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2017-04-13
Fast Converging CFIE-MoM Analysis of Electromagnetic Scattering from PEC Polygonal Cross-Section Closed Cylinders
By
Progress In Electromagnetics Research B, Vol. 74, 109-121, 2017
Abstract
The analysis of the electromagnetic scattering from perfectly electrically conducting (PEC) objects with edges and corners performed by means of surface integral equation formulations has drawbacks due to the interior resonances and divergence of the fields on geometrical singularities. The aim of this paper is to show a fast converging method for the analysis of the scattering from PEC polygonal cross-section closed cylinders immune from the interior resonance problems. The problem, formulated as combined field integral equation (CFIE) in the spectral domain, is discretized by means of Galerkin method with expansion functions reconstructing the behaviour of the fields on the wedges with a closed-form spectral domain counterpart. Hence, the elements of the coefficients' matrix are reduced to single improper integrals of oscillating functions efficiently evaluated by means of an analytical asymptotic acceleration technique.
Citation
Mario Lucido, Francesca Di Murro, Gaetano Panariello, and Chiara Santomassimo, "Fast Converging CFIE-MoM Analysis of Electromagnetic Scattering from PEC Polygonal Cross-Section Closed Cylinders," Progress In Electromagnetics Research B, Vol. 74, 109-121, 2017.
doi:10.2528/PIERB17011803
References

1. Harrington, R. F., Field Computation by Moment Methods, ser. IEEE Press Series on Electromagnetic Wave Theory, Wiley-IEEE Press, 1993.
doi:10.1109/9780470544631

2. Correia, L. M., "A comparison of integral equations with unique solution in the resonant region for scattering by conducting bodies," IEEE Trans. Antennas Propag., Vol. 41, No. 1, 52-58, Jan. 1993.
doi:10.1109/8.210115        Google Scholar

3. Schenck, H. A., "Improved integral formulation for acoustic radiation problems," J. Acoust. Soc. Amer., Vol. 44, 41-48, Jul. 1968.
doi:10.1121/1.1911085        Google Scholar

4. Waterman, P. C., "Numerical solution of electromagnetic scattering problems," Computer Techniques for Electromagnetics, 1987.        Google Scholar

5. Mittra, R. and C. A. Klein, "Stability and convergence of moment method solution," Numerical and Asymptotic Techniques in Electromagnetics, R. Mittra, Ed., Springer-Verlag, New York, 1975.        Google Scholar

6. Mautz, J. R. and R. F. Harrington, "A combined-source formulation for radiation and scattering from a perfectly conducting body," IEEE Trans. Antennas Propag., Vol. 27, 445-454, Jul. 1979.        Google Scholar

7. Tobin, R., A. D. Yaghjian, and M. M. Bell, "Surface integral equations for multi-wavelength arbitrary shaped, perfectly conducting bodies," Proc. Dig. 19th URSI Radio Sci. Meet., 7, Boulder, CO, Jan. 1987.        Google Scholar

8. Mautz, J. R. and R. F. Harrington, "H-field, E-field, and combined field solutions for conducting bodies of revolution," AEU, Vol. 32, No. 4, 159-164, Apr. 1978.        Google Scholar

9. Colton, D. and R. Kress, Integral Equation Methods in Scattering Theory, Wiley, 1993.

10. Bolomey, J. C. and W. Tabbara, "Numerical aspects on coupling between complementary boundary value problems," IEEE Trans. Antennas Propag., Vol. 21, 356-363, May 1973.
doi:10.1109/TAP.1973.1140500        Google Scholar

11. Contopanagos, H., B. Dembart, M. Epton, J. J. Ottusch, V. Rokhlin, J. L. Visher, and S. M. Wandzura, "Well-conditioned boundary integral equations for three-dimensional electromagnetic scattering," IEEE Trans. Antennas Propag., Vol. 50, No. 12, 1824-1830, Dec. 2002.
doi:10.1109/TAP.2002.803956        Google Scholar

12. Liu, Z., R. J. Adams, and L. Carin, "Well-conditioned MLFMA formulation for closed PEC targets in the vicinity of a half space," IEEE Trans. Antennas Propag., Vol. 51, No. 10, 2822-2829, Oct. 2003.        Google Scholar

13. Adams, R. J., "Combined field integral equation formulations for electromagnetic scattering from convex geometries," IEEE Trans. Antennas Propag., Vol. 52, No. 5, 1294-1303, May 2004.
doi:10.1109/TAP.2004.827246        Google Scholar

14. Borel, S., D. P. Levadoux, and F. Alouges, "A new well-conditioned integral formulation for Maxwell equations in three dimensions," IEEE Trans. Antennas Propag., Vol. 53, No. 9, 2995-3004, Sep. 2005.
doi:10.1109/TAP.2005.854561        Google Scholar

15. Smith, M. H. and A. F. Peterson, "Numerical solution of the CFIE using vector bases and dual interlocking meshes," IEEE Trans. Antennas Propag., Vol. 53, No. 10, 3334-3339, Oct. 2005.
doi:10.1109/TAP.2005.856332        Google Scholar

16. Andriulli, F. and E. Michielssen, "A regularized combined field integral equation for scattering from 2-D perfect electrically conducting objects," IEEE Trans. Antennas Propag., Vol. 55, No. 9, 2522-2529, Sep. 2007.
doi:10.1109/TAP.2007.904083        Google Scholar

17. Yla-Oijala, P., M. Taskinen, and J. Seppo, "Analysis of surface integral equations in electromagnetic scattering and radiation problems," Eng. Anal. Boundary Elements, Vol. 32, 196-209, 2008.
doi:10.1016/j.enganabound.2007.08.004        Google Scholar

18. Chew, W. C., M. S. Tong, and B. Hu, Integral Equation Methods for Electromagnetic and Elastic Waves, Morgan & Claypool, 2009.

19. Nosich, I., "Method of analytical regularization in computational photonics," Radio Science, Vol. 51, No. 8, 1421-1430, Aug. 2016.
doi:10.1002/2016RS006044        Google Scholar

20. Rius, J. M., E. Ubeda, and J. Parron, "On the testing of the magnetic field integral equation with RWG basis functions in method of moments," IEEE Trans. Antennas Propag., Vol. 49, No. 11, 1550-1553, Nov. 2001.
doi:10.1109/8.964090        Google Scholar

21. Ergul, O. and L. Gurel, "Linear-linear basis functions for MLFMA solutions of magnetic field and combined field integral equations," IEEE Trans. Antennas Propag., Vol. 55, No. 4, 1103-1110, Apr. 2007.
doi:10.1109/TAP.2007.893393        Google Scholar

22. Gibson, W. C., The Method of Moments in Electromagnetics, Chapman & Hall, Taylor & Francis Group, Boca Raton, 2008.

23. Yan, S., J.-M. Jin, and Z. Nie, "Improving the accuracy of the second-kind Fredholm integral equations by using the Buffa-Christiansen functions," IEEE Trans. Antennas Propag., Vol. 59, No. 4, 1299-1310, Apr. 2011.
doi:10.1109/TAP.2011.2109364        Google Scholar

24. Ubeda, E., J. M. Tamayo, J. M. Rius, and A. Heldring, "Stable discretization of the electricmagnetic field integral equation with the Taylor-orthogonal basis functions," IEEE Trans. Antennas Propag., Vol. 61, No. 3, 1484-1490, Mar. 2013.
doi:10.1109/TAP.2012.2227925        Google Scholar

25. Zalevsky, G. S., O. I. Sukharevsky, V. A. Vasilets, and S. V. Nechitaylo, "Secondary radiation of resonance perfectly conducting objects," Journal of Communications Technology and Electronics, Vol. 59, No. 12, 1321-1332, 2014.
doi:10.1134/S1064226914100106        Google Scholar

26. Sukharevsky, O. I., G. S. Zalevsky, and V. A. Vasilets, "Modeling of ultrawideband (UWB) impulse scattering by aerial and subsurface resonant objects based on integral equation solving," Advanced Ultrawideband Radar: Signals, Targets, and Applications, J. D. Taylor, Ed., CRC Press, Taylor & Francis Group, Boca Raton, London, New York, 2016.        Google Scholar

27. Kolmogorov, S. Fomin, Elements of the Theory of Functions and Functional Analysis, Dover, 1999.

28. Eswaran, K., "On the solutions of a class of dual integral equations occurring in diffraction problems," Proc. Roy. Soc. London, Ser. A, Vol. 429, 399-427, 1990.
doi:10.1098/rspa.1990.0066        Google Scholar

29. Veliev, E. I. and V. V. Veremey, "Numerical-analytical approach for the solution to the wave scattering by polygonal cylinders and flat strip structures," Analytical and Numerical Methods in Electromagnetic Wave Theory, M. Hashimoto, M. Idemen, and O. A. Tretyakov (eds.), Science House, Tokyo, 1993.        Google Scholar

30. Davis, M. J. and R. W. Scharstein, "Electromagnetic plane wave excitation of an open-ended finitelength conducting cylinder," Journal of Electromagnetic Waves and Applications, Vol. 7, 301-319, 1993.
doi:10.1163/156939393X00354        Google Scholar

31. Hongo, K. and H. Serizawa, "Diffraction of electromagnetic plane wave by rectangular plate and rectangular hole in the conducting plate," IEEE Trans. Antennas Propag., Vol. 47, No. 6, 1029-1041, Jun. 1999.
doi:10.1109/8.777128        Google Scholar

32. Bliznyuk, N. Y., A. I. Nosich, and A. N. Khizhnyak, "Accurate computation of a circular-disk printed antenna axisymmetrically excited by an electric dipole," Microwave and Optical Technology Letters, Vol. 25, No. 3, 211-216, 2000.
doi:10.1002/(SICI)1098-2760(20000505)25:3<211::AID-MOP15>3.0.CO;2-D        Google Scholar

33. Tsalamengas, J. L., "Rapidly converging direct singular integral-equation techniques in the analysis of open microstrip lines on layered substrates," IEEE Trans. Microw. Theory Tech., Vol. 49, No. 3, 555-559, Mar. 2001.
doi:10.1109/22.910563        Google Scholar

34. Losada, V., R. R. Boix, and F. Medina, "Fast and accurate algorithm for the short-pulse electromagnetic scattering from conducting circular plates buried inside a lossy dispersive halfspace," IEEE Trans. Geosci. Remote Sensing, Vol. 41, 988-997, May 2003.
doi:10.1109/TGRS.2003.810678        Google Scholar

35. Lucido, M., G. Panariello, and F. Schettino, "Accurate and efficient analysis of stripline structures," Microwave and Optical Technology Letters, Vol. 43, No. 1, 14-21, Oct. 2004.
doi:10.1002/mop.20361        Google Scholar

36. Lucido, M., G. Panariello, and F. Schettino, "Analysis of the electromagnetic scattering by perfectly conducting convex polygonal cylinders," IEEE Trans. Antennas Propag., Vol. 54, 1223-1231, Apr. 2006.
doi:10.1109/TAP.2006.872662        Google Scholar

37. Hongo, K. and Q. A. Naqvi, "Diffraction of electromagnetic wave by disk and circular hole in a perfectly conducting plane," Progress In Electromagnetics Research, Vol. 68, 113-150, 2007.
doi:10.2528/PIER06073102        Google Scholar

38. Lucido, M., G. Panariello, and F. Schettino, "Electromagnetic scattering by multiple perfectly conducting arbitrary polygonal cylinders," IEEE Trans. Antennas Propag., Vol. 56, 425-436, Feb. 2008.
doi:10.1109/TAP.2007.915419        Google Scholar

39. Lucido, M., G. Panariello, and F. Schettino, "TE scattering by arbitrarily connected conducting strips," IEEE Trans. Antennas Propag., Vol. 57, 2212-2216, Jul. 2009.        Google Scholar

40. Coluccini, G., M. Lucido, and G. Panariello, "TM scattering by perfectly conducting polygonal cross-section cylinders: A new surface current density expansion retaining up to the second-order edge behavior," IEEE Trans. Antennas Propag., Vol. 60, No. 1, 407-412, Jan. 2012.
doi:10.1109/TAP.2011.2167924        Google Scholar

41. Lucido, M., "An analytical technique to fast evaluate mutual coupling integrals in spectral domain analysis of multilayered coplanar coupled striplines," Microwave and Optical Technology Letters, Vol. 54, No. 4, 1035-1039, Apr. 2012.
doi:10.1002/mop.26674        Google Scholar

42. Lucido, M., "A new high-efficient spectral-domain analysis of single and multiple coupled microstrip lines in planarly layered media," IEEE Trans. Microw. Theory Tech., Vol. 60, No. 7, 2025-2034, Jul. 2012.
doi:10.1109/TMTT.2012.2195025        Google Scholar

43. Coluccini, G., M. Lucido, and G. Panariello, "Spectral domain analysis of open single and coupled microstrip lines with polygonal cross-section in bound and leaky regimes," IEEE Trans. Microw. Theory Tech., Vol. 61, No. 2, 736-745, Feb. 2013.
doi:10.1109/TMTT.2012.2231424        Google Scholar

44. Lucido, M., "An efficient evaluation of the self-contribution integrals in the spectral-domain analysis of multilayered striplines," IEEE Antennas and Wireless Propagation Letters, Vol. 12, 360-363, 2013.
doi:10.1109/LAWP.2013.2252139        Google Scholar

45. Coluccini, G. and M. Lucido, "A new high efficient analysis of the scattering by a perfectly conducting rectangular plate," IEEE Trans. Antennas Propag., Vol. 61, No. 5, 2615-2622, May 2013.
doi:10.1109/TAP.2012.2237533        Google Scholar

46. Lucido, M., "Complex resonances of a rectangular patch in a multilayered medium: A new accurate and efficient analytical technique," Progress In Electromagnetics Research, Vol. 145, 123-132, 2014.
doi:10.2528/PIER14020204        Google Scholar

47. Lucido, M., "Electromagnetic scattering by a perfectly conducting rectangular plate buried in a lossy half-space," IEEE Trans. Geosci. Remote Sensing, Vol. 52, No. 10, 6368-6378, Oct. 2014.
doi:10.1109/TGRS.2013.2296353        Google Scholar

48. Lucido, M., G. Panariello, and F. Schettino, "An EFIE formulation for the analysis of leakywave antennas based on polygonal cross-section open waveguides," IEEE Antennas and Wireless Propagation Letters, Vol. 13, 983-986, May 2014.
doi:10.1109/LAWP.2014.2323431        Google Scholar

49. Lucido, M., "Scattering by a tilted strip buried in a lossy half-space at oblique incidence," Progress In Electromagnetics Research M, Vol. 37, 51-62, 2014.
doi:10.2528/PIERM14041507        Google Scholar

50. Corsetti, F., M. Lucido, and G. Panariello, "Effective analysis of the propagation in coupled rectangular-core waveguides," IEEE Photonics Technology Letters, Vol. 26, No. 18, 1855-1858, Sep. 2014.
doi:10.1109/LPT.2014.2338074        Google Scholar

51. Lucido, M., G. Panariello, D. Pinchera, and F. Schettino, "Cut-off wavenumbers of polygonal cross section waveguides," IEEE Microwave and Wireless Components Letters, Vol. 24, No. 10, 656-658, Oct. 2014.
doi:10.1109/LMWC.2014.2340735        Google Scholar

52. Di Murro, F., M. Lucido, G. Panariello, and F. Schettino, "Guaranteed-convergence method of analysis of the scattering by an arbitrarily oriented zero-thickness PEC disk buried in a lossy half-space," IEEE Trans. Antennas Propag., Vol. 63, No. 8, 3610-3620, Aug. 2015.
doi:10.1109/TAP.2015.2438336        Google Scholar

53. Lucido, M., M. D. Migliore, and D. Pinchera, "A new analytically regularizing method for the analysis of the scattering by a hollow finite-length PEC circular cylinder," Progress In Electromagnetics Research B, Vol. 70, 55-71, 2016.
doi:10.2528/PIERB16081404        Google Scholar

54. Lucido, M., G. Panariello, and F. Schettino, "Scattering by a zero-thickness PEC disk: A new analytically regularizing procedure based on Helmholtz decomposition and Galerkin method," Radio Science, Vol. 52, No. 1, 2-14, Jan. 2017.
doi:10.1002/2016RS006140        Google Scholar

55. Meixner, J., "The behavior of electromagnetic fields at edges," IEEE Trans. Antennas Propag., Vol. 20, 442-446, 1972.
doi:10.1109/TAP.1972.1140243        Google Scholar

56. Jones, D. S., The Theory of Electromagnetism, Pergamon Press, 1964.

57. Abramowitz, M. and I. A. Stegun, "Handbook of Mathematical Functions," Verlag Harri Deutsch, 1984.        Google Scholar

58. Overfelt, P. L. and D. J. White, "TE and TM modes of some triangular cross-section waveguides using superposition of plane waves," IEEE Trans. Microw. Theory Tech., Vol. 34, 161-167, 1986.
doi:10.1109/TMTT.1986.1133294        Google Scholar