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IEEE Transactions on Antennas and Propagation
Volume 46 Number 10, October 1998

Table of Contents for this issue

Complete paper in PDF format

Direct Singular Integral Equation Methods in Scattering and Propagation in Strip- or Slot-Loaded Structures

John L. Tsalamengas, Member, IEEE

Page 1560.

Abstract:

Problems of three-dimensional (3-D) scatter-ing/hybrid-wave propagation for strip- or slot-loaded structures are often formulated in terms of systems of singular integral-integrodifferential equations (SIE-SIDE) of the first kind. Proper handling of the singular part of the kernels constitutes a major difficulty in carrying out method of moments (MoM). Three powerful techniques explored in the present paper provide efficient solutions by direct recourse to the theory of singular integral equations. In contrast to low-frequency methods wherein similar concepts are utilized for electrically narrow strips/slots, the proposed procedures are applicable uniformly to the whole range of widths from very narrow to very wide scatterers with remarkable accuracy. Numerical results are presented to validate and compare to one another the various numerical codes.

References

  1. A. I. Kalandiya, Mathematical Methods of Two-Dimensional Elasticity.Moscow, Russia: Mir, 1982.
  2. V. Z. Parton and P. I. Perlin, Integral Equations in Elasticity.Moscow, Russia: Mir, 1982.
  3. R. Mitra and S. W. Lee, Analytical Techniques in the Theory of Guided Waves.New York: Macmillan, 1971.
  4. N. I Muskhelishvili, Singular Integral Equations.Groningen, Holland: Noordhoff, 1953.
  5. F. D. Gakhov, Boundary Value Problems.Oxford, U.K.: Pergamon, 1966.
  6. J. G. Fikioris, J. L. Tsalamengas, and G. J. Fikioris, "Exact solutions for shielded lines by the Carleman-Vekua method," IEEE Trans. Microwave Theory Tech., vol. 37, pp. 21-33, Jan. 1989.
  7. A. Matsushima and T. Itakura, "Singular integral equation approach to electromagnetic scattering from a finite periodic array of conducting strips," JEWA, vol. 5, no. 6, pp. 545-562, 1991.
  8. L. Lewin, "The use of singular integral equations in the solution of waveguide problems," in Advances of Microwaves, Leo Young, Ed.New York: Academic, 1966, vol. 1.
  9. J. L. Tsalamengas and J. G. Fikioris, "Efficient solutions for scattering from strips and slots in the presence of a dielectric half-space: Extension to wide scatterers--Part I: Theory," J. Appl. Phys., vol. 70, no. 3, pp. 1121-1131, Aug. 1991.
  10. A. Frenkel, "External modes of two-dimensional thin scatterers," Proc. Inst. Elect. Eng., vol. 130, pt. H, no. 3, pp. 209-214, 1983.
  11. S. Krenk, "On the use of the interpolation polynomial for solutions of singular integral equations," Quart. Appl. Math., vol. 33, pp. 479-483, Jan. 1975.
  12. --, "On quadrature formulas for singular integral equations of the first and the second kind," Quart. Appl. Math., vol. 33, pp. 225-232, Oct. 1975.
  13. E. I. Veliev, "Numerical-analytical methods of solution of integral equations of two-dimensional diffraction problems," in Math. Methods Electromagn. Theory, Proc. 3rd Int. School Seminal, Crimea, Ukraine, Apr. 1990.
  14. Z. T. Nazarchuk, "Singular integral equations in two-dimensional diffraction problems," in Math. Methods Electromagn. Theory Proc. 3rd Int. School Seminal, Crimea, Ukraine, Apr. 1990.
  15. Z. Nazarchuk and O. Ovsyannikov, "Electromagnetic scattering by screens in an open planar waveguide," JEWA, vol. 8, no. 11, pp. 1481-1498, 1994.
  16. R. Kress, "Numerical solution of boundary integral equations in time-harmonic electromagnetic scattering," Electromagn., vol. 10, pp. 1-20, 1990.
  17. J. L. Tsalamengas, "TE scattering by conducting strips right on the planar interface of a three-layered medium," IEEE Trans. Antennas Propagat., vol. 45, Dec. 1993.
  18. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions.New York: Dover, 1972.
  19. I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products, 4th ed.New York: Academic, 1965 (English transl., A. Jeffrey).