1998 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 46 Number 12, December 1998

Table of Contents for this issue

Complete paper in PDF format

A Novel Exact Two-Point Field Equation (2PFE) for Solving Electromagnetic Scattering Problems

Yong-Lun Luo, Kwai-Man Luk, Senior Member, IEEE, and Siu-Ming Shum

Page 1833.

Abstract:

The finite-difference (FD) method is a basic technique for solving differential equation. The disadvantage of it for electromagnetic (EM) problems of an open region is that the mesh needs to be terminated with the application of a proper boundary condition. In this paper, a novel exact two-point field equation (2PFE) is derived from rigorous analysis of the radiation field and it is proposed to be used as the termination boundary condition (BC) for solving EM scattering problems in the open region by the iterative FD method. This 2PFE-BC approaches its exact solution through the iteration process and, at the same time, the scattered field and the induced current density approach their exact solutions. The novel 2PFE is simple in concept and easy to apply. The validity of the 2PFE and the iterative FD method has been tested. Several two-dimensional (2-D) scattering problems have been successfully solved. The results agree very well with those obtained by method of moments (MoM) or measured equation of invariance (MEI).

References

  1. V. H. Rumsey, "The reaction concept in electromagnetic theory," Phys. Rev. Ser. 2, vol. 94, pp. 1483-1491, 1954.
  2. J. H. Richmond, "Digital computer solutions of the rigorous equations for scattering problems," Proc. IEEE, vol. 53, pp. 796-804, Aug. 1965.
  3. R. F. Harrington, Field Computation by Moment Methods.Piscataway, NJ: IEEE Press, 1992.
  4. --, "The method of moments in electromagnetics," J. Elect. Waves Appl., vol. 1, no. 3, pp. 181-200, 1987.
  5. K. K. Mei and J. G. Van Bladel, "Scattering by perfectly-conducting rectangular cylinders," IEEE Trans. Antennas Propagat., vol. AP-11, pp. 185-192, Mar. 1963.
  6. M. G. Andreasen, "Scattering from parallel metallic cylinders with arbitrary cross sections," IEEE Trans. Antennas Propagat., vol. AP-12, pp. 746-754, Nov. 1964.
  7. D. R. Wilton and C. M. Butler, "Effective methods for solving integral and integro-differential equations," Electromagn., vol. 1, pp. 289-308, July-Sept. 1981.
  8. T. K. Sarkar, "A note on the variational method (Rayleigh-Ritz), Galerkin's method, and the method of least squares," Radio Sci., vol. 18, pp. 1207-1224, Nov./Dec. 1983.
  9. 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, May 1982.
  10. E. H. Newman, "An overview of the hybrid MM/Green's function method in electromagnetics," Proc. IEEE, vol. 76, pp. 270-282, Mar. 1988.
  11. X. Yuan, "Three-dimensional electromagnetic scattering from inhomogeneous objects by the hybrid moment and finite element method," IEEE Trans. Microwave Theory Tech., vol. 38, pp. 1053-1058, Aug. 1990.
  12. A. Bayliss, M. Gunzburger, and E. Turkel, "Boundary conditions for the numerical solution of elliptic equations in exterior regions," SIAM, J. Appl. Math., vol. 42, pp. 430-451, 1982.
  13. B. Engquist and A. Majda, "Absorbing boundary conditions for the numerical simulation of waves," Math Computat., vol. 31, pp. 421-435, 1977.
  14. R. L. Higdon, "Absorbing boundary conditions for difference approximations to the multidimensional wave equation," Math. Computat., vol. 47, pp. 437-459, 1986.
  15. B. Stupfel and R. Mittra, "A theoretical study of numerical absorbing conditions," IEEE Trans. Antennas Propagat., vol. 43, pp. 478-487, May 1995.
  16. K. K. Mei, R. Pouse, Z. Q. Chen, Y. W. Liu, and M. D. Prouty, "Measured equation of invariance: A new concept in field computations," in Int. Dig. IEEE Antennas Propagat. Soc., Chicago, IL, July 1992, pp. 2047-2050.
  17. --, "Measured equation of invariance: A new concept in field computations," IEEE Trans. Antennas Propagat., vol. 42, pp. 320-328, Mar. 1994.
  18. R. Pouse, "The measured equation of invariance: A new concept in field computation," Ph.D. dissertation, Univ. California, Berkeley, 1992.
  19. Y. L. Chow, Y. W. Liu, Y. L. Luo, K. M. Luk, K. K. Mei, and E. K. N. Yung, "A simplification of field method, from moment to MEI," in Dig. USNC/URSI Radio Sci. Meet., Baltimore, MD, July 1996, p. 52.
  20. J. O. Jevtic and R. Lee, "An analytical characterization of the error in the measured equation of invariance," IEEE Trans. Antennas Propagat., vol. 43, pp. 1109-1115, Oct. 1995.
  21. --, "A theoretical and numerical analysis of the measured equation of invariance," IEEE Trans. Antennas Propagat., vol. 42, pp. 1097-1105, Aug. 1994.
  22. A. C. Cangellaris and D. B. Wright, "Application of the measured equation of invariance to electromagnetic scattering by penetrable bodies," IEEE Trans. Magn., vol. 29, pp. 1628-1631, 1993.
  23. Y. L. Luo, K. M. Luk, Y. W. Liu, K. M. Mei, and E. K. N. Yung, "Electromagnetic scattering and radiation from perfectly-conducting cylindrical parabolic reflector by MEI," in Proc. Int. Symp. Antennas Propagat., Chiba, Japan, Aug. 1996, pp. 1161-1164.
  24. T. Roy, T. K. Sarkar, A. R. Djordjevic, and M. Salazar-Palma, "A hybrid method for terminating the finite-element mesh (electrostatic case)," Microwave Opt. Technol. Lett., vol. 8, no. 6, pp. 282-287, 1995.
  25. A. R. Djordjevic, T. K. Sarkar, T. Roy, S. M. Rao, and M. Salazar, "An exact method for simulating boundary conditions for mesh termination in finite-difference techniques," Microwave Opt. Technol. Lett., vol. 8, no. 6, pp. 319-321, 1995.
  26. A. R. Djordjevic, T. K. Sarkar, and T. Roy, "Finite-difference solution of scattering (TE case) using exact mesh termination," Microwave Opt. Technol. Lett., vol. 10, no. 1, pp. 56-59, 1995.
  27. R. E. Collin, Foundations of Microwave Engineering.New York: McGraw-Hill, 1966.
  28. J. A. Kong, Electromagnetic Wave Theory.New York: Wiley, 1986.