1999 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.

IEEE Transactions on Antennas and Propagation
Volume 47 Number 2, February 1999

Table of Contents for this issue

Complete paper in PDF format

A Combined Field Approach to Scattering from Infinite Elliptical Cylinders Using the Method of Ordered Multiple Interactions

Robert J. Adams, Student Member, IEEE, and Gary S. Brown, Fellow, IEEE

Page 364.

Abstract:

The method of ordered multiple interactions (MOMI) is an iterative procedure which has been demonstrated to provide a rapidly convergent series for the problem of wave scattering from perfectly conducting surfaces rough in a single dimension. In this paper, we consider the extension of this technique to the problem of scattering from infinite elliptical cylinders. For an incident plane wave having its electric field polarized along the axis of the cylinder a combined field formulation of the scattering problem is found to provide a rapidly convergent MOMI series. The determination of an optimal combined field representation for the scattering problem in this case is also discussed. An extension of the MOMI method is necessary to properly treat the remaining polarization.

References

  1. E. K. Miller, "A selective survey of computational electromagnetics," IEEE Trans. Antennas Propagat., vol. 36, pp. 1281-1305, Sept. 1988.
  2. W. C. Chew, J. H. Jin, C. C. Lu, E. Michielssen, and J. M. Song, "Fast solution methods in electromagnetics," IEEE Trans. Antennas Propagat., vol. 45, no. 3, pp. 553-543, Mar. 1997.
  3. R. F. Harrington, Field Computation by Moment Methods.Piscataway, NJ: IEEE Press, 1993.
  4. A. F. Peterson and R. Mittra, "Convergence of the conjugate gradient method when applied to matrix equations representing electromagnetic scattering problems," IEEE Trans. Antennas Propagat., vol. AP-34, pp. 1447-1454, Dec. 1986.
  5. C. F. Smith, A. F. Peterson, and R. Mittra, "The biconjugate gradient method for electromagnetic scattering," IEEE Trans. Antennas Propagat., vol. 38, pp. 938-940, June 1990.
  6. R. J. Adams and G. S. Brown, "On the use of the fast multipole method with the method of ordered multiple interactions," Electron. Lett., vol. 34, pp. 2219-2220, Nov. 1998.
  7. D. A. Kapp and G. S. Brown, "A new numerical method for rough-surface scattering calculations," IEEE Trans. Antennas Propagat., vol. 44, pp. 711-721, May 1996.
  8. R. J. Adams, R. Awadallah, J. Toporkov, and G. S. Brown, "Computational methods for rough surface scattering: The method of ordered multiple interactions," in Proc. 4th Int. SIAM Conf. Math. Numer. Aspects Wave Propagat., Golden, CO, June 1998, pp. 79-83.
  9. N. Morita, N. Kumagai, and J. R. Mautz, Integral Equation Methods for Electromagnetics.Norwood, MA: Artech House, 1990.
  10. J. M. Elson, P. Tran, and F. J. Escobar, "Application of the MOMI method to the magnetic field integral equation," in Radar Processing, Technol., Applicat. Proc. SPIE Photon. West Conf., San Diego, CA, July 1997, pp. 29-37.
  11. D. Torrungrueng and E. H. Newman, "The multiple sweep method of moments (MSMM) analysis of electrically large bodies," IEEE Trans. Antennas Propagat., vol. 45, pp. 1252-1258, Aug. 1997.
  12. R. J. Adams and G. S. Brown, "Scattering from randomly rough dielectric surfaces using the method of ordered multiple interactions," in Proc. Int. Conf. Electromagn. Adv. Applicat., Torino, Italy, Sept. 1997, pp. 359-361.
  13. --, "An iterative solution for two-dimensional rough surface scattering problems based on a factorization of the Helmholtz operator," IEEE Trans. Antennas Propagat., to be published.
  14. --, "An iterative procedure for two first kind integral equations of scattering theory," Radio Sci., to be published.
  15. J. V. Toporkov, R. T. Mar.and, and G. S. Brown, "On the discretization of the integral equation describing scattering by rough conducting surfaces," IEEE Trans. Antennas Propagat., vol. 46, pp. 150-161, Jan. 1998.
  16. D. Holliday, L. L. DeRaad Jr., and G. J. St-Cyr, "Forward-backward: A new method for computing low-grazing scattering," IEEE Trans. Antennas Propagat., vol. 44, pp. 722-729, May 1996.
  17. R. F. Harrington, Time-Harmonic Electromagnetic Fields.New York: McGraw Hill, 1961.
  18. A. C. Pipkin, A Course on Integral Equations.Boston, MA: Springer-Verlag, 1991.
  19. N. Engheta, W. D. Murphy, V. Rokhlin, and M. S. Vassiliou, "The fast multipole method (FMM) for electromagnetic scattering problems," IEEE Trans. Antennas Propagat., vol. 40, pp. 634-641, June 1992.
  20. W. D. Murphy, V. Rokhlin, and M. S. Vassiliou, "Acceleration methods for the iterative solution of electromagnetic scattering problems," Radio Sci., vol. 28, no. 1, pp. 1-12, 1993.
  21. M. B. Woodworth and A. D. Yaghjian, "Derivation, application, and conjugate gradient solution of dual-surface integral equations for three-dimensional, multiwavelength perfect conductors," in PIER 5: Application of Conjugate Gradient Method to Electromagnetics and Signal Analysis, J. A. Kong and T. A. Sarkar, Eds.New York: Elsevier, 1991, ch. 4.
  22. J. R. Mautz and R. F. Harrington, "H-field, E-field, and combined-field solutions for conducting bodies of revolution," Archiv Elektronik Ubertragungstechnik (Electron. Communicat.), vol. 32, no. 4, pp. 157-164, 1978.
  23. M. Abramowitz and I. E. Stegun,Eds., Handbook of Mathematical Functions.New York: Dover, 1980 (9th printing).
  24. A. F. Peterson, "The "interior resonance" problem associated with surface integral equations of electromagnetics: Numerical consequences and a survey of remedies," Electromagn., vol. 10, pp. 293-312, 1990.
  25. D. R. Wilton and J. E. Wheeler III, "Comparison of convergence rates of the conjugate gradient method applied to various integral equation formulations," in PIER 5: Application of Conjugate Gradient Method to Electromagnetics and Signal Analysis, J. A. Kong and T. A. Sarkar, Eds.New York: Elsevier, 1991, ch. 5.
  26. R. J. Adams and G. S. Brown, "A rapidly convergent iterative method for two-dimensional closed body scattering problems," Microwave Opt. Technol. Lett., vol. 20, pp. 179-183, Feb. 1999.