volume | PIER Journals

Abstract

In this paper, the Sherman-Morrison-Woodbury (SMW) Formula-based algorithm (SMWA) is used to enable the fast direct solution of conducting-dielectric arrays. To speed up the direct solution of the matrix equation, the dense impedance matrix is transformed into a product of several block diagonal matrices via the SMW formula. In the grouping process, the situation that the elements of an array simultaneously belong to two different subgroups at peer level is avoided in order to promote the efficiency. The SMWA conducts the calculation with a respectable reduction in the computational time as well as memory.

1. Aksun, M. I., A. Alparslan, and E. P. Karabulut, "Determining the effective constitutive parameters of finite periodic structures: Photonic crystals and metamaterials," IEEE Trans. Microw. Theory Tech., Vol. 56, No. 6, 1423-1434, Jun. 2008.
doi:10.1109/TMTT.2008.923870

2. Wu, T. X. and D. L. Jaggard, "Scattering of chiral periodic structure," IEEE Trans. Antennas Propag., Vol. 52, 1859-1870, Jul. 2004.

3. Gibson, W. C., The Method of Moments in Electromagnetics, CRC Press, Boca Raton, FL, 2007.
doi:10.1201/9781420061468

4. Lu, C. C. and W. C. Chew, "A coupled surface-volume integral equation approach for the calculation of electromagnetic scattering from composite metallic and material targets," IEEE Trans. Antennas Propag., Vol. 48, No. 12, 1866-1868, Dec. 2000.
doi:10.1109/8.901277

5. Song, J. M., C. C. Lu, and W. C. Chew, "Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects," IEEE Trans. Antennas Propag., Vol. 45, No. 10, 1488-1493, 1997.
doi:10.1109/8.633855

6. Ewe, W. B., L. W. Li, and M. S. Leong, "Fast solution of mixed dielectric/conducting scattering problem using volume-surface adaptive integral method," IEEE Trans. Antennas Propag., Vol. 52, No. 11, 3071-3077, 2004.
doi:10.1109/TAP.2004.835147

7. Nie, X. C., N. Yuan, L.W. Li, Y. B. Gan, and T. S. Yeo, "A fast volume-surface integral equation solver for scattering from composite conducting-dielectric objects," IEEE Trans. Antennas Propag., Vol. 53, No. 2, 818-824, 2005.
doi:10.1109/TAP.2004.841323

8. Chen, X., C. Gu, J. Ding, Z. Li, and Z. Niu, "Multilevel fast adaptive cross-approximation algorithm with characteristic basis functions," IEEE Trans. Antennas Propag., Vol. 63, No. 9, 3994-4002, Sep. 2015.
doi:10.1109/TAP.2015.2447033

9. Kong, W. Y., J. Bremer, and V. Rokhlin, "An adaptive fast direct solver for boundary integral equations in two dimensions," Applied and Computational Harmonic Analysis, Vol. 31, No. 3, 346-369, 2011.
doi:10.1016/j.acha.2011.01.008

10. Ambikasaram, S. and E. Darve, "An O(NlogN) fast direct solver for partial hierarchically semi-separable matrices with application to radial basis function interpolation," Journal of Scientific Computing, Vol. 57, No. 3, 477-501, 2013.
doi:10.1007/s10915-013-9714-z

11. Chen, X., C. Gu, Z. Niu, and Z. Li, "Direct solution of MoM matrix equation using Sherman-Morrison-Woodbury formula-based algorithm with ACA-SVD," Asia-Pacific Microwave Conference, Dec. 2015.

12. Chen, X., C. Gu, Z. Li, and Z. Niu, "Accelerated direct solution of electromagnetic scattering via characteristic basis function method with Sherman-Morrison-Woodbury formula-based algorithm," IEEE Trans. Antennas Propag., to be published (Early Access), DOI 10.1109/TAP.2016.2587743.

13. Zhang, Y., X. Chen, C. Fei, Z. Li, and C. Gu, "Fast direct solution of dielectric array using adaptive cross approximation with Sherman-Morrison-Woodbury formula," 2016 IEEE 5th Asia-Pacific Conference on Antennas and Propagation (APCAP), 171-172, Jul. 2016.

14. Hager, W., "Updating the inverse of a matrix," SIAM Rev., Vol. 31, No. 2, 221-239, 1989.
doi:10.1137/1031049

15. Golub, G. H. and C. F. Van Loan, Matrix Computations, The Johns Hopkins Univ., Press, Baltimore, MD, 1996.

16. Zhao, K., M. N. Vouvakis, and J.-F. Lee, "The adaptive cross approximation algorithm for accelerated method of moments computations of EMC," IEEE Trans. Electromagn. Compat., Vol. 47, No. 4, 763-773, 2005.
doi:10.1109/TEMC.2005.857898

17. Kobidze, G. and B. Shanker, "Integral equation based analysis of scattering from 3-D inhomogeneous anisotropic bodies," IEEE Trans. Antennas and Propag., Vol. 52, No. 10, 2650-2658, Oct. 2004.
doi:10.1109/TAP.2004.834439

18. Chen, X., C. Gu, Z. Niu, and Z. Li, "Fast solution of volume-surface integral equation for scattering from composite conducting-dielectric targets using multilevel fast dipole method," International Journal of RF and Microwave Computer-aided Engineering, Vol. 25, No. 5, 624-631, Sep. 2012.
doi:10.1002/mmce.20620

19. Rao, S. M., D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas and Propag., Vol. 30, No. 2, 409-418, May 1982.
doi:10.1109/TAP.1982.1142818

20. Schaubert, D. H., D. R. Wilton, and A. W. Glisson, "A tetrahedral modeling method for electromagnetic scattering by arbitrarily shaped inhomogeneous dielectric bodies," IEEE Trans. Antennas and Propag., Vol. 32, 77-85, 1984.
doi:10.1109/TAP.1984.1143193

Dr. Yang Zhang

Prof. Xinlei Chen

Dr. Chao Fei

Prof. Zhuo Li

Prof. Chang Qing Gu