Enhanced CPML Based on the Autoformer Network for 2D, WCS-FDTD Method

作者

  • Yumeng Wu Engineering Research Center of Smart Microsensors and Microsystems, Ministry of Education, Hangzhou Dianzi University, Hangzhou 310018, China, State Key Laboratory of Millimeter Waves, Southeast University, Nanjing 210096, China
  • Ning Xu Engineering Research Center of Smart Microsensors and Microsystems, Ministry of Education, Hangzhou Dianzi University, Hangzhou 310018, China, State Key Laboratory of Millimeter Waves, Southeast University, Nanjing 210096, China
  • Yexin Li Engineering Research Center of Smart Microsensors and Microsystems, Ministry of Education, Hangzhou Dianzi University, Hangzhou 310018, China
  • Kuiwen Xu Engineering Research Center of Smart Microsensors and Microsystems, Ministry of Education, Hangzhou Dianzi University, Hangzhou 310018, China
  • Juan Chen School of Information and Communication Engineering, Xi’an Jiaotong University, Xi’an 710049, China

##plugins.pubIds.doi.readerDisplayName##:

https://doi.org/10.13052/2026.ACES.J.410103

关键词:

weakly conditionally stable finite-difference time-domain (WCS-FDTD), convolutional perfectly matched layer (CPML), data-driven, Autoformer

摘要

This paper proposes a novel convolutional perfectly matched layer (CPML) for the weakly conditionally stable finite-difference time-domain (WCSFDTD) method. The Autoformer neural network is introduced to replace the conventional multi-layer CPML. Employing only a single-layer structure, the Auto-former-driven CPML considerably reduces both the computational domain scale and algorithmic complexity. By leveraging sequence decomposition and sparse attention mechanisms, the wave-absorption performance of this method is significantly improved. Integrated into the 2D WCS-FDTD framework, the proposed method overcomes Courant-Friedrichs-Lewy (CFL) stability constraints for FDTD intelligent absorbing boundaries, with its time step size independent of fine grid sizes in any direction. Numerical results demonstrate that the proposed method can achieve excellent wave-absorption performance with high computational efficiency, while maintaining satisfactory robustness in complex scenarios.

##plugins.generic.usageStats.downloads##

##plugins.generic.usageStats.noStats##

##submission.authorBiographies##

##submission.authorWithAffiliation##

Yumeng Wu was born in Zhejiang, China, in 2004. He is currently working toward the B.S. degree in Electronic Science and Technology at Hangzhou Dianzi University, China. His current research interests include computational electromagnetics and deep learning.

##submission.authorWithAffiliation##

Ning Xu received the Ph.D. degree in electromagnetic fields and microwave techniques at Xi’an Jiaotong University, Xi’an, China, in 2021. She was a visiting student with the On-Chip Electromagnetics Group, School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, USA. She now serves as a researcher at Hangzhou Dianzi University, China. Her current research interests include computational electromagnetics especially the FDTD method, graphene and terahertz electronics.

##submission.authorWithAffiliation##

Yexin Li was born in Anhui, China. He received the B.E. degree from Anhui Agricultural University, China, in 2019, in electronic information engineering. He is currently pursuing an M.S. degree at Hangzhou Dianzi University. His research interests include computational electromagnetism and deep learning.

##submission.authorWithAffiliation##

Kuiwen Xu (Member, IEEE) received his B.E. degree in Electronics and Information Engineering from Hangzhou Dianzi University, Hangzhou, China, in 2009, and his Ph.D. degree from the Department of Information and Electronic Engineering at Zhejiang University, Hangzhou, 2014. He was invited to the State Key Laboratory of Terahertz and Millimeter Waves, City University of Hong Kong, Hong Kong, as a Visiting Professor, in 2018. Since September 2015, he has been with Hangzhou Dianzi University, Hangzhou, where he is currently a professor. His research interests include electromagnetic inverse problems, RF measurement and microwave imaging, and AI-inspired inverse design of RF devices.

##submission.authorWithAffiliation##

Juan Chen was born in Chongqing, China. She received the Ph.D. degree from Xi’an Jiaotong University, Xi’an, China, in 2008, in electromagnetic field and microwave technology. She is currently working in Xi’an Jiaotong University, Xi’an, as a professor. Her research interests include the computational electromagnetics and microwave device design.

参考

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. Boston, MA, USA: Artech House, 2005.

W. Sun, “Automatic and efficient surface FDTD mesh generation for analysis of EM scattering and radiation,” Applied Computational Electromagnetics Society (ACES) Journal, vol. 9, no. 2, pp. 162–169, July 2022.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propagat., vol. AP-14, pp. 302–307, 1966.

R. Courant, K. Friedrichs, and H. Lewy, “On the partial difference equations of mathematical physics,” IBM J. Res. Dev., vol. 11, no. 2, pp. 215–234, Mar. 1967.

J. Chen and J. Wang, “A novel WCS-FDTD method with weakly conditional stability,” IEEE Trans. Electromagn. Compat., vol. 49, no. 2, pp. 419–426, 2007.

J. Chen, “Improved weakly conditionally stable finite-difference time-domain method,” Applied Computational Electromagnetics Society (ACES) Journal, vol. 27, no. 5, pp. 413–419, Feb. 2022.

J. Chen and H. Mai, “A review of weakly conditional stable finite-difference time-domain method for modeling electromagnetic problems with fine structures,” Int. J. Numer. Model.: Electron. Networks, Devices Fields, vol. 31, no. 5, p. e2341, 2018.

G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagn. Compat., vol. EMC-23, no. 4, pp. 377–382, 1981.

B. Engquist and A. Majda, “Absorbing boundary conditions for the numerical simulation of waves,” Math. Comput., vol. 31, no. 139, pp. 629–651, 1977.

J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys., vol. 114, no. 2, pp. 185–200, 1994.

J.-P. Berenger, “Perfectly matched layer for the FDTD solution of wave-structure interaction problems,” IEEE Trans. Antennas Propag., vol. 44, no. 1, pp. 110–117, 1996.

A. P. Zhao, “Uniaxial perfectly matched layer media for an unconditionally stable 3-D ADI-FD-TD method,” IEEE Microw. Wireless Compon. Lett., vol. 12, no. 12, pp. 497–499, 2002.

L. Bernard, R. R. Torrado, and L. Pichon, “Efficient implementation of the UPML in the generalized finite-difference time-domain method,” IEEE Trans. Magn., vol. 46, no. 8, pp. 3492–3495, 2010.

J. A. Roden and S. D. Gedney, “Convolutional PML (CPML): An efficient FDTD implementation of the CFS-PML for arbitrary media,” Microw. Opt. Technol. Lett., vol. 27, no. 5, pp. 334–339, 2000.

S. D. Gedney, “An auxiliary differential equation formulation for the complex-frequency shifted PML,” IEEE Trans. Antennas Propag., vol. 58, no. 3, pp. 838–847, 2010.

R. Martin and D. Komatitsch, “An unsplit convolutional perfectly matched layer technique improved at grazing incidence for the viscoelastic wave equation,” Geophys. J. Int., vol. 179, no. 1, pp. 333–344, 2009.

H. M. Yao and L. Jiang, “Machine-learning-based PML for the FDTD method,” IEEE Antennas Wireless Propag. Lett., vol. 18, no. 1, pp. 192–196, 2018.

H. M. Yao and L. Jiang, “Enhanced PML based on the long short-term memory network for the FDTD method,” IEEE Access, vol. 8, pp. 21028–21035, 2020.

H. H. Zhang, H. M. Yao, L. Jiang, and M. Ng, “Deep long short-term memory networks-based solving method for the FDTD method: 2-D case,” IEEE Microw. Wirel. Technol. Lett., vol. 33, no. 5, pp. 499–502, May 2023.

L. Guo, M. Li, S. Xu, F. Yang, and L. Liu, “Electromagnetic modeling using an FDTD-equivalent recurrent convolution neural network: Accurate computing on a deep learning framework,” IEEE Antennas Propag. Mag., vol. 65, no. 1, pp. 93–102, Feb. 2023.

N. Feng, Y. Chen, Y. Zhang, M. S. Tong, Q. Zeng, and G. P. Wang, “An expedient DDF-based implementation of perfectly matched monolayer,” IEEE Microwave and Wireless Components Letters, vol. 31, no. 6, pp. 541–544, June 2021.

Y. Chen, Y. Zhang, H. Wang, N. Feng, L. Yang, and Z. Huang, “Differentiable-decision-tree-based neural Turing machine model integrated into FDTD for implementing EM problems,” IEEE Trans. Electromagn. Compat., vol. 65, no. 6, pp. 1579–1586, Dec. 2023.

N. Feng, H. Wang, Z. Zhu, Y. Zhang, L. Yang, and Z. Huang, “Gradient boosting decision tree-based PMM model integrated into FDTD method for solving subsurface sensing problems,” IEEE Transactions on Antennas and Propagation, vol. 72, no. 7, pp. 5892–5899, July 2024.

H.-Y. Ren, X.-H. Wang, T. Wei, and L. Wang, “Recurrent neural network-assisted truncation of convolutional perfectly matched layers for FDTD,” IEEE Antennas Wireless Propag. Lett., vol. 23, no. 5, pp. 1493–1497, 2024.

H. Wu, J. Xu, J. Wang, and M. Long, “Autoformer: Decomposition transformers with auto-correlation for long-term series forecasting,” Adv. Neural Inf. Process. Syst., vol. 34, pp. 22419–22430, 2021.

Z. Shen, J. Lu, L. Gui, J. Li, Y. He, D. Yin, and X. Sun, “SSA: A content-based sparse attention mechanism,” Int. Conf. Knowl. Sci. Eng. Manag. Dig., pp. 669–680, 2022.

##submission.downloads##

已出版

2026-01-30