volume | PIER Journals

Abstract

In this paper, a novel technique is proposed to solve the electromagnetic scattering by large finite arrays by combining the tangential equivalence principle algorithm (T-EPA) with multilevel fast multipole algorithm (MLFMA). The equivalence principle algorithm (EPA) is a kind of domain decomposition scheme for the electromagnetic scattering and radiation problems based on integral equation (IE). For the array with same elements, only one scattering matrix needs to be constructed and stored. T-EPA has better accuracy than the original EPA. But the calculating for the impedance matrix in T-EPA is still time consuming. MLFMA is proposed to speed up the matrix-vector multiplication in T-EPA. Numerical results are shown to demonstrate the accuracy and efficiency of the proposed technique.

1. Losada, V., R. R. Boix, and F. Medina, "Radar cross section of stacked circular microstrip patches on anisotropic and chiral substrates," IEEE Trans. Antenn. Propag., Vol. 51, No. 5, 1136-1139, May 2003.
doi:10.1109/TAP.2003.811528 Google Scholar

2. Gustafsson, M., "RCS reduction of integrated antenna arrays with resistive sheets," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 1, 27-40, 2006.
doi:10.1163/156939306775777323 Google Scholar

3. Yeo, J. and D. Kim, "Novel tapered AMC structures for backscattered RCS reduction," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 5-6, 697-709, 2009.
doi:10.1163/156939309788019804 Google Scholar

4. Wang, W. T., S. X. Gong, X. Wang, H. W. Yuan, J. Ling, and T. T. Wan, "RCS reduction of array antenna by using bandstop FSS reflector," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 11-12, 1505-1514, 1995. Google Scholar

5. Pozar, D. M. and D. H. Schaubert, "Analysis of an infinite array of rectangular micristrip patches with idealized feed," IEEE Trans. Antenn. Propag., Vol. 35, No. 10, 1101, Oct. 1984. Google Scholar

6. Liu, Z. F., P. S. Kooi, L. W. Li, M. S. Leong, and T. S. Yeo, "A method of moments analysis of a microtrip phased array in three layered structures," Progress In Electromagnetics Research, Vol. 31, 155-179, 2001.
doi:10.2528/PIER00062201 Google Scholar

7. Mcgrath, D. T. and V. P. Pyati, "Phased array antenna analysis with the hybrid finite element method," IEEE Trans. Antennas Propag., Vol. 42, No. 12, 1625-1630, Dec. 1994.
doi:10.1109/8.362811 Google Scholar

8. Hua, Y. and J. Li, "Analysis of longitudinal shunt waveguide slots using FEBI," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 14-15, 2041-2046, 2009.
doi:10.1163/156939309789932520 Google Scholar

9. Ozgun, O. and M. Kuzuoglu, "Finite element analysis of electromagnetic scattering problems via iterative leap-field domain decomposition method," Journal of Electromagnetic Waves and Applications, Vol. 22, No. 2-3, 251-266, 2008.
doi:10.1163/156939308784160668 Google Scholar

10. Lee, S. C., M. N. Vouvakis, and J. F. Lee, "A non-overlapping domain decomposition method with non-matching grids for modeling large finite antenna arrays ," J. Comput. Phys., Vol. 203, 1-21, Feb. 2005. Google Scholar

11. Holloway, C. L., P. M. McKenna, R. A. Dalke, R. A. Perala, and C. L. Devor, "Time-domain modeling, characterization, and measurements of anechoic and semi-anechoic electromagnetic test chambers," IEEE Trans. Electro. Compat., Vol. 44, No. 1, 102-118, Feb. 2002.
doi:10.1109/15.990716 Google Scholar

12. Song, J. M., C. C. Lu, and W. C. Chew, "Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects," IEEE Trans. Antenn. Propag., Vol. 45, 1488-1493, Oct. 1997.
doi:10.1109/8.633855 Google Scholar

13. Hu, J. and Z. P. Nie, "Multilevel fast multipole algorithm for solving scattering from 3-D electrically large object," Chinese Journal of Radio Science, Vol. 19, 509-514, May 2004. Google Scholar

14. Wallen, H. and J. Sarvas, "Translation procedures for broadband MLFMA," Progress In Electromagnetics Research, Vol. 55, 47-78, 2005.
doi:10.2528/PIER05021001 Google Scholar

15. Ouyang, J., J., F. Yang, S. W. Yang, and Z. P. Nie, "Exact simulation method VSWIE+MLFMA for analysis radiation pattern of pro-feed conformal microstrip antennas and the application of synthesis radiation pattern of conformal array mounted on finite-length PEC circular cylinder with des," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 14, 1995-2008, 2007.
doi:10.1163/156939307783152803 Google Scholar

16. Hu, J., Z. P. Nie, L. Lei, and L. J. Tian, "Fast solution of scattering from conducting structures by local MLFMA based on improved electric field integral equation," IEEE Trans. Electromagn. Compat., Vol. 50, No. 4, Nov. 2008. Google Scholar

17. Ping, X. W., T. J. Cui, and W. B. Lu, "The combination of bcgstab with multifrontal algorithm to solve FEBI-MLFMA linear systems arising from inhomogeneous electromagnetic scattering problems," Progress In Electromagnetics Research, Vol. 93, 91-105, 2009.
doi:10.2528/PIER09050604 Google Scholar

18. Peng, Z., X. Q. Sheng, and F. Yin, "An efficient twofold iterative algorithm of FE-BI-MLFMA using multilevel inverse-based ilu preconditioning," Progress In Electromagnetics Research, Vol. 93, 369-384, 2009.
doi:10.2528/PIER09060305 Google Scholar

19. Taboada, J. M., M. G. Araujo, J. M. Bertolo, L. Landesa, F. Obelleiro, and J. L. Rodriguez, "MLFMA-FFT parallel algorithm for the solution of large-scale problems in elemtromagnetic," Progress In Electromagnetics Research, Vol. 105, 15-30, 2010.
doi:10.2528/PIER10041603 Google Scholar

20. Blesznski, E. and M. Bleszynski, "AIM: Adaptive integral method for solving large scale electromagnetic scattering and radiation problems," Radio Science, Vol. 31, 1225-1251, Sep. 1996.
doi:10.1029/96RS02504 Google Scholar

21. Hu, L., L. W. Li, and T. S. Yeo, "Analysis of scattering by large inhomogeneous bi-anisotropic objects using AIM," Progress In Electromagnetics Research, Vol. 99, 21-36, 2009.
doi:10.2528/PIER09101204 Google Scholar

22. Seo, S. M. and J.-F. Lee, "A fast IE-FFT algorithm for solving PEC scattering problems," IEEE Transactions on Magnetics, Vol. 41, No. 9, 1476-1479, Oct. 1997. Google Scholar

23. Yin, J. L., J. Hu, X. F. Que, and Z. P. Nie, "A fast IE-FFT solution of 3D coating scatterers," Micro. Opt. Tech. Lett., Vol. 52, No. 1, 241-244, Jan. 2010.
doi:10.1002/mop.24846 Google Scholar

24. Li, M. K. and W. C. Chew, "A domain decomposition scheme based on equivalence theorem," Micro. Opt. Tech. Lett., Vol. 48, No. 9, 1853-1857, Sep. 2006.
doi:10.1002/mop.21777 Google Scholar

25. Li, M. K. and W. C. Chew, "Using tap basis to implement the equivalence principle algorithm for domain decomposition in integral equations," Micro. Opt. Tech. Lett., Vol. 48, No. 11, 2218-2222, Nov. 2006.
doi:10.1002/mop.21933 Google Scholar

26. Li, M. K. and W. C. Chew, "Wave-field interaction with complex structures using equivalence principle algorithm," IEEE Trans. Antenn. Propag., Vol. 55, No. 1, 130-138, Jan. 2007.
doi:10.1109/TAP.2006.888453 Google Scholar

27. Li, M. K. and W. C. Chew, "Multiscale simulation of complex structures using equivalence principle algorithm with high-order field point sampling scheme," IEEE Trans. Antenn. Propag., Vol. 56, No. 8, 2389-2397, Aug. 2008.
doi:10.1109/TAP.2008.926785 Google Scholar

28. Xiao, G. B., J. F. Mao, and B. Yuan, "Generalized transition matrix for arbitrarily shaped scatterers or scatterer groups," IEEE Trans. Antenn. Propag., Vol. 56, No. 12, 3723-3732, Dec. 2008.
doi:10.1109/TAP.2008.2007283 Google Scholar

29. Yla-Oijala, P. and M. Taskinen, "Electromagnetic scattering by large and complex structures with surface equivalence principle algorithm," Waves in Random and Complex Media, Vol. 19, No. 1, Feb. 2009.
doi:10.1080/17455030802585365 Google Scholar

30. Yla-Oijala, P. and M. Taskinen, "Solving electromagnetic scattering by multiple targets with surface equivalence principle algorithm," 3rd European Conference on Antenna and Propagation, 88-92, Mar. 2009. Google Scholar

31. Yla-Oijala, P., O. Ergul, L. Gurel, and M. Taskinen, "Efficient surface integral equation methods for the analysis of complex metamaterial structures ," 3rd European Conference on Antenna and Propagation, 1560-1564, Mar. 2009. Google Scholar

32. Graglia, R. D., D. R. Wilton, and A. F. Peterson, "Higher order interpolatory vector bases for computational electromagnetics," IEEE Trans. Antenn. Propag., Vol. 45, No. 3, 329-342, Mar. 1997.
doi:10.1109/8.558649 Google Scholar

33. Hu, J., Z. P. Nie, and L. Lin, "Solving 3-D electromagnetic scattering from conducting object by MLFMA with curvilinear RWG basis ," IEEE Antennas and Propagation Society Int. Symp., 460-463, 2003.

34. 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. Antenn. Propag., Vol. 48, No. 12, 1866-1868, Dec. 2000.
doi:10.1109/8.901277 Google Scholar

35. Yuan, N., T. S. Yeo, X. C. Nie, and L. W. Li, "RCS computation of composite conductiong-dielectric objects with junctions using the hybrid volume-surface integral equation," Journal of Electromagnetic Waves and Applications, Vol. 19, No. 1, 19-36, 2005.
doi:10.1163/1569393052955107 Google Scholar

36. Velamparambil, S., W. C. Chew, and J. M. Song, "10 Million unknowns: Is it that big?," IEEE Trans. Antenn. Propag., Vol. 45, No. 2, 43-58, Apr. 1997. Google Scholar

Dr. Hanru Shao

Prof. Jun Hu

Professor Zai-Ping Nie

Dr. Guo Han

Dr. Shiquan He