A basis function with the traveling wave phase factor, called as the phase extracted (PE) basis functions in this paper, has been applied for efficient solution of scattering from 3 dimensional (3- D) electrically large objects. In this paper, a rigorous derivation is given as a physical insight of this basis function. Defined on large patches and containing propagating wave phase dependence, this kind of bases exhibits very strong directivity, leading to a highly sparsed impedance matrix. Based on such observation, a matrix sparsification technique and an impedance prediction technique have been developed in this paper. The total memory requirement and computational time could be reduced significantly with methods proposed in this paper. The basic requirements of basis functions, i.e., current continuity and absence of charge accumulation are demonstrated, and the excellent behavior of PE basis functions in wideband applications has been summarized briefly. Several numerical examples have been given to show its good accuracy and high efficiency in solving scattering from electrically large complex objects.
"On the Basis Functions with Traveling Wave Phase Factor for Efficient Analysis of Scattering from Electrically Large Targets," Progress In Electromagnetics Research,
Vol. 85, 83-114, 2008. doi:10.2528/PIER08081905
1. Hatamzadeh-Varmazyar, S., M. Naser-Moghadasi, and Z. Masouri, "A moment method simulation of electromagnetic scattering from conducting bodies," Progress In Electromagnetics Research, Vol. 81, 99-119, 2008. doi:10.2528/PIER07122502
2. Wang, S., X. Guan, D.Wang, X. Ma, and Y. Su, "Electromagnetic scattering by mixed conducting/dielectric objects using higher order MOM," Progress In Electromagnetics Research, Vol. 66, 51-63, 2006. doi:10.2528/PIER06092101
3. Li, C. and Z. Shen, "Electromagnetic scattering by a conducting cylinder coated with metamaterials," Progress In Electromagnetics Research, Vol. 42, 91-105, 2003. doi:10.2528/PIER03012901
4. Yuan, H. W., S. X. Gong, X. Wang, and W. T. Wang, "Scattering analysis of a printed dipole antenna using PBG structures," Progress In Electromagnetics Research B, Vol. 1, 189-195, 2008. doi:10.2528/PIERB07102302
5. Varmazyar, S. H. and M. N. Moghadasi, "An integral equation modeling of electromagnetic scattering from the surfaces of arbitrary resistance distribution ," Progress In Electromagnetics Research B, Vol. 3, 157-172, 2008. doi:10.2528/PIERB07121404
6. Varmazyar, S. H. and M. N. Moghadasi, "New numerical method for determining the scattered electromagnetic fields from thin wires," Progress In Electromagnetics Research B, Vol. 3, 207-218, 2008. doi:10.2528/PIERB07121303
7. Song, J. M., C. C. Lu, and W. C. Chew, "Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects," IEEE Trans. Antennas Propagat., Vol. 45, No. 10, 1488-1493, Oct. 1997. doi:10.1109/8.633855
8. Engheta, N., W. D. Murphy, V. Rokhlin, et al. "The Fast Multipole Method (FMM) for electromagnetic scattering problems," IEEE Trans. Antennas Propagat., Vol. 40, No. 6, 634-641, 1992. doi:10.1109/8.144597
9. Lu, C. C. and W. C. Chew, "Fast algorithm for solving hybrid integral equations," IEE Proceedings-H, Vol. 140, No. 6, 455-460, 1993.
10. Song, J. M. and W. C. Chew, "Fast multipole method solution using parametric geometry," Microwave and Optical Technology Letters, Vol. 7, No. 16, 760-765, 1994. doi:10.1002/mop.4650071612
11. Chew, W. C., J. M. Jin, E. Michielssen, and J. M. Song, Fast and Efficient Algorithms in Computational Electromagnetics, Ch. 3, Artech House, Boston, 2001.
12. Rui, P. L., R. S. Chen, Z. W. Liu, and Y. N. Gan, "Schwarz-Krylov subspace method for MLFMM analysis of electromagnetic wave scattering problems," Progress In Electromagnetics Research, Vol. 82, 51-63, 2008. doi:10.2528/PIER08013003
13. Zhang, Y. J. and E. P. Li, "Fast multipole accelerated scattering matrix method for multiple scattering of a large number of cylinders," Progress In Electromagnetics Research, Vol. 72, 105-126, 2007. doi:10.2528/PIER07030503
14. Wan, J. X., T. M. Xiang, and C. H. Liang, "The fast multipole algorithm for analysis of large-scale microstrip antenna arrays," Progress In Electromagnetics Research, Vol. 49, 239-255, 2004. doi:10.2528/PIER04042201
15. Pan, Y. C. and W. C. Chew, "A fast multipole metho for embedded structure in a stratified medium," Progress In Electromagnetics Research, Vol. 44, 1-38, 2004. doi:10.2528/PIER03050602
16. Jorgensen, E., J. L. Volakis, P. Meincke, and O. Breinbjerg, "Higher order hierarchical Legendre basis functions for iterative integral equation solvers with curvilinear surface modeling," IEEE Antennas and Propagation SocietyInternational Symposium, Vol. 4, 618-621, June 2002.
17. Jorgensen, E., J. L. Volakis, P. Meincke, and O. Breinbjerg, "Higher order hierarchical Legendre basis functions for electromagnetic modeling," IEEE Trans. Antennas Propagat., Vol. 52, No. 11, 2985-2995, Nov. 2004. doi:10.1109/TAP.2004.835279
18. Altman, Z. and R. Mittra, "Combining an extrapolation technique with the method of moments for solving large scattering problems involving bodies of revolution," IEEE Trans. Antennas Propagat., Vol. 44, 548-553, Apr. 1996. doi:10.1109/8.489307
19. Altman, Z. and R. Mittra, "A technique for extrapolating numerically rigorous solutions of electromagnetic scattering problems to higher frequencies and their scaling properties," IEEE Trans. Antennas Propagat., Vol. 47, No. 4, 744-751, Apr. 1999. doi:10.1109/8.768815
20. Kwon, D. H., R. J. Burkholder, and P. H. Pathak, "Efficient method of moments formulation for large pec scattering problems using Asymptotic Phasefront Extraction (APE)," IEEE Trans. Antennas Propagat., Vol. 49, No. 4, 583-591, Apr. 2001. doi:10.1109/8.923318
21. Aberegg, K. R. and A. F. Peterson, "Application of the integral equation-asymptotic phase method to two-dimensional scattering ," IEEE Trans. Antennas Propagat., Vol. 43, 534-537, May 1995. doi:10.1109/8.384199
22. Kowalski, M. E., B. Singh, L. C. Kempel, K. D. Trott, and J.-M. Jin, "Application of the integral equation asymptotic phase (IE-AP) method to three-dimensional scattering ," J. of Electromagn. Waves and Appl., Vol. 15, 885-900, July 2001.
23. Taboada, J. M., F. Obelleiro, J. L. Rodriguez, I. Garcia-Tunon, and L. Landesa, "Incorporation of linear-phase progression in RWG basis functions," Microwave and Optical TechnologyL etters, Vol. 44, No. 2, 106-112, January 2005. doi:10.1002/mop.20560
24. Abboud, T., J. C. Nedelec, and B. Zhou, "Improvement of the integral equation method for high frequency problems," Third International Conference on Mathematical Aspects of Wave Propagation, SIAM, 178-187, 1995.
25. Aberegg, K. R., "Electromagnetic scattering using the integral equation - asymptotic phase method,", Ph.D. dissertation, Georgia Institute of Technology, 1995.
26. Shen, X., A. W. Davis, K. R. Aberegg, and A. F. Peterson, "Highly parallel implementation of the 3D integral equation asymptotic phase method for electromagnetic scattering," Applied Computational Electromagnetics Society(A CES) Journal, Vol. 13, 107-115, July 1998.
27. Darrigrand, E., "Coupling of fast multipole method and microlocal discretization for the 3-D Helmholtz equation," J. Computational Physics, Vol. 181, 126-154, 2002. doi:10.1006/jcph.2002.7091
28. Graglia, R. D., D. R. Wilton, and A. F. Peterson, "Higher order interpolatory vector bases for computational electromagnetics," IEEE Trans. Antennas Propagat., Vol. 45, No. 3, 329-342, Mar. 1997. doi:10.1109/8.558649
29. Wilkes, D. L. and C. C. Cha, "Method of moments solution with parametric curved triangular patches," Antennas and Propagation SocietyInternational Symposium, Vol. 3, 1512-1515, June 1991.
30. Zhu, N. Y. and F. M. Landstorfer, "Application of curved parametric triangular and quadrilateral edge elements in the moment solution of the EFIE," IEEE Microwave and Guided Wave Letters, Vol. 3, No. 9, 319-321, Sept. 1993. doi:10.1109/75.244865
31. Brown, W. J. and D. R. Wilton, "Singular basis functions and curvilinear triangles in the solution of the electric field integral equation," IEEE Trans. Antennas Propagat., Vol. 47, No. 2, 347-353, Feb. 1999. doi:10.1109/8.761075
32. Wagner, R. L. and W. C. Chew, "A study of wavelets for the solution of electromagnetic integral equations," IEEE Trans. Antennas Propagat., Vol. 43, No. 8, 802-810, Aug. 1995. doi:10.1109/8.402199
33. Yan, S. and Z. Nie, "A novel mixed basis function for method of moment," Proceedings of Asia-Pacific Microwave Conference 2005, Vol. 3, Suzhou, China, Dec. 4–7, 2005.
34. Ergul, O. and L. Gurel, "Linear-linear basis functions for MLFMA solutions of magnetic-field and combined-field integral equations," IEEE Trans. Antennas Propagat., Vol. 55, No. 4, 1103-1110, Apr. 2007. doi:10.1109/TAP.2007.893393