volume | PIER Journals

Abstract

To address the convergence inefficiency of the conventional CS-Krylov-block method in solving electromagnetic scattering problems, this paper presents an adaptive Krylov subspace basis function method (AKSBFM) based on spectral energy thresholds. In this method, Krylov subspace basis functions (KSBFs) are first generated within each extended subdomain using localized self-impedance matrices. Singular value decomposition (SVD) is performed on the candidate basis set to evaluate energy contributions, and only the dominant components exceeding a predefined energy threshold are retained. As a result, the number of basis functions per subdomain is automatically adjusted, and a compact, well-conditioned reduced matrix system is constructed. This energy-guided truncation significantly eliminates redundant modes, yielding improved numerical stability and reducing the condition number by up to two orders of magnitude. Numerical experiments demonstrate that, compared with the traditional CS-Krylov-block method, AKSBFM improves computational efficiency while ensuring computational accuracy.

1. Harrington, R. F., "Field computation by moment methods," The Macmillan Comp., Vol. 130, No. 6, 276-280, 1968.

2. Burke, G. J., E. K. Miller, S. Chakrabarti, and K. Demarest, "Using model-based parameter estimation to increase the efficiency of computing electromagnetic transfer functions," IEEE Transactions on Magnetics, Vol. 25, No. 4, 2807-2809, Jul. 1989.
doi:10.1109/20.34291

3. Coifman, R., V. Rokhlin, and S. Wandzura, "The fast multipole method for the wave equation: A pedestrian prescription," IEEE Antennas and Propagation Magazine, Vol. 35, No. 3, 7-12, Jun. 1993.
doi:10.1109/74.250128

4. Hu, Jun, Zaiping Nie, Xiaofeng Que, and Min Meng, "Fast computation of scattering from 3D complex structures by MLFMA," Journal of Systems Engineering and Electronics, Vol. 19, No. 5, 872-877, Oct. 2008.
doi:10.1016/S1004-4132(08)60166-8

5. Xu, X. M. and Q. H. Liu, "Fast spectral-domain method for acoustic scattering problems," IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Vol. 48, No. 2, 522-529, Mar. 2001.
doi:10.1109/58.911735

6. Nie, Xiao Chun, Ning Yuan, Le Wei Li, and Yeow Beng Gan, "Fast analysis of RCS over a frequency band using pre-corrected FFT/AIM and asymptotic waveform evaluation technique," IEEE Transactions on Antennas and Propagation, Vol. 56, No. 11, 3526-3533, Nov. 2008.
doi:10.1109/TAP.2008.2005455

7. Zhao, Kezhong, M. N. Vouvakis, and Jin-Fa Lee, "The adaptive cross approximation algorithm for accelerated method of moments computations of EMC problems," IEEE Transactions on Electromagnetic Compatibility, Vol. 47, No. 4, 763-773, Nov. 2005.
doi:10.1109/TEMC.2005.857898

8. Donoho, D. L., "Compressed sensing," IEEE Transactions on Information Theory, Vol. 52, No. 4, 1289-1306, Apr. 2006.
doi:10.1109/TIT.2006.871582

9. Lucente, Eugenio, Agostino Monorchio, and Raj Mittra, "An iteration-free MoM approach based on excitation independent characteristic basis functions for solving large multiscale electromagnetic scattering problems," IEEE Transactions on Antennas and Propagation, Vol. 56, No. 4, 999-1007, Apr. 2008.
doi:10.1109/TAP.2008.919166

10. Wang, Pan, Zhonggen Wang, Yufa Sun, and Wenyan Nie, "A characteristic mode basis function method for solving wide-angle electromagnetic scattering problems," Journal of Electromagnetic Waves and Applications, Vol. 36, No. 14, 1968-1979, Mar. 2022.
doi:10.1080/09205071.2022.2051211

11. Cao, Xinyuan, Mingsheng Chen, Qi Qi, Meng Kong, Jinhua Hu, Liang Zhang, and Xianliang Wu, "Solving electromagnetic scattering problems by underdetermined equations and Krylov subspace," IEEE Microwave and Wireless Components Letters, Vol. 30, No. 6, 541-544, Jun. 2020.
doi:10.1109/LMWC.2020.2988166

12. Wang, Zhong-Gen, Wen-Yan Nie, and Han Lin, "Characteristic basis functions enhanced compressive sensing for solving the bistatic scattering problems of three-dimensional targets," Microwave and Optical Technology Letters, Vol. 62, No. 10, 3132-3138, Oct. 2020.
doi:10.1002/mop.32432

13. Brown, Peter N. and Youcef Saad, "Hybrid Krylov methods for nonlinear systems of equations," SIAM Journal on Scientific and Statistical Computing, Vol. 11, No. 3, 450-481, 1990.
doi:10.1137/0911026

14. Kong, Meng, Ming Sheng Chen, Bo Wu, and Xian Liang Wu, "Fast and stabilized algorithm for analyzing electromagnetic scattering problems of bodies of revolution by compressive sensing," IEEE Antennas and Wireless Propagation Letters, Vol. 16, 198-201, 2017.
doi:10.1109/LAWP.2016.2569605

15. Wang, Zhonggen, Haoran Yuan, Yufa Sun, Wenyan Nie, and Pan Wang, "Block-based Krylov subspace basis functions for solving bistatic scattering problems," IEEE Antennas and Wireless Propagation Letters, Vol. 22, No. 10, 2561-2565, Oct. 2023.
doi:10.1109/LAWP.2023.3296720

16. Wang, Zhonggen, Pan Wang, Yufa Sun, and Wenyan Nie, "Fast analysis of bistatic scattering problems for three-dimensional objects using compressive sensing and characteristic modes," IEEE Antennas and Wireless Propagation Letters, Vol. 21, No. 9, 1817-1821, Sep. 2022.
doi:10.1109/LAWP.2022.3181602

17. Park, Chan-Sun, Yi-Ru Jeong, Ic-Pyo Hong, and Jong-Gwan Yook, "Block size optimization of CBFM for scattering problems," IEEE Transactions on Antennas and Propagation, Vol. 66, No. 10, 5370-5377, Oct. 2018.
doi:10.1109/TAP.2018.2860047

18. Kong, Meng, Ming Sheng Chen, Xin Yuan Cao, Jia Bing Zhu, Xiao Jing Kuang, Qi Qi, and Xian Liang Wu, "Fast electromagnetic scattering analysis of inhomogeneous dielectric objects over a wide incident angle," IEEE Antennas and Wireless Propagation Letters, Vol. 20, No. 8, 1527-1531, Aug. 2021.
doi:10.1109/LAWP.2021.3089629

19. Wang, Zhonggen, Pan Wang, Yufa Sun, Wenyan Nie, Juan Wu, and Han Lin, "Fast analysis of wideband scattering problems using universal characteristic mode basis functions," Microwave and Optical Technology Letters, Vol. 64, No. 11, 1937-1943, Jul. 2022.
doi:10.1002/mop.33403

20. Kumar, N., K. J. Vinoy, and S. Gopalakrishnan, "A reduced order model for electromagnetic scattering using multilevel Krylov subspace splitting," 2015 IEEE International Conference on Computational Electromagnetics, 341-343, Hong Kong, China, Mar. 2015.
doi:10.1109/COMPEM.2015.7052655

21. Konno, Keisuke, Qiang Chen, Kunio Sawaya, and Toshihiro Sezai, "Optimization of block size for CBFM in MoM," IEEE Transactions on Antennas and Propagation, Vol. 60, No. 10, 4719-4724, Oct. 2012.
doi:10.1109/TAP.2012.2207330

Dr. Jianhao Xiang

Professor Zhonggen Wang

Dr. Haoran Yuan

Professor Wenyan Nie