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 10, October 1999

Table of Contents for this issue

Complete paper in PDF format

A Boundary-Element Solution of the Leontovitch Problem

Abderrahmane Bendali, M'B. Fares, and Jean Gay

Page 1597.

Abstract:

A boundary-element method is introduced for solving electromagnetic scattering problems in the frequency domain relative to an impedance boundary condition (IBC) on an obstacle of arbitrary shape. The formulation is based on the field approach; namely, it is obtained by enforcing the total electromagnetic field, expressed by means of the incident field and the equivalent electric and magnetic currents and charges on the scatterer surface, to satisfy the boundary condition. As a result, this formulation is well-posed at any frequency for an absorbing scatterer. Both of the equivalent currents are discretized by a boundary-element method over a triangular mesh of the surface scatterer. The magnetic currents are then eliminated at the element level during the assembly process. The final linear system to be solved keeps all of the desirable properties provided by the application of this method to the usual perfectly conducting scatterer; that is, its unknowns are the fluxes of the electric currents across the edges of the mesh and its coefficient matrix is symmetric.

References

  1. M. Artola and M. Cessenat, "Diffraction d'une onde electromagnetique par un obstacle borne a` permittivite et permeabilite elevees," C. R. Acad. Sci. Paris, Serie I (in French with abridged English version--Diffraction Electromagn. Wave by Body with High Permittivity and Permeability), vol. 314, pp. 349-354, 1992.
  2. J. S. Asvestas, "Scattering by an indentation satisfying a dyadic impedance boundary condition," IEEE Trans. Antennas Propagat., vol. 45, pp. 28-33, Jan. 1997.
  3. A. Bendali, "Numerical analysis of the exterior boundary value problem for the time-harmonic Maxwell equations by a boundary finite-element method--Part 2: The discrete problem," Math. Comput., vol. 43, pp. 47-68, 1984.
  4. A. Bendali and M'B. Fares, "The CERFACS electromagnetic solver code," Tech. Rep., CERFCAS, Toulouse, France, 1998.
  5. P. G. Ciarlet, "Basic error estimates for elliptic problems," in Handbook of Numerical Analysis, Finite Element Methods (Part 1), P. G. Ciarlet and J. L. Lions, Eds.Amsterdam, The Netherlands: Elsevier, North-Holland, 1991, vol. II, pp. 17-351.
  6. G. Chen and J. Zhou, Boundary Element Methods.New York: Academic, 1992.
  7. L. Chety, F. Clerc, and W. Tabbara, "Surface equivalente radar d'objets composes de conducteur et de dielectrique de forme arbitraires," Ann. Telecommun. (in French); "Radar cross section arbitrary shaped conducting dielectric bodies," vol. 45, pp. 419-428, 1990 (English).
  8. D. Colton and R. Kress, Integral Equation Methods in Scattering Theory.New York: Wiley, 1983.
  9. D. Colton and R. Kress, "The impedance boundary value problem for the time harmonic Maxwell equations," Math. Meth. Appl. Sci., vol. 3, pp. 475-487, 1981.
  10. M. Costabel and W. L. Wendland, "Strong ellipticity of boundary integral operators," J. Reine Angew. Math., vol. 372, pp. 39-63, 1985.
  11. G. Dahlquist and A˚. Björck, Numerical Methods.Englewood Cliffs, NJ: Prentice-Hall, 1974.
  12. B. Despres, P. Joly, and J. Roberts, A Domain Decomposition Method for the Harmonic Maxwell's Equations.Amsterdam, The Netherlands: North-Holland, 1992, pp. 475-484.
  13. S. Ghanemi, F. Collino, and P. Joly, "Domain decomposition method for harmonic wave equations," 3th Int. Conf. Math. Numer. Aspects Wave Propagat., Mandelieu, France, Apr. 1995, pp. 663-672.
  14. P. M. Goggans and T. H. Shumpert, "A new surface impedance function for the aperture surface of a conducting body with a dielectric-filled cavity," IEEE Trans. Antennas Propagat., vol. 39, pp. 960-967, 1991.
  15. G. C. Hsiao and R. F. Kleinman, "Mathematical foundations for error estimations in numerical solutions of integral equations in electromagnetics," IEEE Trans. Antennas Propagat., vol. 45, pp. 316-328, Mar. 1997.
  16. G. C. Hsiao and W. L. Wendland, "A finite element method for some integral equations of the first kind," J. Math. Anal. Appl., vol. 58, pp. 449-481, 1977.
  17. P. L. Huddleston and D. S. Wang, "An impedance boundary condition approach to radiation by uniformly coated antennas," Radio Sci., vol. 24, pp. 427-432, 1989.
  18. J. Jin, The Finite Element Method in Electromagnetics.New York: Wiley, 1993.
  19. W. Jingguo and J. D. Layers, "Modified surface impedance boundary conditions fo 3-D eddy currents problems," IEEE Trans. Magn., vol. 29, pp. 1826-1829, 1993.
  20. G. Krishnasamy, F. Rizzo, and T. Rudolphi, "Hypersingular boundary integral equations: Their occurrence, interpretation, regularization, and computation," in Developments in Boundary Elements Methods Adv. Dynamic Analysis, P. K. Banerjee and S. Kobayashi, Eds.Amsterdam, The Netherlands: Elsevier, 1991, vol. 7, pp. 207-252.
  21. V. Lange, "Equations integrales espace-temps pour les equations de Maxwell, Calcul du champ diffracte pâr un obstacle dissipatif," Ph.D. dissertation, Univ. Bordeaux I, France, 1995.
  22. J. R. Mautz and R. F. Harrington, "H-field, E-field, and combined-field solutions for conducting bodies of revolution," Arch. F. Electron. Übertragungstech., Electron. Commun, vol. 32, pp. 159-264, 1978.
  23. L. N. Medgyesi-Mitschang and J. M. Putnam, "Integral equation formulations for imperfectly conducting scatterers," IEEE Trans. Antennas Propagat., vol. AP-33, pp. 206-214, Feb. 1985.
  24. J. C. Nedelec, "Integral equations with nonintegrable kernels," Integral Equation Operator Theory, vol. 5, pp. 561-572, 1982.
  25. 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.
  26. S. M. Rao, D. R. Wilton, A. W. Glisson, and B. S. Vidula, "A simple numerical solution procedure for statics problems involving arbitrary-shaped surfaces," IEEE Trans. Antennas Propagat., vol. AP-27, pp. 604-607, Sept. 1979.
  27. J. R. Rogers, "Moment-method scattering solutions to impedance boundary condition integral equations," IEEE AP-S Int. Symp., Boston, MA, 1984, pp. 347-350.
  28. V. H. Rumsey, "Reaction concept in electromagnetic theory," Phys. Rev., vol. 94, pp. 1483-1491, 1954.
  29. T. B. A. Senior, "Impedance boundary conditions for imperfectly conducting surfaces," Appl. Sci. Res., SectionB, vol. 8, pp. 418-436, 1960.
  30. B. Stupfel, R. Le Martret, P. Bonnemason, and B. Scheurer, "Combined boundary-element and finite-element method for the scattering problem by axisymmetrical penetrable objects," Mathematical and Numerical Aspects of Wave Propagation, G. Cohen, L. Halpern, and P. Joly, Eds., Strasbourg, France, Apr. 1991, pp. 332-341.
  31. I. P. Theron and J. H. Cloete, "On the surface impedance used to model the conductor losses of microstrip structures," Inst. Elect. Eng. Proc. Microwave Antennas Propagat., vol. 142, pp. 35-40, 1995.
  32. J. Van Bladel, Electromagnetic Fields.New York: McGraw-Hill, 1964.
  33. A. Van Herk, "Three dimensional analysis of magnetic fields in recording head configuration," IEEE Trans. Magn., vol. 5 MAG-16, pp. 890-892, Sept. 1980.
  34. D.-S. Wang, "Limits and validity of the impedance boundary condition on penetrable surfaces," IEEE Trans. Antennas Propagat., vol. AP-35, pp. 453-457, Apr. 1987.
  35. K. W. Whites, E. Michielssen, and R. Mittra, "Approximating the scattering by a material-filled 2-D trough in an infinite plane using the impedance boundary condition," IEEE Trans. Antennas Propagat., vol. 41, pp. 146-153, Feb. 1993.