Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
Home | Search | Notification | Authors | Submission | PIERS Home | EM Academy
Home > Vol. 115 > pp. 131-146


By K. Xiao, F. Zhao, S.-L. Chai, J.-J. Mao, and J. L.-W. Li

Full Article PDF (1,460 KB)

In this paper, an improved CBFM/p-FFT algorithm is presented, which can be applied to solve electromagnetic scattering problems of large-scale periodic composite metallic/dielectric arrays, even when the array has electrically small periodicity or separating distance. Using characteristic basis function method (CBFM), scattering characteristics of any inhomogeneous targets can be represented by special responses derived from a set of incident plane waves (PWs). In order to reserve the dominant scattering characteristics of the targets and remove the redundancy of the overfull responses, a singular value decomposition (SVD) procedure is applied, then, new series of basis functions are built based on the left singular vectors after SVD whose corresponding singular values beyond a predefined threshold. However, the algorithm of CBFM combined with method of moments (MoM) still requires a lot of memory and CPU resources to some large scale problems, so the precorrected-fast Fourier transform (p-FFT) method is applied based on the novel built basis functions, with which, the required memory and solve time for solution can be reduced in an extraordinary extent. For a near correction technique is applied to process the interactions between cells placed within a distance less than a predefined near-far field threshold, arrays with electrically small periodicity can be analyzed accurately. Moreover, the incomplete LU factorization with thresholding (ILUT) preconditioner is applied to improve the condition number of the combined algorithm, which improves the convergence speed greatly.

K. Xiao, F. Zhao, S.-L. Chai, J.-J. Mao, and J. L.-W. Li, "Scattering Analysis of Periodic Arrays Using Combined Cbf/P-FFT Method," Progress In Electromagnetics Research, Vol. 115, 131-146, 2011.

1. Joannopoulos, J. D., S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, Princeton University Press, 2008.

2. Schurig, D., J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science, Vol. 314, 977-980, 2006.

3. Buonanno, A., M. D'Urso, M. Cicolani, and S. Mosca, "Large phased arrays diagnostic via distributional approach," Progress In Electromagnetics Research, Vol. 92, 153-166, 2009.

4. Watanabe, K. and K. Yasumoto, "Accuracy improvement of the fourier series expansion method for Floquet-mode analysis of photonic crystal waveguides," Progress In Electromagnetics Research, Vol. 92, 209-222, 2009.

5. Bahadori, H., H. Alaeian, and R. Faraji-Dana, "Computation of periodic Green's functions in layered media using complex images technique," Progress In Electromagnetics Research, Vol. 112, 225-240, 2011.

6. Guo, J. L., J. Y. Li, and Q. Z. Liu, "Analysis of antenna array with arbitrarily shaped radomes using fast algorithm based on VSIE," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 10, 1399-1410, 2006.

7. Shi, Y., X. Luan, J. Qin, C. J. Lv, and C. H. Liang, "Multilevel Green's function interpolation method solution of volume-surface integral equation for mixed conducting/bi-isotropic objects," Progress In Electromagnetics Research, Vol. 107, 239-252, 2010.

8. Thiele, G. A. and T. H. Newhouse, "A hybrid technique for combining moment methods with the geometrical theory of diffraction," IEEE Trans. Antennas Propagat., Vol. 23, No. 1, 62-69, Jan. 1975.

9. Lertwiriyaprapa, T., P. H. Pathak, and J. L. Volakis, "An approximate UTD ray solution for the radiation and scattering by antennas near a junction between two different thin planar material slab on ground plane," Progress In Electromagnetics Research, Vol. 102, 227-248, 2010.

10. Eibert, T. F., Ismatullah, E. Kaliyaperumal, and C. H. Schmidt, "Inverse equivalent surface current method with hierarchical higher order basis functions, full probe correction and multi-level fast multipole acceleration," Progress In Electromagnetics Research, Vol. 106, 377-394, 2010.

11. Suter, E. and J. Mosig, "A subdomain multilevel approach for the MoM analysis of large planar antennas," Microwave Opt. Technol. Lett., Vol. 26, No. 4, 270-277, Aug. 2000.

12. Du, P., B. Z. Wang, H. Li, and G. Zheng, "Scattering analysis of large-scale periodic structures using the sub-entire domain basis function method and characteristic function method," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 14, 2085-2094, 2007.

13. Gan, H. and W. C. Chew, "Discrete BCG-FFT algorithm for solving 3D inhomogeneous scatterer problems," Journal of Electromagnetic Waves and Applications, Vol. 9, No. 10, 1339-1357, 1995.

14. Brandfass, M. and W. C. Chew, "A multilevel fast multipole based approach for efficient reconstruction of perfectly conducting scatterers," Journal of Electromagnetic Waves and Applications, Vol. 15, No. 1, 81-106, 2001.

15. Taboada, J. M., M. G. Araújo, J. M. Bértolo, L. Landesa, F. Obelleiro, and J. L. Rodriguez, "MLFMA-FFT parallel algorithm for the solution of large-scale problems in electromagnetics," Progress In Electromagnetics Research, Vol. 105, 15-30, 2010.

16. Ling, F., C. F. Wang, and J. M. Jin, "Application of adaptive integral method to scattering and radiation analysis of arbitrarily shaped planar structures," Journal of Electromagnetic Waves and Applications, Vol. 12, No. 8, 1021-1037, 1998.

17. Nie, X. C., L. W. Li, and N. Yuan, "Precorrected-FFT algorithm for solving combined field integral equations in electromagnetic scattering," Journal of Electromagnetic Waves and Applications, Vol. 16, No. 8, 1171-1187, 2002.

18. Phillips, J. R. and J. K. White, "A precorrected-FFT method for electrostatic analysis of complicated 3-D structures," IEEE Trans. Computer-aided Design of Integrated Circuits and Systems, Vol. 16, No. 10, 1059-1072, Oct. 1997.

19. Yuan, N., T. S. Yeo, X. C. Nie, L. W. Li, and Y. B. Gan, "Analysis of scattering from composite conducting and dielectric targets using the precorrected-FFT algorithm," Journal of Electromagnetic Waves and Applications, Vol. 17, No. 3, 499-515, 2003.

20. Yuan, N., X. C. Nie, Y. B. Gan, T. S. Yeo, and L. W. Li, "Accurate analysis of conformal antenna arrays with finite and curved frequency selective surfaces," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 13, 1745-1760, 2007.

21. Lucente, E., A. Monorchio, and R. Mittra, "An iteration-free MoM approach based on excitation independent characteristic basis functions for solving large multiscale electromagnetic scattering problems," IEEE Trans. Antennas Propagat., Vol. 56, No. 4, 999-1007, Apr. 2008.

22. Laviada, J., R. G. Ayestarán, M. R. Pino, and F. Las-Heras Andrés R. Mittra, "Synthesis of phased arrays in complex environments with the multilevel characteristic basis function method," Progress In Electromagnetics Research, Vol. 92, 347-360, 2009.

23. Wan, J. X. and C. H. Liang, "A fast analysis of scattering from microstrip antennas over a wide band," Progress In Electromagnetics Research, Vol. 50, 187-208, 2005.

24. Hu, L. and L. W. Li, "CBFM-based p-FFT method: A new algorithm for solving large-scale finite periodic arrays scattering problems," APMC: Asia Pacific Microwave Conference, 88-91, 2009.

25. Hu, L., L. W. Li, and R. Mittra, "Electromagnetic scattering by finite periodic arrays using the characteristic basis function and adaptive integral methods," IEEE Trans. Antennas Propagat., Vol. 58, No. 9, 3086-3090, Sep. 2010.

26. Balanis, C. A., Advanced Engineering Electromagnetics, Wiley-Interscience, New York, 1989.

27. Saad, Y., "A dual threshold incomplete LU preconditioner," Numerical and Linear Algebra and its Applications, Vol. 1, No. 4, 387-402, 1994.

28. Saad, Y., "GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems," SIME J. Sci. Stat. Comput., Vol. 7, No. 3, 856-869, 1986.

© Copyright 2014 EMW Publishing. All Rights Reserved