Pole Location in GMT

  • James E. RichieEmail author
Part of the Springer Series on Atomic, Optical, and Plasma Physics book series (SSAOPP, volume 99)


This chapter begins with an overview of the variety of methods and techniques used to choose discrete pole locations in the family of Generalized Multipole Techniques (GMT). The heuristic rules and guidelines that are described are often quite successful. In addition, studies of the performance of GMT methods for canonical problems are reviewed. It has been shown that there are at least two sources of error when using GMT: analytically-based error and numerically-based error. The effective spatial bandwidth (EBW) of fields along the boundary of scatterers is described and used to show the conditions necessary to obtain stable solutions from GMT techniques. The EBW for two-dimensional circular boundaries is applied to some examples. In addition, an extension of EBW for non-circular boundaries is described and applied to elliptically shaped boundaries.


  1. 1.
    T. Wriedt (ed.), Generalized Multipole Techniques for Electromagnetic and Light Scattering, Computational Methods in Mechanics, vol. 4 (Elsevier Science B. V, New York, 1999)Google Scholar
  2. 2.
    R.F. Harrington, Field Computation by Moment Methods (R. E. Krieger, Malabar, 1968)Google Scholar
  3. 3.
    A.F. Peterson, S.L. Ray, R. Mittra, Computational Methods for Electromagnetics (IEEE Press, New York, 1998)zbMATHGoogle Scholar
  4. 4.
    C. Hafner, The Generalized Multipole Technique for Computational Electromagnetics (Artech House, Boston, 1990)Google Scholar
  5. 5.
    P. Leuchtmann, F. Bomholt, IEEE Trans. Electromagn. Compat. 35(2), 170 (1993)CrossRefGoogle Scholar
  6. 6.
    A.C. Ludwig, in IEEE AP-S International Symposium Digest, Dallas, TX (1990), pp. 48–51Google Scholar
  7. 7.
    Y. Leviatan, IEEE Trans. Antennas Propag. 38(8), 1259 (1990)ADSCrossRefGoogle Scholar
  8. 8.
    Y. Leviatan, A. Boag, IEEE Trans. Antennas Propag. 35, 1119 (1987)ADSCrossRefGoogle Scholar
  9. 9.
    Y. Leviatan, A. Boag, A. Boag, IEEE Trans. Antennas Propag. 36, 1026 (1988)ADSCrossRefGoogle Scholar
  10. 10.
    Y. Leviatan, A. Boag, A. Boag, IEEE Trans. Antennas Propag. 36(12), 1722 (1988)ADSCrossRefGoogle Scholar
  11. 11.
    I.N. Vekua, New Methods for Solving Elliptic Equations (Wiley, New York, 1967)zbMATHGoogle Scholar
  12. 12.
    D.I. Kaklamani, H.T. Anastassiu, IEEE Antennas Propag. Mag. 44(3), 48 (2002)ADSCrossRefGoogle Scholar
  13. 13.
    K. Beshir, J.E. Richie, IEEE Trans. Electromagn. Compat. 38(2), 177 (1996)CrossRefGoogle Scholar
  14. 14.
    S. Eisler, Y. Leviatan, IEE Proc. Pt. H 136(6), 431 (1989)Google Scholar
  15. 15.
    P. Leuchtmann, IEEE Trans. Mag. 19(6), 2371 (1983)ADSCrossRefGoogle Scholar
  16. 16.
    E. Moreno, D. Erni, C. Hafner, R. Vahldieck, J. Opt. Soc Am. A 19(1), 101 (2002)ADSCrossRefGoogle Scholar
  17. 17.
    A.K. Bandyopadhyay, C. Tomassoni, A.S. Omar, in IEEE MTT-S International Symposium Digest (2004), pp. 1381–1384Google Scholar
  18. 18.
    I.I. Heretakis, P.J. Papakanellos, C.N. Capsalis, J. Electromagn. Waves Appl. 16(11), 1555 (2002)CrossRefGoogle Scholar
  19. 19.
    I.I. Heretakis, P.J. Papakanellos, C.N. Capsalis, IEEE Trans. Antennas Propag. 53(3), 938 (2005)ADSCrossRefGoogle Scholar
  20. 20.
    R.S. Zaridze, R. Jobava, G. Bit-Banik, D. Karkasbadze, J. Electromagn. Waves Appl. 12, 1491 (1998)MathSciNetCrossRefGoogle Scholar
  21. 21.
    R.S. Zaridze, G. Bit-Babik, K. Tavzarashvili, D.P. Economou, K.K. Uzunoglu, IEEE Trans. Antennas Propag. 50(1), 50 (2002)ADSCrossRefGoogle Scholar
  22. 22.
    G. Fikioris, IEEE Trans. Antennas Propag. 54(7), 2022 (2006)ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    C.A. Valagiannopoulos, N.L. Tsitsas, G. Fikioris, J. Opt. Soc. Am. A 29(1), 1 (2012)ADSCrossRefGoogle Scholar
  24. 24.
    H.T. Anastassiu, D.G. Lymperopoulos, D.I. Kaklamani, IEEE Trans. Antennas Propag. 52(6), 1541 (2004)ADSCrossRefGoogle Scholar
  25. 25.
    K.F. Warnick, W.C. Chew, IEEE Trans. Microw. Theory Tech. 48, 1652 (2000)ADSCrossRefGoogle Scholar
  26. 26.
    H.T. Anastassiu, D.I. Kaklamani, J. Electromagn. Waves Appl. 18(10), 1283 (2004)CrossRefGoogle Scholar
  27. 27.
    H.T. Anastassiu, D.I. Kaklamani, Radio Sci. 39(5), RS5015 (2004).
  28. 28.
    H.T. Anastassiu, Prog. Electromagn. Res. PIER 52, 109 (2005)CrossRefGoogle Scholar
  29. 29.
    O.M. Bucci, G. Franceschetti, IEEE Trans. Antennas Propag. 35(12), 1445 (1987)ADSCrossRefGoogle Scholar
  30. 30.
    J.E. Richie, IEEE Trans. Antennas Propag. 58(11), 3610 (2010)ADSMathSciNetCrossRefGoogle Scholar
  31. 31.
    J.E. Richie, IEEE Trans. Antennas Propag. 59(12), 4861 (2011)ADSCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Marquette UniversityMilwaukeeUSA

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