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 11, November 1998

Table of Contents for this issue

Complete paper in PDF format

Solution of Combined-Field Integral Equation Using Multilevel Fast Multipole Algorithm for Scattering by Homogeneous Bodies

Xing Qing Sheng, Jian-Ming Jin, Senior Member, IEEE, Jiming Song, Member, IEEE, Weng Cho Chew, Fellow, IEEE, and Cai-Cheng Lu, Member, IEEE

Page 1718.

Abstract:

In this paper, we present an accurate method of moments (MoM) solution of the combined field integral equation (CFIE) using the multilevel fast multipole algorithm (MLFMA) for scattering by large, three-dimensional (3-D), arbitrarily shaped, homogeneous objects. We first investigate several different MoM formulations of CFIE and propose a new formulation, which is both accurate and free of interior resonances. We then employ MLFMA to significantly reduce the memory requirement and computational complexity of the MoM solution. Numerical results are presented to demonstrate the accuracy and capability of the proposed method. The method can be extended in a straightforward manner to scatterers composed of different homogeneous dielectric and conducting objects.

References

  1. A. J. Poggio and E. K. Miller, "Integral equation solutions of three dimensional scattering problems," in Computer Techniques for Electromagnetics.Oxford, U.K.: Permagon, 1973, chap. 4.
  2. J. R. Mautz and R. F. Harrington, "Electromagnetic scattering from a homogeneous material body of revolution," AEU, vol. 33, pp. 71-80, Feb. 1979.
  3. R. F. Harrington, "Boundary integral formulations for homogeneous material bodies," J. Electromagn. Waves Applicat., vol. 3, no. 1, pp. 1-15, 1989.
  4. J. R. Mautz and R. F. Harrington, "H-field, E-field, and combined-field solutions for conducting body of revolution," AEU, vol. 32, pp. 157-164, Apr. 1978.
  5. S. M. Rao and D. R. Wilton, "E-field, H-field, and combined field solution for arbitrarily shaped three-dimensional dielectric bodies," Electromagn., vol. 10, no. 4, pp. 407-421, 1990.
  6. 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.
  7. K. R. Umashankar, A. Taflove, and S. M. Rao, "Electromagnetic scattering by arbitrary shaped three-dimensional homogeneous lossy dielectric objects," IEEE Trans. Antennas Propagat., vol. AP-34, pp. 758-766, June 1986.
  8. S. M. Rao, C. C. Cha, R. L. Cravey, and D. Wilkes, "Electromagnetic scattering from arbitrary shaped conducting bodies coated with lossy materials of arbitrary thickness," IEEE Trans. Antennas Propagat., vol. 39, pp. 627-631, May 1991.
  9. L. N. Medgyesi-Mitschang, J. M. Putnam, and M. B. Gedera, "Generalized method of moments for three-dimensional penetrable scatterers," J. Opt. Soc. Amer. A, vol. 11, no. 4, pp. 1383-1398, Apr. 1994.
  10. Y. Chang and R. F. Harrington, "A surface formulation for characteristic modes of material bodies," IEEE Trans. Antennas Propagat., vol. AP-25, pp. 789-795, 1977.
  11. T. K. Wu and L. L. Tsai, "Scattering from arbitrarily-shaped lossy dielectric bodies of revolution," Radio Sci., vol. 12, pp. 709-718, 1977.
  12. J. M. Jin, The Finite Element Method in Electromagnetics.New York: Wiley, 1993.
  13. V. Rokhlin, "Rapid solution of integral equations of scattering theory in two dimensions," J. Comput. Phys., vol. 86, pp. 414-439, Feb. 1990.
  14. R. Coifman, V. Rokhlin, and S. Wandzura, "The fast multipole method for the wave equation: A pedestrian prescription," IEEE Antennas Propagat. Mag., vol. 35, pp. 7-12, June 1993.
  15. C. C. Lu and W. C. Chew, "A multilevel algorithm for solving boundary integral equations of wave scattering," Microwave Opt. Tech. Lett., vol. 7, no. 10, pp. 466-470, July 1994.
  16. J. M. Song and W. C. Chew, "Multilevel fast-multipole algorithm for solving combined field integral equations of electromagnetic scattering," Microwave Opt. Tech. Lett., vol. 10, no. 1, pp. 14-19, Sept. 1995.
  17. B. Dembart and E. Yip, "A 3-D fast multipole method for electromagnetics with multiple levels," 11th Ann. Rev. Progress Appl. Computat. Electromagn., pp. 621-628, Mar. 1995.
  18. J. M. Song, C. C. Lu, and W. C. Chew, "MLFMA for electromagnetic scattering by large complex objects," IEEE Trans. Antennas Propagat., vol. 45, pp. 1488-1493, Oct. 1997.