2000 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 48 Number 11, November 2000

Table of Contents for this issue

Complete paper in PDF format

Accurate Solution of the Volume Integral Equation for High-Permittivity Scatterers

Jörg P. Kottmann and Olivier J. F. Martin

Page 1719.

Abstract:

We present a formalism based on the method of moment to solve the volume integral equation using tetrahedral (3-D) and triangular (2-D) elements. We introduce a regularization scheme to handle the strong singularity of the Green's tensor. This regularization scheme is extended to neighboring elements, which dramatically improves the accuracy and the convergence of the technique. Scattering by high-permittivity scatterers, like semiconductors,can be accurately computed. Furthermore, plasmon-polariton resonances in dispersive materials can also be reproduced.

References

  1. Landolt-Börnstein, Numerical Data and Functional Relationships in Science and Technology, Berlin: Springer-Verlag, 1982,vol. 17a.
  2. P. Gay-Balmaz and J. R. Morsig, "3D planar radiating structures in stratified media", Int. J. Microwave Millimeter Wave CAE, vol. 3, pp.  330-343, 1997.
  3. E. M. Purcell and C. R. Pennypacker, "Scattering and absorption of light by nonspherical dielectric grains", Astrophys. J., vol. 186, pp.  705-714,  1973.
  4. O. J. F. Martin and N. B. Piller, "Electromagnetic scattering in polarizable backgrounds", Phys. Rev. E, vol. 58, no. 3, pp.  3909-3915, 1998.
  5. M. F. Iskander, H. Y. Chen and J. E. Penner, "Optical scattering and absorption by branched chains of aerosols", Appl. Opt., vol. 28, no.  15, pp.  3083-3091, 1989.
  6. C. E. Dungey and C. F. Bohren, "Light scattering by nonspherical particles: A refinement to the coupled-dipole method", J. Opt. Soc. Amer. A, vol. 8, no. 1, pp.  81-87, 1991.
  7. N. B. Piller and O. J. F. Martin, "Increasing the performances of the coupled-dipole approximation: A spectral approach", IEEE Trans. Antennas Propagat., vol. 46, pp.  1126-1137, Aug.  1998.
  8. B. T. Draine and P. J. Flatau, "Discrete-dipole approximation for scattering calculations", J. Opt. Soc. Amer. A, vol. 11, no. 4, pp.  1491-1499, 1994.
  9. J. H. Richmond, "A wire grid model for scattering by conducting bodies", IEEE Trans. Antennas Propagat., vol. 14, pp.  782-786, June  1966.
  10. D. H. Schaubert, D. R. Wilton and A. W. Glisson, "A tetrahedral modeling method for electromagnetic scattering by arbitrarily shaped inhomogeneous dielectric bodies", IEEE Trans. Antennas Propagat., vol. AP-32, pp.  77-85,  1984.
  11. P. P. Silvester and R. L. Ferrari, Finite Elements for Electrical Engineers, 2nd ed.   Cambridge: U.K.: Cambridge Univ. Press, 1990.
  12. R. D. Graglia, "The use of parametric elements in the moment method solution of static and dynamic volume integral equations", IEEE Trans. Antennas Propagat., vol. 36, pp.  636-646, May  1988.
  13. J. L. Volakis, A. Chatterjee and L. C. Kempel, "Review of the finite-element method for three-dimensional electromagnetic scattering", J. Opt. Soc. Amer. A, vol. 11, no. 4, pp.  1422-1433, 1994.
  14. D. R. Wilton, "Review of current status and trends in the use of integral equations in computational electromagnetics", Electromagnetics , vol. 12, pp.  287-341, 1992.
  15. A. D. Yaghjian, "Electric dyadic Green's functions in the source region", Proc. IEEE, vol. 68, pp.  248-263, 1980.
  16. C.-T. Tai, Dyadic Green Function in Electromagnetic Theory, New York: IEEE Press, 1994.
  17. A. P. Papagiannakis, "Application of a point-matching mom reduced scheme to scattering from finite cylinders", IEEE Trans. Microwave Theory Tech., vol. 45, pp.  1545-1553, Sept.  1997.
  18. C.-T. Tsai, H. Massoudi, C. H. Durney and M. F. Iskander, "A procedure for calculating fields inside arbitrarily shaped, inhomogeneous dielectric bodies using linear basis functions with the moment method", IEEE Trans. Microwave Theory Tech., vol. 34, pp.  1131-1138, Nov.  1986.
  19. A. P. M. Zwamborn and P. M. van den Berg, "The three-dimensional weak form of the conjugate gradient FFT method for solving scattering problems", IEEE Trans. Microwave Theory Tech., vol. 40, pp.  1757-1766, Sept.  1992.
  20. M. F. Catedra, E. Gago and L. Nuño, "A numerical scheme to obtain the RCS of three-dimensional bodies of resonant size using the conjugate gradient method and the fast fourier transform", IEEE Trans. Antennas Propagat., vol. 37, pp.  528-537, May  1989.
  21. H. Gan and W. C. Chew, "A discrete BCG-FFT algorithm for solving 3-D inhomogeneous scatterer problems", J. Electromagn. Waves Applicat., vol. 9, no. 10, 1995.
  22. Y. A. Eremin and V. I. Ivakhnenko, "Modeling of light scattering by nonspherical inhomogeneous particles", J. Quant. Spectrosc. Radiat. Transfer, vol. 60, no. 3, pp.  1-8, 1998.
  23. T. K. Sarkar, S. M. Rao and A. R. Djordjevic, "Electromagnetic scattering and radiation from finite microstrip structures", IEEE Trans. Microwave Theory Tech., vol. 38, pp.  1568-1575, Nov.  1990.
  24. D. A. Vechinski, S. M. Rao and T. K. Sarkar, "Transient scattering from three-dimensional arbitrarily shaped dielectric bodies", J. Opt. Soc. Amer. A, vol. 11, no. 4, pp.  1458-1469, 1994.
  25. L. Mendes and E. Arvas, "TE-scattering from dense homogeneous infinite dielectric cylinders of arbitrary cross-section", IEEE Trans. Magn. , vol. 27, pp.  4295-4298, May  1991.
  26. S.-W. Lee, J. B. Boersma, C.-L. Law and G. A. Deschamps, "Singularity in Green's function and its numerical evaluation", IEEE Trans. Antennas Propagat., vol. 28, pp.  311-317, Mar.  1980.
  27. D. R. Wilton and C. M. Butler, "Effective methods for solving integral and integro-differential equations", Electromagnetics, vol. 1, no.  3, pp.  289-308, 1981.
  28. S. A. Jenkins and J. R. Bowler, "Numerical evaluation of singular matrix elements in three dimensions", IEEE Trans. Magn., vol. 27, pp.  4438-4444,  June  1991.
  29. J. Rejeb, T. Sarkar and E. Arvas, "Extension of the MoM Laplacian solution to the general Helmholtz equation", IEEE Trans. Microwave Theory Tech., vol. 43, pp.  2579-2584, Nov.  1995.
  30. O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method, London: McGraw-Hill, 1967.
  31. I. M. Gel'fand and G. E. Shirkov, Generalized Functions, New York: Academic, 1964.
  32. K. W. Morton, "Basic course in finite element methods", Comput. Phys. Rep., vol. 6, pp.  1-72, 1987.
  33. G. R. Cowper, "Gaussian quadrature formulas for triangles", Int. J. Numer. Methods Eng., vol. 7, no. 3, pp.  405 -408,  1973.
  34. P. Hillion, "Numerical integration on a triangle", Int. J. Numer. Methods Eng., vol. 11, pp.  797-815, 1977.
  35. K. S. Sunder and R. A. Cookson, "Integration points for triangles and tetrahedrons obtained from the Gaussian quadrature points for a line", Comput. Struct., vol. 21, no. 5, pp.  881-885, 1985.
  36. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles, New York: Wiley, 1983.