volume | PIER Journals

Abstract

In this paper, a dual-model based adaptive sampling method is proposed for the fast calculation of broadband electromagnetic scattering. The difference between the rational function model (RFM) and cubic-spline (CS) based polynomial model issued to generate new frequency samples adaptively. Then, the cubic Hermite interpolation is used to approximate the final broadband RCS curve. The radar cross section (RCS) at each frequency sample is computed by the method of moment (MoM) which is accelerated by the adaptive cross approximation (ACA). Numerical results demonstrate that the proposed method is able to obtain the broadband RCS curve with high accuracy and reduce the computation time significantly. Compared with the method of moment and adaptive cross approximation method, the adaptive algorithm improves the computational efficiency by 77.13% in the sphere case, 83.79% in the rail model and nearly 90.72% in the missile example. In addition, the method proposed in this paper has the characteristics of nonuniform sampling and strong applicability and flexibility, which is able to combine other matrix compressed methods to effectively solve problems in electromagnetic field.

1. Lu, C. C. and W. C. Chew, "Fast algorithm for solving hybrid integral equations," IEEE Proceedings - H, Vol. 140, No. 6, 455-460, 1993.
doi:10.1049/ip-d.1993.0060

2. Harrington, R. F., Field Computation by Moment Methods, Wiley-IEEE Press, 1993.
doi:10.1109/9780470544631

3. Gibson, W. C., The Method of Moments in Electromagnetics, Chapman & Hall/CRC, 2008.

4. Seo, S. M., "A fast IE-FFT algorithm to analyze electrically large planar microstrip antenna arrays," IEEE Antennas and Wireless Propagation Letters, Vol. 17, No. 6, 983-987, Jun. 2018.
doi:10.1109/LAWP.2018.2828158

5. Liu, Y., X. Pan, and X. Sheng, "A fast algorithm for volume integral equation using interpolative decomposition and multilevel fast multipole algorithm," 2016 11th International Symposium on Antennas, Propagation and EM Theory (ISAPE), 519-522, 2016.

6. Bebendorf, M., "Approximation of boundary element matrices," Numerische Mathematik, Vol. 86, No. 4, 565-589, 2000.
doi:10.1007/PL00005410

7. Zhao, K. Z., M. N. Vouvakis, and J.-F. 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, 2005.
doi:10.1109/TEMC.2005.857898

8. Liu, Z., X. Wang, D. Tang, Y. Zhang, S. Jie, and X. Liu, "MLFMA-ACA based method for efficient calculation of scattering from underground targets," 2018 IEEE International Conference on Computational Electromagnetics (ICCEM), 1-3, 2018.

9. Carpentieri, B., I. S. Duff, L. Giraud, et al. "Combining fast multipole techniques and an approximate inverse preconditioner for large electromagnetism calculations," SIAM Journal on Scientific Computing, Vol. 27, No. 3, 774-792, 2005.
doi:10.1137/040603917

10. Pan, X., W. Pi, M. Yang, Z. Peng, and X. Sheng, "Solving problems with over one billion unknowns by the MLFMA," IEEE Transactions on Antennas and Propagation, Vol. 60, No. 5, 2571-2574, May 2012.
doi:10.1109/TAP.2012.2189746

11. Carpentieri, B., "Algebraic preconditioners for the fast multipole method in electromagnetic scattering analysis from large structures: Trends and problems," Electronic Journal of Boundary Elements, Vol. 7, No. 1, 2009.
doi:10.14713/ejbe.v7i1.952

12. Miller, E. K., "Using adaptive sampling to minimize the number of samples needed to represent a transfer function," IEEE Antennas and Propagation Society International Symposium. 1996 Digest, Vol. 1, 588-591, Baltimore, MD, USA, 1996.

13. Miller, E. K., "Adaptive sparse sampling to estimate radiation and scattering patterns to a specified uncertainty with model-based parameter estimation: Compute patterns using as few as two to four samples per lobe," IEEE Antennas and Propagation Magazine, Vol. 57, No. 4, 103-113, Aug. 2015.
doi:10.1109/MAP.2015.2453920

14. Cockrell, C. R. and F. B. Beck, "Asymptotic waveform evaluation (AWE) technique for frequency domain electromagnetic analysis," NASA Tech. Memo., 110292, Nov. 1996.

15. Wu, B. and X. Sheng, "Application of asymptotic waveform evaluation to hybrid FE-BI-MLFMA for fast RCS computation over a frequency band," IEEE Transactions on Antennas and Propagation, Vol. 61, No. 5, 2597-2604, May 2013.
doi:10.1109/TAP.2013.2246532

16. Jeong, Y., I. Hong, H. Chun, Y. B. Park, Y. Kim, and J. Yook, "Fast analysis over a wide band using Chebyshev approximation with Clenshaw-Lord approximation," The 8th European Conference on Antennas and Propagation (EuCAP 2014), 1353-1355, 2014.
doi:10.1109/EuCAP.2014.6902029

17. Monje-Real, A. and V. de la Rubia, "Electric field integral equation fast frequency sweep for scattering of nonpenetrable objects via the reduced-basis method," IEEE Transactions on Antennas and Propagation, Vol. 68, No. 8, 6232-6244, Aug. 2020.
doi:10.1109/TAP.2020.2992882

18. Wu, L., et al. "MLACE-MLFMA combined with reduced basis method for efficient wideband electromagnetic scattering from metallic targets," IEEE Transactions on Antennas and Propagation, Vol. 67, No. 7, 4738-4747, Jul. 2019.
doi:10.1109/TAP.2019.2911352

19. Kong, W., J. Xie, F. Zhou, X. Yang, R. Wang, and K. Zheng, "An efficient FG-FFT with optimal replacement scheme and inter/extrapolation method for analysis of electromagnetic scattering over a frequency band," IEEE Access, Vol. 7, 127511-127520, 2019.
doi:10.1109/ACCESS.2019.2939484

20. Song, J. M. and W. C. Chew, "Broadband time-domain calculation using FISC," IEEE Antennas and Propagation Society International Symposium, 552, 2002.
doi:10.1109/APS.2002.1018273

21. Lu, C. C., "An extrapolation method based on current for rapid frequency and angle sweeps in far-field calculation in an integral equation algorithm," ACES Journal, Vol. 21, No. 1, 90-98, 2006.

22. Erdemli, Y. E., J. Gong, C. J. Reddy, and J. L. Volakis, "Fast RCS pattern fill using AWE technique," IEEE Transactions on Antennas and Propagation, Vol. 46, No. 11, 1752-1753, Nov. 1998.
doi:10.1109/8.736639

23. Reddy, C. J., M. D. Deshpande, C. R. Cockrell, and F. B. Beck, "Fast RCS computation over a frequency band using method of moments in conjunction with asymptotic waveform evaluation technique," IEEE Transactions on Antennas and Propagation, Vol. 46, No. 8, 1229-1233, Aug. 1998.
doi:10.1109/8.718579

24. Chew, W. C., J. M. Song, E. Michielssen, et al. Fast and Efficient Algorithms in Computational Electromagnetics, Artech House, 2001.

25. Surma, M., "Efficient wideband analysis of electromagnetic scattering and radiation problems," 15th International Conference on Microwaves, Radar and Wireless Communications, 291-294, 2004.
doi:10.1109/MIKON.2004.1356922

26. Peng, Z. and X. Sheng, "A bandwidth estimation approach for the asymptotic waveform evaluation technique," IEEE Transactions on Antennas and Propagation, Vol. 56, No. 3, 913-917, Mar. 2008.
doi:10.1109/TAP.2008.917017

27. Lehmensiek, R. and P. Meyer, "An efficient adaptive frequency sampling algorithm for model-based parameter estimation as applied to aggressive space mapping," Microwave and Optical Technology Letters, Vol. 24, No. 1, 71-78, 2000.
doi:10.1002/(SICI)1098-2760(20000105)24:1<71::AID-MOP20>3.0.CO;2-O

28. Wu, L., Y. Zhao, Q. Cai, Z. Zhang, and J. Hu, "An adaptive segmented reduced basis method for fast interpolating the wideband scattering of the dielectric-metallic targets," IEEE Antennas and Wireless Propagation Letters, Vol. 19, No. 12, 2235-2239, Dec. 2020.
doi:10.1109/LAWP.2020.3028455

29. Wu, J. W. and T. J. Cui, "Minimal rational interpolation and its application in fast broadband simulation," IEEE Access, Vol. 7, 177813-177826, 2019.
doi:10.1109/ACCESS.2019.2958369

30. Wang, X., H. Gong, S. Zhang, Y. Liu, R. Yang, and C. Liu, "Efficient RCS computation over a broad frequency band using subdomain MoM and chebyshev approximation technique," IEEE Access, Vol. 8, 33522-33531, 2020.
doi:10.1109/ACCESS.2020.2974070

31. Liu, Z. W., R. S. Chen, and J. Q. Chen, "Adaptive sampling cubic-spline interpolation method for efficient calculation of monostatic RCS," Microwave and Optical Technology Letters, Vol. 50, No. 3, 751-755, 2008.
doi:10.1002/mop.23211

32. Liu, Z. W., D. Z. Ding, Z. F. Fan, et al. "Adaptive sampling bicubic spline interpolation method for fast calculation of monostatic RCS," Microwave and Optical Technology Letters, Vol. 50, No. 7, 1851-1857, 2008.
doi:10.1002/mop.23540

33. Lehmensiek, R. and P. Meyer, "Creating accurate multivariate rational interpolation models of microwave circuits by using efficient adaptive sampling to minimize the number of computational electromagnetic analyses," IEEE Transactions on Microwave Theory and Techniques, Vol. 49, No. 8, 1419-1430, Aug. 2001.
doi:10.1109/22.939922

34. Rao, S., D. Wilton, and A. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Transactions on Antennas and Propagation, Vol. 30, No. 3, 409-418, May 1982.
doi:10.1109/TAP.1982.1142818

Dr. Ziyue Cheng

Dr. Yueyuan Zhang

Dr. Longfeng Xi

Dr. Zhiwei Liu