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 4, April 2000

Table of Contents for this issue

Complete paper in PDF format

Analysis of Transient Electromagnetic Scattering Phenomena Using a Two-Level Plane Wave Time-Domain Algorithm

Balasubramaniam Shanker, Member, IEEE A. Arif Ergin, Student Member, IEEE Kemal Aygün, Student Member, IEEE and Eric Michielssen Senior Member, IEEE

Page 510.

Abstract:

A fast algorithm is presented for solving electric, magnetic,and combined field time-domain integral equations pertinent to the analysis of surface scattering phenomena. The proposed two-level plane wave time-domain (PWTD) algorithm permits a numerically rigorous reconstruction of transient near fields from their far-field expansion and augments classical marching-on in-time (MOT) based solvers. The computational cost of analyzing surface scattering phenomena using PWTD-enhanced MOT schemes scales as O(NtNs3/2 log Ns) as opposed to O(NtNs2) for classical MOT methods, where Nt and Ns are the numbers of temporal and spatial basis functions discretizing the scatterer current. Numerical results that demonstrate the efficacy of the proposed solver in analyzing transient scattering from electrically large structures and that confirm the above complexity estimate are presented.

References

  1. A. Taflove, Computational Electrodynamics: The Finite Difference Time Domain Method, Boston, MA: Artech House, 1995.
  2. K. S. Kunz and R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics, Boca Raton, FL: CRC, 1993 .
  3. C. L. Bennet, "A technique for computing approximate impulse response for conducting bodies", Ph.D. Thesis, Purdue Univ., West Lafayette, IN, 1968.
  4. A. J. Poggio and E. K. Miller, Computer Techniques for Electromagnetics, Oxford: U.K.: Pergamon, 1973, ch. 4.
  5. R. Mittra, Transient Electromagnetic Fields , New York: Springer-Verlag, 1976, ch. 2.
  6. B. P. Rynne and P. D. Smith, "Stability of time marching algorthms for the electric field integral equations", J. Electromagn. Waves Applicat., vol. 12, pp.  1181-1205, 1990.
  7. E. K. Miller, "A selective survey of computational electromagnetics", IEEE Trans. Antennas Propagat., vol. 36, pp.  1281-1305, Sept.  1988.
  8. A. G. Tijhuis, Electromagnetic Inverse Profiling, Utrecht, The Netherlands: VNU Sci., 1987.
  9. D. A. Vechinski and S. M. Rao, "A stable procedure to calculate the transient scattering by conducting surfaces of arbitrary shape", IEEE Trans. Antennas Propagat., vol. 40, pp.  661-665, June  1992.
  10. B. P. Rynne, "Stability and convergence of time marching methods in scattering problems", Int. J. Appl. Math., vol. 35, pp.  297-310, 1985.
  11. W. Pinello, A. Ruehli and A. Cangellaris, "Stabilization of time domain solutions of the efie based on the partial element equivalent circuit models", in Proc. IEEE Antennas Propagat. Soc. Int. Symp., vol. 3, Montreal, Canada, July 1997, pp.  966-969. 
  12. M. J. Bluck and S. P. Walker, "Time-domain BIE analysis of large three dimensional electromagnetic scattering problems", IEEE Trans. Antennas Propagat., vol. 45, pp.  894-901,  May  1997.
  13. S. Dodson, S. P. Walker and M. J. Bluck, "Implicitness and stability of time domain integral equation scattering analysis", Appl. Comp. Electromagn. Soc. J., vol. 13, no. 3, pp.  291-301, 1998.
  14. S. P. Walker, "Scattering analysis via time-domain integral equations: Methods to reduce the scaling of cost with frequency", IEEE Antennas Propagat. Mag., vol.  39, pp.  13-20, Oct.  1997.
  15. 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.
  16. 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 .
  17. A. A. Ergin, B. Shanker and E. Michielssen, "Fast evaluation of transient wave fields using diagonal translation operators", J. Comp. Phys., vol. 146, pp.  157-180, 1998.
  18. A. A. Ergin, B. Shanker and E. Michielssen, "Fast transient analysis of acoustic wave scattering from rigid bodies using a two-level plane wave time domain algorithm", J. Acoust. Soc. Amer., vol. 106, pp.  2405-2416, 1999.
  19. J. R. Mautz and R. F. Harrington, "H -field, e -field and combined field solutions for conducting bodies of revolution", AEÜ, vol. 32, pp.  157-164, 1978.
  20. B. Shanker, A. A. Ergin, K. Agyün and E. Michielssen, "Analysis of transient electromagnetic scattering from closed surfaces using the combined field integral equation", IEEE Trans. Antennas Propagat.,
  21. D. S. Jones, Methods in Electromagnetic Wave Propagation, Oxford: U.K.: Oxford Sci., 1994.
  22. S. M. Rao and D. R. Wilton, "Transient scattering by conducting surfaces of arbitrary shape", IEEE Trans. Antennas Propagat., vol.  39, pp.  56-61, 1991.
  23. 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.  408-418, May  1982.
  24. P. D. Smith, "Instabilities in time marching methods for scattering: Cause and rectification", Electromagn., vol. 10, pp.  439-451, 1990.
  25. G. Manara, A. Monorchio and R. Reggiannini, "A space-time discretization criterion for a stable time-marching solution of the electric field integral equation", IEEE Trans. Antennas Propagat., vol. 45, pp.  527-532, Mar.  1997.
  26. Y. Saad, Iterative Methods for Sparse Linear Systems, New York: PWS, 1996.
  27. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, New York: Dover, 1972.
  28. M. Tygel and P. Hubral, Transient Waves in Layered Media, Amsterdam: The Netherlands: Elsevier, 1987.
  29. E. Heyman, "Time-depenent plane-wave spectrum representations for radiation from volume source distributions", J. Math. Phys., vol. 37, pp.  658-681, 1996.
  30. J. J. Knab, "Interpolation of bandlimited functions using the approximate prolate series", IEEE Trans. Inform. Theory, vol. IT-25, pp.  717-720, Nov.  1979.
  31. O. M. Bucci and G. Franceschitti, "On the spatial bandwidth of scattered fields", IEEE Trans. Antennas Propagat., vol. AP-35, pp.  1445-1455, Dec.  1987.
  32. O. M. Bucci, C. Gennarelli and C. Savarse, "Optimal interpolation of radiated fields over a sphere", IEEE Trans. Antennas Propagat., vol. 39, pp.  1633-1643,  Nov.  1991.
  33. A. A. Ergin, B. Shanker and E. Michielssen, "The plane wave time domain algorithm for the fast analysis of transient wave phenomena", IEEE Antennas Propag. Mag., vol. 41, pp.  39-52, Aug.  1999.
  34. W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, Numerical Recipies in Fortran 77, Cambridge: U.K.: Cambridge Univ. Press, 1992.
  35. A. C. Woo, H. T. G. Wang, M. J. Schuh and M. L. Sanders, "Benchmark radar targets for the validation of computational electromagnetics programs", IEEE Antennas Propagat. Mag., vol.  35, pp.  84-89, Aug.  1993.