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

Table of Contents for this issue

Complete paper in PDF format

Singular Basis Functions and Curvilinear Triangles in the Solution of the Electric Field Integral Equation

William J. Brown and Donald R. Wilton, Fellow, IEEE

Page 347.

Abstract:

Basis functions are formulated that account for singularities in the charge density near an edge on a conducting body. The formulation is general and the basis functions are valid for planar as well curvilinear geometries. In principle, singularities of any order can be treated, but best results are obtained for so-called "knife edge" singularities. Results are compared with exact solutions or measurements where available for some simple problems.

References

  1. S. M. Rao, D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas Propagat., vol. AP-30, pp. 409-418, 1982.
  2. G. E. Antilla, "Radiation and scattering from complex three-dimensional geometries using a curvilinear hybrid finite element-integral equation approach," Ph.D. dissertation, Univ. California, 1993.
  3. D. Wilkes and C. C. Cha, "Method of moments solution with parametric curved triangular patches," in Proc. IEEE Int. Symp. Antennas Propagat., 1991, pp. 1512-1515.
  4. M. S. Ingber and R. H. Ott, "Application of the boundary element method to the magnetic field integral equation," IEEE Trans. Antennas Propagat., vol. 39, pp. 606-611, 1991.
  5. H. Cam, S. Toutain, P. Gelin, and G. Landrac, "Study of a Fabry-Perot cavity in the microwave frequency range by the boundary element method," IEEE Trans. Microwave Theory Tech., vol. 40, pp. 298-304, 1992.
  6. S. Wandzura, "Electric current basis functions for curved surfaces," Electromagn., vol. 12, no. 1, pp. 77-91, 1992.
  7. N. Y. Zhu and F. M. Landstorfer, "Application of curved parametric triangular and quadrilateral edge elements in the moment method solution of the EFIE," IEEE Microwave Guided Wave Lett., vol. 3, pp. 319-321, 1993.
  8. J. Meixner, "The behavior of electromagnetic fields at edges," New York Univ., Rep. EM-72, New York, 1954.
  9. J. Van Bladel, Singular Electromagnetic Fields and Sources.New York: Oxford Univ. Press, 1991.
  10. J. H. Richmond, "On the edge mode in the theory of TM scattering by a strip or strip grating," IEEE Trans. Antennas Propagat., vol. AP-28, pp. 883-887, 1980.
  11. D. R. Wilton and S. Govind, "Incorporation of edge conditions in moment method solution," IEEE Trans. Antennas Propagat., vol. AP-25, pp. 845-850, 1977.
  12. T. Andersson, "Moment method calculations on apertures using singular basis functions," IEEE Trans. Antennas Propagat., vol. 41, pp. 1709-1716, 1993.
  13. R. D. Graglia, D. R. Wilton, and A. F. Peterson, "Higher order interpolatory vector bases for computational electromagnetics," IEEE Trans. Antennas Propagat., vol. 45, pp. 329-342, 1997.
  14. G. Dhatt and G. Touzot, The Finite Element Method Displayed.New York: Wiley, 1984.
  15. W. J. Brown, "Higher order modeling of surface integral equations," Ph.D. dissertation, Univ. Houston, Houston, TX, Dec. 1996.
  16. R. W. Ziolkowski and W. A. Johnson, "Electromagnetic scattering of an arbitrary plane wave from a spherical shell with a circular aperture," J. Math. Phys., vol. 28, no. 6, pp. 1293-1314, 1987.
  17. S. V. Yesantharao, "EMPACK--A software toolbox of potential integrals for computational electromagnetics," Master's thesis, Univ. Houston, Houston, TX, Dec. 1989.
  18. K. Iizuka and J. L. Yen, "Surface currents on triangular and square metal cylinders," IEEE Trans. Antennas Propagat., vol. AP-15, pp. 795-801, 1967.