Abstract

A novel and fast integral-equation-based scheme is presented for analyzing transient electromagnetic scattering from homogeneous, isotropic, and nondispersive bodies. The computational complexity of classical marching-on-in-time (MOT) methods for solving time-domain integral equations governing electromagnetic scattering phenomena involving homogeneous penetrable bodies scales as O(NtNs2). Here, Nt represents the number of time steps in the analysis, and Ns denotes the number of spatial degrees of freedom of the discretized electric and magnetic currents on the body’s surface. In contrast, the computational complexity of the proposed plane-wave–time-domain-enhanced MOT solver scales as O(NtNs log2 Ns). Numerical results that demonstrate the accuracy and the efficacy of the scheme are presented.

© 2002 Optical Society of America

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  1. A. Shlivinski, E. Heyman, R. Kastner, “Antenna characterization in the time domain,” IEEE Trans. Antennas Propag. 45, 1140–1149 (1997).
    [CrossRef]
  2. W. R. Stone, Radar Cross Sections of Complex Objects (Institute of Electrical and Electronics Engineers, New York, 1990).
  3. E. G. Loewen, E. Popov, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997).
  4. A. A. Ergin, B. Shanker, E. Michielssen, “The plane wave time domain algorithm for the fast analysis of transient wave phenomena,” IEEE Antennas Propag. Mag. 41, 39–52 (1999).
    [CrossRef]
  5. A. A. Ergin, B. Shanker, E. Michielssen, “Fast evaluation of three-dimensional transient wave fields using diagonal translation operators,” J. Comput. Phys. 146, 157–180 (1998).
    [CrossRef]
  6. R. Coifman, V. Rokhlin, S. Wandzura, “The fast multipole method for the wave equation: a pedestrian prescription,” IEEE Antennas Propag. Mag. 35, 7–12 (1993).
    [CrossRef]
  7. B. Shanker, A. A. Ergin, E. Michielssen, “The multilevel plane wave time domain algorithm for the fast analysis of transient scattering phenomena,” in Proceedings of the IEEE International Symposium on Antennas and Propagation (Institute of Electrical and Electronics Engineers, New York, 1999), Vol. 2, pp. 1342–1345.
  8. B. Shanker, A. A. Ergin, K. Aygun, E. Michielssen, “Analysis of transient electromagnetic scattering phenomena using a two-level plane wave time domain algorithm,” IEEE Trans. Antennas Propag. 48, 510–523 (2000).
    [CrossRef]
  9. A. A. Ergin, B. Shanker, E. Michielssen, “Fast transient analysis of acoustic wave scattering from rigid bodies using two-level plane wave time domain algorithm,” J. Acoust. Soc. Am. 106, 2405–2416 (1999).
    [CrossRef]
  10. A. A. Ergin, B. Shanker, E. Michielssen, “Fast analysis of transient acoustic wave scattering from rigid bodies using the multilevel plane wave time domain algorithm,” J. Acoust. Soc. Am. 107, 1168–1178 (2000).
    [CrossRef] [PubMed]
  11. S. M. Rao, D. R. Wilton, “Transient scattering by conducting surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. 39, 56–61 (1991).
    [CrossRef]
  12. S. M. Rao, T. K. Sarkar, “An efficient method to evaluate the time-domain scattering from arbitrarily shaped conducting bodies,” Microwave Opt. Technol. Lett. 17, 321–325 (1998).
    [CrossRef]
  13. H. Mieras, C. L. Bennet, “Space–time integral equation approach to dielectric targets,” IEEE Trans. Antennas Propag. AP-30, 2–9 (1982).
    [CrossRef]
  14. C. Müller, Foundations of the Mathematical Theory of Electromagnetic Waves (Springer-Verlag, Berlin, 1969).
  15. E. Schlemmer, W. M. Rucker, K. R. Richter, “Boundary element computations of 3D scattering from lossy dielectric objects,” IEEE Trans. Magn. 29, 1524–1527 (1993).
    [CrossRef]
  16. B. P. Rynne, “Time domain scattering from dielectric bodies,” Electromagnetics 14, 181–193 (1994).
    [CrossRef]
  17. D. A. Vechinski, S. M. Rao, T. K. Sarkar, “Transient scattering from three dimensional arbitrarily shaped dielectric bodies,” J. Opt. Soc. Am. A 11, 1458–1470 (1994).
    [CrossRef]
  18. M. D. Pocock, M. J. Bluck, S. P. Walker, “Electromagnetic scattering from 3-D curved dielectric bodies using time-domain integral equations,” IEEE Trans. Antennas Propag. 46, 1212–1219 (1998).
    [CrossRef]
  19. R. F. Harrington, “Boundary integral formulations for homogeneous material bodies,” J. Electromagn. Waves Appl. 3, 1–15 (1989).
    [CrossRef]
  20. S. M. Rao, D. R. Wilton, A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. AP-30, 408–418 (1982).
  21. Y. Saad, Iterative Methods for Sparse Linear Systems (PWS, New York, 1996).
  22. R. W. Freund, “A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems,” SIAM (Soc. Ind. Appl. Math.) J. Sci. Comput. 14, 470–482 (1993).
    [CrossRef]
  23. M. Tygel, P. Hubral, Transient Waves in Layered Media (Elsevier, Amsterdam, 1987), Vol. 26.
  24. O. M. Bucci, G. Franceschetti, “On the spatial bandwidth of scattered fields,” IEEE Trans. Antennas Propag. AP-35, 1445–1455 (1987).
    [CrossRef]
  25. O. M. Bucci, C. Gennarelli, C. Savarese, “Optimal interpolation of radiated fields over a sphere,” IEEE Trans. Antennas Propag. 39, 1633–1643 (1991).
    [CrossRef]
  26. J. J. Knab, “Interpolation of band-limited functions using the approximate prolate series,” IEEE Trans. Inf. Theory IT-25, 717–720 (1979).
    [CrossRef]
  27. R. Jakob-Chien, B. K. Alpert, “A fast spherical filter with uniform resolution,” J. Comput. Phys. 136, 580–584 (1997).
    [CrossRef]
  28. A. C. Woo, H. T. G. Wang, M. J. Schuh, M. L. Sanders, “Benchmark radar targets for the validation of computational electromagnetics programs,” IEEE Antennas Propag. Mag. 35, 84–89 (1993).
    [CrossRef]

2000 (2)

B. Shanker, A. A. Ergin, K. Aygun, E. Michielssen, “Analysis of transient electromagnetic scattering phenomena using a two-level plane wave time domain algorithm,” IEEE Trans. Antennas Propag. 48, 510–523 (2000).
[CrossRef]

A. A. Ergin, B. Shanker, E. Michielssen, “Fast analysis of transient acoustic wave scattering from rigid bodies using the multilevel plane wave time domain algorithm,” J. Acoust. Soc. Am. 107, 1168–1178 (2000).
[CrossRef] [PubMed]

1999 (2)

A. A. Ergin, B. Shanker, E. Michielssen, “Fast transient analysis of acoustic wave scattering from rigid bodies using two-level plane wave time domain algorithm,” J. Acoust. Soc. Am. 106, 2405–2416 (1999).
[CrossRef]

A. A. Ergin, B. Shanker, E. Michielssen, “The plane wave time domain algorithm for the fast analysis of transient wave phenomena,” IEEE Antennas Propag. Mag. 41, 39–52 (1999).
[CrossRef]

1998 (3)

A. A. Ergin, B. Shanker, E. Michielssen, “Fast evaluation of three-dimensional transient wave fields using diagonal translation operators,” J. Comput. Phys. 146, 157–180 (1998).
[CrossRef]

S. M. Rao, T. K. Sarkar, “An efficient method to evaluate the time-domain scattering from arbitrarily shaped conducting bodies,” Microwave Opt. Technol. Lett. 17, 321–325 (1998).
[CrossRef]

M. D. Pocock, M. J. Bluck, S. P. Walker, “Electromagnetic scattering from 3-D curved dielectric bodies using time-domain integral equations,” IEEE Trans. Antennas Propag. 46, 1212–1219 (1998).
[CrossRef]

1997 (2)

A. Shlivinski, E. Heyman, R. Kastner, “Antenna characterization in the time domain,” IEEE Trans. Antennas Propag. 45, 1140–1149 (1997).
[CrossRef]

R. Jakob-Chien, B. K. Alpert, “A fast spherical filter with uniform resolution,” J. Comput. Phys. 136, 580–584 (1997).
[CrossRef]

1994 (2)

1993 (4)

A. C. Woo, H. T. G. Wang, M. J. Schuh, M. L. Sanders, “Benchmark radar targets for the validation of computational electromagnetics programs,” IEEE Antennas Propag. Mag. 35, 84–89 (1993).
[CrossRef]

E. Schlemmer, W. M. Rucker, K. R. Richter, “Boundary element computations of 3D scattering from lossy dielectric objects,” IEEE Trans. Magn. 29, 1524–1527 (1993).
[CrossRef]

R. W. Freund, “A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems,” SIAM (Soc. Ind. Appl. Math.) J. Sci. Comput. 14, 470–482 (1993).
[CrossRef]

R. Coifman, V. Rokhlin, S. Wandzura, “The fast multipole method for the wave equation: a pedestrian prescription,” IEEE Antennas Propag. Mag. 35, 7–12 (1993).
[CrossRef]

1991 (2)

S. M. Rao, D. R. Wilton, “Transient scattering by conducting surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. 39, 56–61 (1991).
[CrossRef]

O. M. Bucci, C. Gennarelli, C. Savarese, “Optimal interpolation of radiated fields over a sphere,” IEEE Trans. Antennas Propag. 39, 1633–1643 (1991).
[CrossRef]

1989 (1)

R. F. Harrington, “Boundary integral formulations for homogeneous material bodies,” J. Electromagn. Waves Appl. 3, 1–15 (1989).
[CrossRef]

1987 (1)

O. M. Bucci, G. Franceschetti, “On the spatial bandwidth of scattered fields,” IEEE Trans. Antennas Propag. AP-35, 1445–1455 (1987).
[CrossRef]

1982 (2)

S. M. Rao, D. R. Wilton, A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. AP-30, 408–418 (1982).

H. Mieras, C. L. Bennet, “Space–time integral equation approach to dielectric targets,” IEEE Trans. Antennas Propag. AP-30, 2–9 (1982).
[CrossRef]

1979 (1)

J. J. Knab, “Interpolation of band-limited functions using the approximate prolate series,” IEEE Trans. Inf. Theory IT-25, 717–720 (1979).
[CrossRef]

Alpert, B. K.

R. Jakob-Chien, B. K. Alpert, “A fast spherical filter with uniform resolution,” J. Comput. Phys. 136, 580–584 (1997).
[CrossRef]

Aygun, K.

B. Shanker, A. A. Ergin, K. Aygun, E. Michielssen, “Analysis of transient electromagnetic scattering phenomena using a two-level plane wave time domain algorithm,” IEEE Trans. Antennas Propag. 48, 510–523 (2000).
[CrossRef]

Bennet, C. L.

H. Mieras, C. L. Bennet, “Space–time integral equation approach to dielectric targets,” IEEE Trans. Antennas Propag. AP-30, 2–9 (1982).
[CrossRef]

Bluck, M. J.

M. D. Pocock, M. J. Bluck, S. P. Walker, “Electromagnetic scattering from 3-D curved dielectric bodies using time-domain integral equations,” IEEE Trans. Antennas Propag. 46, 1212–1219 (1998).
[CrossRef]

Bucci, O. M.

O. M. Bucci, C. Gennarelli, C. Savarese, “Optimal interpolation of radiated fields over a sphere,” IEEE Trans. Antennas Propag. 39, 1633–1643 (1991).
[CrossRef]

O. M. Bucci, G. Franceschetti, “On the spatial bandwidth of scattered fields,” IEEE Trans. Antennas Propag. AP-35, 1445–1455 (1987).
[CrossRef]

Coifman, R.

R. Coifman, V. Rokhlin, S. Wandzura, “The fast multipole method for the wave equation: a pedestrian prescription,” IEEE Antennas Propag. Mag. 35, 7–12 (1993).
[CrossRef]

Ergin, A. A.

A. A. Ergin, B. Shanker, E. Michielssen, “Fast analysis of transient acoustic wave scattering from rigid bodies using the multilevel plane wave time domain algorithm,” J. Acoust. Soc. Am. 107, 1168–1178 (2000).
[CrossRef] [PubMed]

B. Shanker, A. A. Ergin, K. Aygun, E. Michielssen, “Analysis of transient electromagnetic scattering phenomena using a two-level plane wave time domain algorithm,” IEEE Trans. Antennas Propag. 48, 510–523 (2000).
[CrossRef]

A. A. Ergin, B. Shanker, E. Michielssen, “Fast transient analysis of acoustic wave scattering from rigid bodies using two-level plane wave time domain algorithm,” J. Acoust. Soc. Am. 106, 2405–2416 (1999).
[CrossRef]

A. A. Ergin, B. Shanker, E. Michielssen, “The plane wave time domain algorithm for the fast analysis of transient wave phenomena,” IEEE Antennas Propag. Mag. 41, 39–52 (1999).
[CrossRef]

A. A. Ergin, B. Shanker, E. Michielssen, “Fast evaluation of three-dimensional transient wave fields using diagonal translation operators,” J. Comput. Phys. 146, 157–180 (1998).
[CrossRef]

B. Shanker, A. A. Ergin, E. Michielssen, “The multilevel plane wave time domain algorithm for the fast analysis of transient scattering phenomena,” in Proceedings of the IEEE International Symposium on Antennas and Propagation (Institute of Electrical and Electronics Engineers, New York, 1999), Vol. 2, pp. 1342–1345.

Franceschetti, G.

O. M. Bucci, G. Franceschetti, “On the spatial bandwidth of scattered fields,” IEEE Trans. Antennas Propag. AP-35, 1445–1455 (1987).
[CrossRef]

Freund, R. W.

R. W. Freund, “A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems,” SIAM (Soc. Ind. Appl. Math.) J. Sci. Comput. 14, 470–482 (1993).
[CrossRef]

Gennarelli, C.

O. M. Bucci, C. Gennarelli, C. Savarese, “Optimal interpolation of radiated fields over a sphere,” IEEE Trans. Antennas Propag. 39, 1633–1643 (1991).
[CrossRef]

Glisson, A. W.

S. M. Rao, D. R. Wilton, A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. AP-30, 408–418 (1982).

Harrington, R. F.

R. F. Harrington, “Boundary integral formulations for homogeneous material bodies,” J. Electromagn. Waves Appl. 3, 1–15 (1989).
[CrossRef]

Heyman, E.

A. Shlivinski, E. Heyman, R. Kastner, “Antenna characterization in the time domain,” IEEE Trans. Antennas Propag. 45, 1140–1149 (1997).
[CrossRef]

Hubral, P.

M. Tygel, P. Hubral, Transient Waves in Layered Media (Elsevier, Amsterdam, 1987), Vol. 26.

Jakob-Chien, R.

R. Jakob-Chien, B. K. Alpert, “A fast spherical filter with uniform resolution,” J. Comput. Phys. 136, 580–584 (1997).
[CrossRef]

Kastner, R.

A. Shlivinski, E. Heyman, R. Kastner, “Antenna characterization in the time domain,” IEEE Trans. Antennas Propag. 45, 1140–1149 (1997).
[CrossRef]

Knab, J. J.

J. J. Knab, “Interpolation of band-limited functions using the approximate prolate series,” IEEE Trans. Inf. Theory IT-25, 717–720 (1979).
[CrossRef]

Loewen, E. G.

E. G. Loewen, E. Popov, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997).

Michielssen, E.

B. Shanker, A. A. Ergin, K. Aygun, E. Michielssen, “Analysis of transient electromagnetic scattering phenomena using a two-level plane wave time domain algorithm,” IEEE Trans. Antennas Propag. 48, 510–523 (2000).
[CrossRef]

A. A. Ergin, B. Shanker, E. Michielssen, “Fast analysis of transient acoustic wave scattering from rigid bodies using the multilevel plane wave time domain algorithm,” J. Acoust. Soc. Am. 107, 1168–1178 (2000).
[CrossRef] [PubMed]

A. A. Ergin, B. Shanker, E. Michielssen, “Fast transient analysis of acoustic wave scattering from rigid bodies using two-level plane wave time domain algorithm,” J. Acoust. Soc. Am. 106, 2405–2416 (1999).
[CrossRef]

A. A. Ergin, B. Shanker, E. Michielssen, “The plane wave time domain algorithm for the fast analysis of transient wave phenomena,” IEEE Antennas Propag. Mag. 41, 39–52 (1999).
[CrossRef]

A. A. Ergin, B. Shanker, E. Michielssen, “Fast evaluation of three-dimensional transient wave fields using diagonal translation operators,” J. Comput. Phys. 146, 157–180 (1998).
[CrossRef]

B. Shanker, A. A. Ergin, E. Michielssen, “The multilevel plane wave time domain algorithm for the fast analysis of transient scattering phenomena,” in Proceedings of the IEEE International Symposium on Antennas and Propagation (Institute of Electrical and Electronics Engineers, New York, 1999), Vol. 2, pp. 1342–1345.

Mieras, H.

H. Mieras, C. L. Bennet, “Space–time integral equation approach to dielectric targets,” IEEE Trans. Antennas Propag. AP-30, 2–9 (1982).
[CrossRef]

Müller, C.

C. Müller, Foundations of the Mathematical Theory of Electromagnetic Waves (Springer-Verlag, Berlin, 1969).

Pocock, M. D.

M. D. Pocock, M. J. Bluck, S. P. Walker, “Electromagnetic scattering from 3-D curved dielectric bodies using time-domain integral equations,” IEEE Trans. Antennas Propag. 46, 1212–1219 (1998).
[CrossRef]

Popov, E.

E. G. Loewen, E. Popov, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997).

Rao, S. M.

S. M. Rao, T. K. Sarkar, “An efficient method to evaluate the time-domain scattering from arbitrarily shaped conducting bodies,” Microwave Opt. Technol. Lett. 17, 321–325 (1998).
[CrossRef]

D. A. Vechinski, S. M. Rao, T. K. Sarkar, “Transient scattering from three dimensional arbitrarily shaped dielectric bodies,” J. Opt. Soc. Am. A 11, 1458–1470 (1994).
[CrossRef]

S. M. Rao, D. R. Wilton, “Transient scattering by conducting surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. 39, 56–61 (1991).
[CrossRef]

S. M. Rao, D. R. Wilton, A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. AP-30, 408–418 (1982).

Richter, K. R.

E. Schlemmer, W. M. Rucker, K. R. Richter, “Boundary element computations of 3D scattering from lossy dielectric objects,” IEEE Trans. Magn. 29, 1524–1527 (1993).
[CrossRef]

Rokhlin, V.

R. Coifman, V. Rokhlin, S. Wandzura, “The fast multipole method for the wave equation: a pedestrian prescription,” IEEE Antennas Propag. Mag. 35, 7–12 (1993).
[CrossRef]

Rucker, W. M.

E. Schlemmer, W. M. Rucker, K. R. Richter, “Boundary element computations of 3D scattering from lossy dielectric objects,” IEEE Trans. Magn. 29, 1524–1527 (1993).
[CrossRef]

Rynne, B. P.

B. P. Rynne, “Time domain scattering from dielectric bodies,” Electromagnetics 14, 181–193 (1994).
[CrossRef]

Saad, Y.

Y. Saad, Iterative Methods for Sparse Linear Systems (PWS, New York, 1996).

Sanders, M. L.

A. C. Woo, H. T. G. Wang, M. J. Schuh, M. L. Sanders, “Benchmark radar targets for the validation of computational electromagnetics programs,” IEEE Antennas Propag. Mag. 35, 84–89 (1993).
[CrossRef]

Sarkar, T. K.

S. M. Rao, T. K. Sarkar, “An efficient method to evaluate the time-domain scattering from arbitrarily shaped conducting bodies,” Microwave Opt. Technol. Lett. 17, 321–325 (1998).
[CrossRef]

D. A. Vechinski, S. M. Rao, T. K. Sarkar, “Transient scattering from three dimensional arbitrarily shaped dielectric bodies,” J. Opt. Soc. Am. A 11, 1458–1470 (1994).
[CrossRef]

Savarese, C.

O. M. Bucci, C. Gennarelli, C. Savarese, “Optimal interpolation of radiated fields over a sphere,” IEEE Trans. Antennas Propag. 39, 1633–1643 (1991).
[CrossRef]

Schlemmer, E.

E. Schlemmer, W. M. Rucker, K. R. Richter, “Boundary element computations of 3D scattering from lossy dielectric objects,” IEEE Trans. Magn. 29, 1524–1527 (1993).
[CrossRef]

Schuh, M. J.

A. C. Woo, H. T. G. Wang, M. J. Schuh, M. L. Sanders, “Benchmark radar targets for the validation of computational electromagnetics programs,” IEEE Antennas Propag. Mag. 35, 84–89 (1993).
[CrossRef]

Shanker, B.

A. A. Ergin, B. Shanker, E. Michielssen, “Fast analysis of transient acoustic wave scattering from rigid bodies using the multilevel plane wave time domain algorithm,” J. Acoust. Soc. Am. 107, 1168–1178 (2000).
[CrossRef] [PubMed]

B. Shanker, A. A. Ergin, K. Aygun, E. Michielssen, “Analysis of transient electromagnetic scattering phenomena using a two-level plane wave time domain algorithm,” IEEE Trans. Antennas Propag. 48, 510–523 (2000).
[CrossRef]

A. A. Ergin, B. Shanker, E. Michielssen, “Fast transient analysis of acoustic wave scattering from rigid bodies using two-level plane wave time domain algorithm,” J. Acoust. Soc. Am. 106, 2405–2416 (1999).
[CrossRef]

A. A. Ergin, B. Shanker, E. Michielssen, “The plane wave time domain algorithm for the fast analysis of transient wave phenomena,” IEEE Antennas Propag. Mag. 41, 39–52 (1999).
[CrossRef]

A. A. Ergin, B. Shanker, E. Michielssen, “Fast evaluation of three-dimensional transient wave fields using diagonal translation operators,” J. Comput. Phys. 146, 157–180 (1998).
[CrossRef]

B. Shanker, A. A. Ergin, E. Michielssen, “The multilevel plane wave time domain algorithm for the fast analysis of transient scattering phenomena,” in Proceedings of the IEEE International Symposium on Antennas and Propagation (Institute of Electrical and Electronics Engineers, New York, 1999), Vol. 2, pp. 1342–1345.

Shlivinski, A.

A. Shlivinski, E. Heyman, R. Kastner, “Antenna characterization in the time domain,” IEEE Trans. Antennas Propag. 45, 1140–1149 (1997).
[CrossRef]

Stone, W. R.

W. R. Stone, Radar Cross Sections of Complex Objects (Institute of Electrical and Electronics Engineers, New York, 1990).

Tygel, M.

M. Tygel, P. Hubral, Transient Waves in Layered Media (Elsevier, Amsterdam, 1987), Vol. 26.

Vechinski, D. A.

Walker, S. P.

M. D. Pocock, M. J. Bluck, S. P. Walker, “Electromagnetic scattering from 3-D curved dielectric bodies using time-domain integral equations,” IEEE Trans. Antennas Propag. 46, 1212–1219 (1998).
[CrossRef]

Wandzura, S.

R. Coifman, V. Rokhlin, S. Wandzura, “The fast multipole method for the wave equation: a pedestrian prescription,” IEEE Antennas Propag. Mag. 35, 7–12 (1993).
[CrossRef]

Wang, H. T. G.

A. C. Woo, H. T. G. Wang, M. J. Schuh, M. L. Sanders, “Benchmark radar targets for the validation of computational electromagnetics programs,” IEEE Antennas Propag. Mag. 35, 84–89 (1993).
[CrossRef]

Wilton, D. R.

S. M. Rao, D. R. Wilton, “Transient scattering by conducting surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. 39, 56–61 (1991).
[CrossRef]

S. M. Rao, D. R. Wilton, A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. AP-30, 408–418 (1982).

Woo, A. C.

A. C. Woo, H. T. G. Wang, M. J. Schuh, M. L. Sanders, “Benchmark radar targets for the validation of computational electromagnetics programs,” IEEE Antennas Propag. Mag. 35, 84–89 (1993).
[CrossRef]

Electromagnetics (1)

B. P. Rynne, “Time domain scattering from dielectric bodies,” Electromagnetics 14, 181–193 (1994).
[CrossRef]

IEEE Antennas Propag. Mag. (3)

A. A. Ergin, B. Shanker, E. Michielssen, “The plane wave time domain algorithm for the fast analysis of transient wave phenomena,” IEEE Antennas Propag. Mag. 41, 39–52 (1999).
[CrossRef]

R. Coifman, V. Rokhlin, S. Wandzura, “The fast multipole method for the wave equation: a pedestrian prescription,” IEEE Antennas Propag. Mag. 35, 7–12 (1993).
[CrossRef]

A. C. Woo, H. T. G. Wang, M. J. Schuh, M. L. Sanders, “Benchmark radar targets for the validation of computational electromagnetics programs,” IEEE Antennas Propag. Mag. 35, 84–89 (1993).
[CrossRef]

IEEE Trans. Antennas Propag. (8)

O. M. Bucci, G. Franceschetti, “On the spatial bandwidth of scattered fields,” IEEE Trans. Antennas Propag. AP-35, 1445–1455 (1987).
[CrossRef]

O. M. Bucci, C. Gennarelli, C. Savarese, “Optimal interpolation of radiated fields over a sphere,” IEEE Trans. Antennas Propag. 39, 1633–1643 (1991).
[CrossRef]

B. Shanker, A. A. Ergin, K. Aygun, E. Michielssen, “Analysis of transient electromagnetic scattering phenomena using a two-level plane wave time domain algorithm,” IEEE Trans. Antennas Propag. 48, 510–523 (2000).
[CrossRef]

A. Shlivinski, E. Heyman, R. Kastner, “Antenna characterization in the time domain,” IEEE Trans. Antennas Propag. 45, 1140–1149 (1997).
[CrossRef]

M. D. Pocock, M. J. Bluck, S. P. Walker, “Electromagnetic scattering from 3-D curved dielectric bodies using time-domain integral equations,” IEEE Trans. Antennas Propag. 46, 1212–1219 (1998).
[CrossRef]

S. M. Rao, D. R. Wilton, A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. AP-30, 408–418 (1982).

S. M. Rao, D. R. Wilton, “Transient scattering by conducting surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. 39, 56–61 (1991).
[CrossRef]

H. Mieras, C. L. Bennet, “Space–time integral equation approach to dielectric targets,” IEEE Trans. Antennas Propag. AP-30, 2–9 (1982).
[CrossRef]

IEEE Trans. Inf. Theory (1)

J. J. Knab, “Interpolation of band-limited functions using the approximate prolate series,” IEEE Trans. Inf. Theory IT-25, 717–720 (1979).
[CrossRef]

IEEE Trans. Magn. (1)

E. Schlemmer, W. M. Rucker, K. R. Richter, “Boundary element computations of 3D scattering from lossy dielectric objects,” IEEE Trans. Magn. 29, 1524–1527 (1993).
[CrossRef]

J. Acoust. Soc. Am. (2)

A. A. Ergin, B. Shanker, E. Michielssen, “Fast transient analysis of acoustic wave scattering from rigid bodies using two-level plane wave time domain algorithm,” J. Acoust. Soc. Am. 106, 2405–2416 (1999).
[CrossRef]

A. A. Ergin, B. Shanker, E. Michielssen, “Fast analysis of transient acoustic wave scattering from rigid bodies using the multilevel plane wave time domain algorithm,” J. Acoust. Soc. Am. 107, 1168–1178 (2000).
[CrossRef] [PubMed]

J. Comput. Phys. (2)

A. A. Ergin, B. Shanker, E. Michielssen, “Fast evaluation of three-dimensional transient wave fields using diagonal translation operators,” J. Comput. Phys. 146, 157–180 (1998).
[CrossRef]

R. Jakob-Chien, B. K. Alpert, “A fast spherical filter with uniform resolution,” J. Comput. Phys. 136, 580–584 (1997).
[CrossRef]

J. Electromagn. Waves Appl. (1)

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Microwave Opt. Technol. Lett. (1)

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B. Shanker, A. A. Ergin, E. Michielssen, “The multilevel plane wave time domain algorithm for the fast analysis of transient scattering phenomena,” in Proceedings of the IEEE International Symposium on Antennas and Propagation (Institute of Electrical and Electronics Engineers, New York, 1999), Vol. 2, pp. 1342–1345.

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Figures (6)

Fig. 1
Fig. 1

Hierarchical division of the computational domain that illustrates the manner in which interactions are classified.

Fig. 2
Fig. 2

RCS patterns of a sphere in the zy plane at (a) 150 MHz and (b) 250 MHz obtained by time-domain (TD) and frequency-domain (FD) solvers. Electric and magnetic currents on the sphere are discretized by using a total of 1584 spatial unknowns.

Fig. 3
Fig. 3

RCS patterns of a NASA almond in the xy plane at (a) 150 MHz and (b) 200 MHz. The currents on the almond are discretized by using 2280 spatial unknowns.

Fig. 4
Fig. 4

RCS patterns of a cone sphere in the zy plane at (a) 500 MHz and (b) 600 MHz. The currents on the cone sphere are discretized by using 3312 spatial unknowns.

Fig. 5
Fig. 5

RCS patterns of a set of electrically large scatterers: (a) cone sphere at 700 MHz, (b) NASA almond at 85 MHz, (c) rectangular box at 200 MHz, (d) rectangular box at 300 MHz. The numbers of spatial unknowns that are used to discretize each of the aforementioned scatters are 7578, 15,342, 33,024, and 66,048, respectively.

Fig. 6
Fig. 6

Computational complexity.

Equations (51)

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Eqtot(r, t)=Eqinc(r, t)+Eqscat(r, t),
Hqtot(r, t)=Hqinc(r, t)+Hqscat(r, t).
Mq(r, t)=-nq(r)×Eqtot(rq, t),
Jq(r, t)=nˆq(r)×Hqtot(rq, t).
Aq(r, t){Jq}=μq4π SdS Jq(r, τq)R,
Fq(r, t){Mq}=εq4π SdS Mq(r, τq)R,
Eqscat(r, t){Jq, Mq}=-0tdt(t2I¯-cq2)·Aq(r, t)-×Fq(r, t)/εq,
Hqscat(r, t){Jq, Mq}=-0tdt(t2I¯-cq2)·Fq(r, t)+×Aq(r, t)/μq.
-nˆ(r)×[E1inc(r1, t)+αE2inc(r2, t)]=(1+α)M(r, t)+nˆ(r)×([E1scat(r1, t)-αE2scat(r2, t)]{J, M}),
-nˆ(r)×[H1inc(r1, t)+βH2inc(r2, t)]=-(1+β)J(r, t)+nˆ(r)×([H1scat(r1, t)-βH2scat(r2, t)]{J, M}).
M(r, t)=n=1NsSn(r)j=1NtMj,nTj(t)=n=1NsSn(r)gn(t)=n=1NsMn(r, t),
J(r, t)=n=1NsSn(r)j=1NtJj,nTj(t)=n=1NsSn(r)fn(t)=n=1NsJn(r, t),
Z¯0Ij=Fj-i=1j-1Z¯iIj-i,
Fj=[FjeT|FjhT]T,
Fj,me=Sm(r), -nˆ(r)×[E1inc(r, t)+αE2inc(r, t)]|t=tj,
Fj,mh=Sm(r), -nˆ(r)×[H1inc(r, t)+βH2inc(r, t)]|t=tj,
Z¯i=Z¯iemZ¯iejZ¯ihmZ¯ihj,
Z¯i,mnem=Sm(r), (1+α)Sn(r)T-i(t)+nˆ(r)×([E1scat(r1, t)-αE2scat(r2, t)]{0, Sn(r)T-1(t)})|t=0,
Z¯i,mnej=Sm(r), nˆ(r)×([E1scat(r1, t)-αE2scat(r2, t)]{Sn(r)T-i(t), 0})|t=0,
Z¯i,mnhm=Sm(r), nˆ(r)×([H1scat(r1, t)-βH2scat(r2, t)]{0, Sn(r)T-i(t)})|t=0,
Z¯i,mnhj=Sm(r),-(1+β)Sn(r)T-i(t)+nˆ(r)×([H1scat(r1, t)-βH2scat(r2, t)]{Sn(r)T-i(t), 0})|t=0.
fn(t)=k=1Kqfn,kq(r, t)=k=1Kql=1MqJ(k-1)Mq+l,nT(k-1)Mq+l(t),
gn(t)=k=1Kqgn,kq(r, t)=k=1Kql=1MqM(k-1)Mq+l,nT(k-1)Mq+l(t),
Jn(r, t)=k=1KqJn,kq(r, t),
Mn(r, t)=k=1KqMn,kq(r, t).
Aq(r, t){Jn}=k=1KqAq(r, t){Jn,kq},
Fq(r, t){Jn}=k=1KqFq(r, t){Mn,kq},
Eq(r, t){Mn, Jn}=k=1KqEq(r, t){Mn,kq, Jn,kq},
Hq(r, t){Mn, Jn}=k=1KqHq(r, t){Mn,kq, Jn,kq}.
A˜q(r, t){Jn,kq}=-μqt8π2cq d2ΩSndS Sn(r)×δ(t-kˆ·(r-r)/cq)*fn,kq(t),
F˜q(r, t){Mn,kq}=-εqt8π2cq d2ΩSndS Sn(r)×δ(t-kˆ·(r-r)/cq)*gn,kq(t),
Aq(r, t){Jn,kq}=0,ttk,2qA˜q(r, t){Jn,kq},t>tk,2q,
Fq(r, t){Mn,kq}=0,ttk,2qF˜q(r, t){Mn,kq},t>tk,2q.
E˜q(r, t){Mn,kq, Jn,kq}=tk,2qtdtμqt38π2cq d2Ω(I¯-kˆkˆ)·SndS Sn(r)δ(t-kˆ·(r-r)/cq)*fn,kq(t)-t38π2cq2 d2Ω kˆ×SndS Sn(r)δ(t-kˆ·(r-r)/cq)*gn,kq(t),
Hˆq(r, t){Mn,kq, Jn,kq}=tk,2qtdtεqt38π2cq d2Ω(I¯-kˆkˆ)·SndS Sn(r)δ(t-kˆ·(r-r)/cq)*gn,kq(t)+t38π2cq2 d2Ω kˆ×SndS Sn(r)δ(t-kˆ·(r-r)/cq)*fn,kq(t).
Eq(r, t){Mn,kq, Jn,kq}=0,ttk,2qE˜q(r, t){Mn,kq, Jn,kq},t>tk,2q,
Hq(r, t){bMn,kq, Jn,kq}=0ttk,2qH˜q(r, t){Mn,kq, Jn,kq},t>tk,2q
Sm(r), nˆ(r)×E˜q(r, t){0, Mn,kq}=tk,2qtdt 18π2cq2 d2Ω[Sq-(kˆ, t, nˆ, Sm)]T*Tq(kˆ, t)*Sq+(kˆ, t, kˆ, Sn)*gn,kq(t),
Sm(r), nˆ(r)×Eˆq(r, t){Jn,kq, 0}=tk,2qtdt μq8π2cq d2Ω[Sq-(kˆ, t, kˆ, Sm)]T*Tq(kˆ, t)*Sq+(kˆ, t, kˆ, Sn)*fn,kq(t),
Sm(r), nˆ(r)×Hˆq(r, t){0, Mn,kq}=tk,2qtdt εq8π2cq d2Ω[Sq-(kˆ, t, kˆ, Sm)]T*Tq(kˆ, t)*Sq+(kˆ, t, kˆ, Sn)*gn,kq(t),
Sm(r), nˆ(r)×H˜q(r, t){Jn,kq, 0}=tk,2qtdt -18π2cq2 d2Ω[Sq-(kˆ, t, nˆ, Sm)]T*Tq(kˆ, t)*Sq+(kˆ, t, kˆ, Sn)*fn,kq(t),
Tq(kˆ, t)=t3δ(t-kˆ·Rc/cq)
Sq±(kˆ, t, νˆ, Ψo)=SodS vˆ×Ψo(r)δ(t±kˆ·(r-roc)/cq)
So(r)=So(r)×nˆ(r)
fˆn,kq(t)=j=(k-1)Mq+1kMqJj,nψ(t-jΔt),
gˆn,kq(t)=j=(k-1)Mq+1kMqMj,nψ(t-jΔt),
 d2Ωv=0Nqp=-NqNqwpvq,
kˆkˆpvq,
Tq(kˆ, t)Tˆq(kˆpvq, t)=cqt32Rc v=0Nq(2v+1)PvcqtRcPv(kˆpvq·Rc),
Tααq=Rc,αα-2Rsq(i)Tsq(i)Tsq(i).
Einc(r, t)=pˆ cos[2πf0(t-r·kˆ/c)]×exp[-(t-r·kˆ/c-tp)2/2σ2],

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