetic functions

Abstract

The synthetic basis functions method (SBFM) is discussed in this work and orthogonal triangle decomposition (QR decomposition) is adopted to extract independent items from solution space in the construction of synthetic functions. Just like singular value decomposition (SVD), accuracy of SBFM+QR improves with the growth of the number of synthetic functions. However, there is an interesting phenomenon for SBFM+QR: only one synthetic function is enough to get the same level of accuracy with method of moments (MoM) when a single body is concerned. Moreover, this feature can be further extended to periodic arrays. In other words, for periodic arrays, one synthetic function is enough to get high accuracy if SBFM+QR is adopted. This is meaningful for large-scale periodic arrays and may lead to benefits such as decreasing memory cost and improving efficiency.

Downloads

Download data is not yet available.

Author Biographies

Yanlin Xu, College of Electronic Science and Technology National University of Defense Technology, Changsha 410073, China

Yanlin Xu received the B.S., M.S., and Ph.D. degrees in electronic science and technology from the National University of Defense Technology (NUDT), Changsha, China, in 2013, 2015, and 2018, respectively. He is currently an Associate Professor with the College of Electronic Science and Technology, NUDT. His current research interests include electromagnetic compatibility and protection, and computational electromagnetism.

Ning Hu, Information Engineering University Zhengzhou 450001, China

Ning Hu (corresponding author) received the B.S. degree in electronic engineering and the M.S. degree in electronic science and technology from National University of Defense Technology (NUDT), Changsha, Hunan, P. R. China, in 2017 and 2019, respectively. He received the Ph.D. degree in information and communication engineering from NUDT in 2023. His research interests include electromagnetic compatibility and protection, and metamaterials and antennas.

Chenxi Liu, College of Electronic Science and Technology National University of Defense Technology, Changsha 410073, China

Chenxi Liu (corresponding author) received the B.S. degree in electrical engineering and the M.S. and Ph.D. degrees in electronic science and technology from the National University of Defense Technology, Changsha, China, in 2013, 2015, and 2019, respectively. He is currently an Associate Professor with the College of Electronic Science, National University of Defense Technology. His research areas of interest include electromagnetically induced transparency analogy based on metamaterial and tunable metamaterials based on active components.

Hao Ding, College of Electronic Science and Technology National University of Defense Technology, Changsha 410073, China

Hao Ding received the B.S. and M.S. degrees from Air Force Engineering University (AFEU), Xian, China, in 2013 and 2016, respectively, and the Ph.D. degree from the University and Institute of Microelectronics, Chinese Academy of Sciences (IMECAS), Beijing, China, and AFEU, in 2020. He is now working as a Lecturer with the National University of Defense Technology, Changsha, China. His research interests include IC and microsystem designs for electromagnetic compatibility and protection.

Jun Li, The Second Representative Office of Changsha Area Changsha 410011, China

Jun Li received the M.S. degree from the National University of Defense Technology (NUDT), Changsha, China, in 2015. He is currently a senior engineer with the second representative office of Changsha area. His current research interests include electromagnetic compatibility antenna, and big data analysis.

References

R. Liu, G. Xiao, and Y. Hu, “Solving surface-volume integral equations for PEC and inhomogeneous/anisotropic materials with multibranch basis functions,” Applied Computational Electromagnetics Society (ACES) Journal, vol. 39, no. 2, pp. 108-114, 2024.

W. Lu, W. Xiang, W. Wu, and W Yang, “The fast algorithms for electromagnetic analysis of the large-scale and finite periodic structures,” Chinese Journal of Radio Science, vol. 35, no. 1, pp. 85-92, 2020.

W. He, Z. Yang, X. Huang, W. Wang, M. Yang, and X. Sheng, “Solving electromagnetic scattering problems with tens of billions of unknowns using GPU accelerated massively parallel MLFMA,” IEEE Trans. Antennas Propag., vol. 70, no. 7, pp. 5672-5682, 2022.

C. Wu, L. Guan, P. Gu, and R. Chen, “Application of parallel CM-MLFMA method to the analysis of array structures,” IEEE Trans. Antennas Propag., vol. 69, no. 9, pp. 6116-6121, 2021.

M. Li, T. Su, and R. Chen, “Equivalence principle algorithm with body of revolution equivalence surface for the modeling of large multiscale structures,” IEEE Trans. Antennas Propag., vol. 64, no. 5, pp. 1818-1828, 2016.

M. Yang, B. Wu, X. Huang, and X. Sheng, “The progress of domain decomposition methods for 3D electromagnetic scattering problems,” Chinese Journal of Radio Science, vol. 35, no. 1, pp. 37-45, 2020.

R. Zhao, Y. Chen, X. Gu, Z. Huang, H. Bagci, and J. Hu, “A local coupling multitrace domain decomposition method for electromagnetic scattering from multilayered dielectric objects,” IEEE Trans. Antennas Propag., vol. 68, no. 10, pp. 7099-7108, 2020.

K. Fan, B. Wei, J. Chen, and B. He. “A spatial modes filtering FETD method combined with domain decomposition for simulating fine electromagnetic structures,” IEEE Microwave and Wireless Components Letters, vol. 32, no. 11, pp. 1259-1262, 2022.

M. Li, M. A. Francavilla, R. Chen, and G. Vecchi, “Wideband fast kernel-independent modeling of large multiscale structures via nested equivalent source approximation,” IEEE Trans. Antennas Propag., vol. 63, no. 5, pp. 2122-2134, 2015.

Y. Xu, H. Yang, R. Shen, L. Zhu, and X. Huang, “Scattering analysis of multiobject electromagnetic systems using stepwise method of moment,” IEEE Trans. Antennas Propag., vol. 67, no. 3, pp. 1740-1747, 2019.

L. Matekovits, G. Vecchi, G. Dassano, and M. Orefice, “Synthetic function analysis of large printed structures: the solution space sampling approach,” IEEE Antennas Propag. Society International Symposium, no. 2, pp. 568-571,2001.

L. Matekovits, V. A. Laza, and G. Vecchi, “Analysis of large complex structures with the synthetic-functions approach,” IEEE Trans. Antennas Propag., vol. 55, no. 9, pp. 2509-2521, 2007.

H. Yuan, S. Gong, Y. Guan, and D. Su, “Scattering analysis of the large array antennas using the synthetic basis function method,” Journal of Electromagnetic Waves and Applications, vol. 23, pp. 309-320, 2009.

B. Zhang, G. Xiao, J. Mao, and Y. Wang, “Analyzing large-scale non-periodic arrays with synthetic basis functions,” IEEE Trans. Antennas Propag., vol. 58, no. 11, pp. 3576-3584, 2010.

W. Chen, G. Xiao, S. Xiang, and J. Mao, “A note on the construction of synthetic basis functions for antenna arrays,” IEEE Trans. Antennas Propag., vol. 60, no. 7, pp. 3509-3512, 2012.

Y. Xu, H. Yang, and W. Yu, “Scattering analysis of periodic composite metallic and dielectric structures with synthetic basis functions,” Applied Computational Electromagnetics (ACES) Society Journal, vol. 30, no. 10, pp. 1059-1067,2015.

Y. Xu, H. Yang, W. Yu, and J. Zhu, “An automatic scheme for synthetic basis functions method,” IEEE Trans. Antennas Propag., vol. 66, no. 3, pp. 1601-1606, 2018.

Y. Xu, X. Huang, C. Liu, S. Zha, and J. Liu, “Synthetic functions expansion: automation, reuse, and parallel,” IEEE Trans. Antennas Propag., vol. 69, no. 3, pp. 1825-1830, 2021.

N. Hu, Y. Xu, and P. Liu, “A numerical analysis of conformal energy selective surface array with synthetic functions expansion,” Applied Computational Electromagnetics Society (ACES) Journal, vol. 39, no. 2, pp. 115-122, 2024.

Y. Xu, C. Liu, Z. Wu, N. Hu, J. Liu, and P. Liu, “Fast electromagnetic simulation method for large-scale quasi-periodic arrays,” Sci. Sin. Inform., vol. 54, no. 2, pp. 430-448, 2024.

W. Lu, T. Cui, Z. Qian, X. Yin, and W. Hong, “Accurate analysis of large-scale periodic structures using an efficient sub-entire-domain basis function method,” IEEE Trans. Antennas Propag., vol. 52, no. 11, pp. 3078-3085, 2004.

V. V. S. Prakash and R. Mittra, “Characteristic basis function method: A new technique for efficient solution of method of moments matrix equations,” Microwave and Optical Technology Letters, vol. 36, no. 2, pp. 95-100, 2003.

C. S. Park, I. P. Hong, Y. J. Kim, and J. G. Yook, “Acceleration of multilevel characteristic basis function method by multilevel multipole approach,” IEEE Trans. Antennas Propag., vol. 68, no. 10, pp. 7109-7120, 2020.

Y. Xu, H. Yang, J. Lu, W. Yu, W. Yin, and D. Peng, “Improved synthetic basis functions method for nonperiodic scaling structures with arbitrary spatial attitudes,” IEEE Trans. Antennas Propag., vol. 65, no. 9, pp. 4728-4741, 2017.

Z. Wu, Y. Xu, P. Liu, T. Tian, and M. Lin, “An ultra-broadband energy selective surface design method: From filter circuits to metamaterials,” IEEE Trans. Antennas Propag., vol. 71, no. 7, pp. 5865-5873, 2023.

Downloads

Published

2025-02-28

How to Cite

[1]
Y. . Xu, N. . Hu, C. . Liu, H. . Ding, and J. . Li, “A Note on Matrix Decomposition for Synthetic Basis Functions Method in the Analysis of Periodic Structures”, ACES Journal, vol. 40, no. 02, pp. 156–164, Feb. 2025.

Issue

2025: Vol 40 Iss 2

Section

Novel CEM methods & applications

Categories