Abstract

A message-passing-interface (MPI)-based parallel finite-difference time-domain (FDTD) algorithm for the electromagnetic scattering from a 1-D randomly rough sea surface is presented. The uniaxial perfectly matched layer (UPML) medium is adopted for truncation of FDTD lattices, in which the finite-difference equations can be used for the total computation domain by properly choosing the uniaxial parameters. This makes the parallel FDTD algorithm easier to implement. The parallel performance with different processors is illustrated for one sea surface realization, and the computation time of the parallel FDTD algorithm is dramatically reduced compared to a single-process implementation. Finally, some numerical results are shown, including the backscattering characteristics of sea surface for different polarization and the bistatic scattering from a sea surface with large incident angle and large wind speed.

© 2009 Optical Society of America

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References

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  1. J. A. Kong, Electromagnetic Wave Theory (Academic, 1986).
  2. D. Holliday, “Resolution of a controversy surrounding the Kirchhoff approach and the small perturbation method in rough surface scattering theory,” IEEE Trans. Antennas Propag. 35, 120-122 (1987).
    [CrossRef]
  3. R. Dusséaux and R. D. Oliveira, “Scattering of a plane wave by a 1-dimensional rough surface study in a nonorthogonal coordinate system,” Electromagn. Waves 34, 63-88 (2001).
    [CrossRef]
  4. D. Torrungrueng, H. T. Chou, and J. T. Johnson, “A novel acceleration algorithm for the computation of scattering from two-dimensional large-scale perfectly conducting random rough surfaces with the forward-backward method,” IEEE Trans. Geosci. Remote Sens. 38, 1656-1667 (2000).
    [CrossRef]
  5. M. Y. Xia, C. H. Chan, S. Q. Li, B. Zhang, and L. Tsang, “An efficient algorithm for electromagnetic scattering from rough surfaces using a single integral equation and multilevel sparse-matrix canonical-grid method,” IEEE Trans. Antennas Propag. 51, 1142-1149 (2003).
    [CrossRef]
  6. P. Liu and Y. Q. Jin, “Numerical simulation of bistatic scattering from a target at low altitude above rough sea surface under an EM-wave incidence at low grazing angle by using the finite element method,” IEEE Trans. Antennas Propag. 52, 1205-1210 (2004).
    [CrossRef]
  7. J. Li, L.-X. Guo, and H. Zeng, “FDTD investigation on the electromagnetic scattering from a target above a randomly rough sea surface,” Waves Random Complex Media 18, 641-650 (2008).
    [CrossRef]
  8. J. Li, L.-X. Guo, and H. Zeng, “FDTD investigation on bistatic scattering from a target above two-layered rough surfaces using upml absorbing condition,” Electromagn. Waves 88, 197-211 (2008).
    [CrossRef]
  9. C. Guiffaut and K. Mahdjoubi, “A parallel FDTD algorithm using the MP/Library,” IEEE Antennas Propag. Mag. 43, 94-103 (2001).
    [CrossRef]
  10. E. I. Thorsos, “The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum,” J. Acoust. Soc. Am. 83, 78-91 (1988).
    [CrossRef]
  11. J. V. Toporkov and G. S. Brown, “Numerical simulations of scattering from time-varying randomly rough surfaces,” IEEE Trans. Geosci. Remote Sens. 38, 1616-1625 (2001).
    [CrossRef]
  12. G. P. Harrison and A. R. Wallace, “Climate sensitivity of marine energy,” Renewable Energy 30, 1801-1817 (2005).
    [CrossRef]
  13. H. X. Ye and Y. Q. Jin, “Parametrization of the tapered incident wave for numerical simulation of electromagnetic scattering from rough surface,” IEEE Trans. Antennas Propag. 53, 1234-1237 (2005).
    [CrossRef]
  14. S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630-1639 (1996).
    [CrossRef]
  15. S. D. Gedney, “An anisotropic PML absorbing media for the FDTD simulation for fields in lossy and dispersive media,” Electromagnetics 16, 425-449 (1996).
    [CrossRef]
  16. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Academic, 2005).
  17. J. S. Juntunen and T. D. Tsiboukis, “Reduction of numerical dispersion in FDTD method through artificial anisotropy,” IEEE Trans. Microwave Theory Tech. 58, 582-588 (2000).
    [CrossRef]
  18. A. K. Fung, M. R. Shah, and S. Tjuatja, “Numerical simulation of scattering from three-dimensional randomly rough surfaces,” IEEE Trans. Geosci. Remote Sens. 32, 986-995 (1995).
    [CrossRef]
  19. G. Ruck, D. E. Barrick, W. D. Stuart, and C. K. Krichbaum, Radar Cross Section Handbook (Academic, 1970).
  20. W. H. Yu, Y. J. Liu, T. Su, N. T. Hunag, and R. Mittra, “A robust parallel conformal finite-difference time-domain processing package using the MPI library,” IEEE Antennas Propag. Mag. 47, 39-59 (2005).
    [CrossRef]
  21. J. Z. Lei, C. H. Liang, W. D. Zhang, and Y. Zhang, “Study on mpi-based parallel modified conformal FDTD for 3-D electrically large coated targets by using effective parameters,” IEEE Antennas Wireless Propag. Lett. 7, 175-178 (2008).
    [CrossRef]
  22. F. T. Ulaby, R. K. Moore, and A. K. Fung, Microwave Remote Sensing (Academic, 1982).
  23. L. Tsang and J. A. Kong, Scattering of Electromagnetic Waves: Numerical Simulations (Academic, 1982).

2008 (3)

J. Li, L.-X. Guo, and H. Zeng, “FDTD investigation on the electromagnetic scattering from a target above a randomly rough sea surface,” Waves Random Complex Media 18, 641-650 (2008).
[CrossRef]

J. Li, L.-X. Guo, and H. Zeng, “FDTD investigation on bistatic scattering from a target above two-layered rough surfaces using upml absorbing condition,” Electromagn. Waves 88, 197-211 (2008).
[CrossRef]

J. Z. Lei, C. H. Liang, W. D. Zhang, and Y. Zhang, “Study on mpi-based parallel modified conformal FDTD for 3-D electrically large coated targets by using effective parameters,” IEEE Antennas Wireless Propag. Lett. 7, 175-178 (2008).
[CrossRef]

2005 (3)

W. H. Yu, Y. J. Liu, T. Su, N. T. Hunag, and R. Mittra, “A robust parallel conformal finite-difference time-domain processing package using the MPI library,” IEEE Antennas Propag. Mag. 47, 39-59 (2005).
[CrossRef]

G. P. Harrison and A. R. Wallace, “Climate sensitivity of marine energy,” Renewable Energy 30, 1801-1817 (2005).
[CrossRef]

H. X. Ye and Y. Q. Jin, “Parametrization of the tapered incident wave for numerical simulation of electromagnetic scattering from rough surface,” IEEE Trans. Antennas Propag. 53, 1234-1237 (2005).
[CrossRef]

2004 (1)

P. Liu and Y. Q. Jin, “Numerical simulation of bistatic scattering from a target at low altitude above rough sea surface under an EM-wave incidence at low grazing angle by using the finite element method,” IEEE Trans. Antennas Propag. 52, 1205-1210 (2004).
[CrossRef]

2003 (1)

M. Y. Xia, C. H. Chan, S. Q. Li, B. Zhang, and L. Tsang, “An efficient algorithm for electromagnetic scattering from rough surfaces using a single integral equation and multilevel sparse-matrix canonical-grid method,” IEEE Trans. Antennas Propag. 51, 1142-1149 (2003).
[CrossRef]

2001 (3)

R. Dusséaux and R. D. Oliveira, “Scattering of a plane wave by a 1-dimensional rough surface study in a nonorthogonal coordinate system,” Electromagn. Waves 34, 63-88 (2001).
[CrossRef]

C. Guiffaut and K. Mahdjoubi, “A parallel FDTD algorithm using the MP/Library,” IEEE Antennas Propag. Mag. 43, 94-103 (2001).
[CrossRef]

J. V. Toporkov and G. S. Brown, “Numerical simulations of scattering from time-varying randomly rough surfaces,” IEEE Trans. Geosci. Remote Sens. 38, 1616-1625 (2001).
[CrossRef]

2000 (2)

J. S. Juntunen and T. D. Tsiboukis, “Reduction of numerical dispersion in FDTD method through artificial anisotropy,” IEEE Trans. Microwave Theory Tech. 58, 582-588 (2000).
[CrossRef]

D. Torrungrueng, H. T. Chou, and J. T. Johnson, “A novel acceleration algorithm for the computation of scattering from two-dimensional large-scale perfectly conducting random rough surfaces with the forward-backward method,” IEEE Trans. Geosci. Remote Sens. 38, 1656-1667 (2000).
[CrossRef]

1996 (2)

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630-1639 (1996).
[CrossRef]

S. D. Gedney, “An anisotropic PML absorbing media for the FDTD simulation for fields in lossy and dispersive media,” Electromagnetics 16, 425-449 (1996).
[CrossRef]

1995 (1)

A. K. Fung, M. R. Shah, and S. Tjuatja, “Numerical simulation of scattering from three-dimensional randomly rough surfaces,” IEEE Trans. Geosci. Remote Sens. 32, 986-995 (1995).
[CrossRef]

1988 (1)

E. I. Thorsos, “The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum,” J. Acoust. Soc. Am. 83, 78-91 (1988).
[CrossRef]

1987 (1)

D. Holliday, “Resolution of a controversy surrounding the Kirchhoff approach and the small perturbation method in rough surface scattering theory,” IEEE Trans. Antennas Propag. 35, 120-122 (1987).
[CrossRef]

Barrick, D. E.

G. Ruck, D. E. Barrick, W. D. Stuart, and C. K. Krichbaum, Radar Cross Section Handbook (Academic, 1970).

Brown, G. S.

J. V. Toporkov and G. S. Brown, “Numerical simulations of scattering from time-varying randomly rough surfaces,” IEEE Trans. Geosci. Remote Sens. 38, 1616-1625 (2001).
[CrossRef]

Chan, C. H.

M. Y. Xia, C. H. Chan, S. Q. Li, B. Zhang, and L. Tsang, “An efficient algorithm for electromagnetic scattering from rough surfaces using a single integral equation and multilevel sparse-matrix canonical-grid method,” IEEE Trans. Antennas Propag. 51, 1142-1149 (2003).
[CrossRef]

Chou, H. T.

D. Torrungrueng, H. T. Chou, and J. T. Johnson, “A novel acceleration algorithm for the computation of scattering from two-dimensional large-scale perfectly conducting random rough surfaces with the forward-backward method,” IEEE Trans. Geosci. Remote Sens. 38, 1656-1667 (2000).
[CrossRef]

Dusséaux, R.

R. Dusséaux and R. D. Oliveira, “Scattering of a plane wave by a 1-dimensional rough surface study in a nonorthogonal coordinate system,” Electromagn. Waves 34, 63-88 (2001).
[CrossRef]

Fung, A. K.

A. K. Fung, M. R. Shah, and S. Tjuatja, “Numerical simulation of scattering from three-dimensional randomly rough surfaces,” IEEE Trans. Geosci. Remote Sens. 32, 986-995 (1995).
[CrossRef]

F. T. Ulaby, R. K. Moore, and A. K. Fung, Microwave Remote Sensing (Academic, 1982).

Gedney, S. D.

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630-1639 (1996).
[CrossRef]

S. D. Gedney, “An anisotropic PML absorbing media for the FDTD simulation for fields in lossy and dispersive media,” Electromagnetics 16, 425-449 (1996).
[CrossRef]

Guiffaut, C.

C. Guiffaut and K. Mahdjoubi, “A parallel FDTD algorithm using the MP/Library,” IEEE Antennas Propag. Mag. 43, 94-103 (2001).
[CrossRef]

Guo, L.-X.

J. Li, L.-X. Guo, and H. Zeng, “FDTD investigation on the electromagnetic scattering from a target above a randomly rough sea surface,” Waves Random Complex Media 18, 641-650 (2008).
[CrossRef]

J. Li, L.-X. Guo, and H. Zeng, “FDTD investigation on bistatic scattering from a target above two-layered rough surfaces using upml absorbing condition,” Electromagn. Waves 88, 197-211 (2008).
[CrossRef]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Academic, 2005).

Harrison, G. P.

G. P. Harrison and A. R. Wallace, “Climate sensitivity of marine energy,” Renewable Energy 30, 1801-1817 (2005).
[CrossRef]

Holliday, D.

D. Holliday, “Resolution of a controversy surrounding the Kirchhoff approach and the small perturbation method in rough surface scattering theory,” IEEE Trans. Antennas Propag. 35, 120-122 (1987).
[CrossRef]

Hunag, N. T.

W. H. Yu, Y. J. Liu, T. Su, N. T. Hunag, and R. Mittra, “A robust parallel conformal finite-difference time-domain processing package using the MPI library,” IEEE Antennas Propag. Mag. 47, 39-59 (2005).
[CrossRef]

Jin, Y. Q.

H. X. Ye and Y. Q. Jin, “Parametrization of the tapered incident wave for numerical simulation of electromagnetic scattering from rough surface,” IEEE Trans. Antennas Propag. 53, 1234-1237 (2005).
[CrossRef]

P. Liu and Y. Q. Jin, “Numerical simulation of bistatic scattering from a target at low altitude above rough sea surface under an EM-wave incidence at low grazing angle by using the finite element method,” IEEE Trans. Antennas Propag. 52, 1205-1210 (2004).
[CrossRef]

Johnson, J. T.

D. Torrungrueng, H. T. Chou, and J. T. Johnson, “A novel acceleration algorithm for the computation of scattering from two-dimensional large-scale perfectly conducting random rough surfaces with the forward-backward method,” IEEE Trans. Geosci. Remote Sens. 38, 1656-1667 (2000).
[CrossRef]

Juntunen, J. S.

J. S. Juntunen and T. D. Tsiboukis, “Reduction of numerical dispersion in FDTD method through artificial anisotropy,” IEEE Trans. Microwave Theory Tech. 58, 582-588 (2000).
[CrossRef]

Kong, J. A.

L. Tsang and J. A. Kong, Scattering of Electromagnetic Waves: Numerical Simulations (Academic, 1982).

J. A. Kong, Electromagnetic Wave Theory (Academic, 1986).

Krichbaum, C. K.

G. Ruck, D. E. Barrick, W. D. Stuart, and C. K. Krichbaum, Radar Cross Section Handbook (Academic, 1970).

Lei, J. Z.

J. Z. Lei, C. H. Liang, W. D. Zhang, and Y. Zhang, “Study on mpi-based parallel modified conformal FDTD for 3-D electrically large coated targets by using effective parameters,” IEEE Antennas Wireless Propag. Lett. 7, 175-178 (2008).
[CrossRef]

Li, J.

J. Li, L.-X. Guo, and H. Zeng, “FDTD investigation on bistatic scattering from a target above two-layered rough surfaces using upml absorbing condition,” Electromagn. Waves 88, 197-211 (2008).
[CrossRef]

J. Li, L.-X. Guo, and H. Zeng, “FDTD investigation on the electromagnetic scattering from a target above a randomly rough sea surface,” Waves Random Complex Media 18, 641-650 (2008).
[CrossRef]

Li, S. Q.

M. Y. Xia, C. H. Chan, S. Q. Li, B. Zhang, and L. Tsang, “An efficient algorithm for electromagnetic scattering from rough surfaces using a single integral equation and multilevel sparse-matrix canonical-grid method,” IEEE Trans. Antennas Propag. 51, 1142-1149 (2003).
[CrossRef]

Liang, C. H.

J. Z. Lei, C. H. Liang, W. D. Zhang, and Y. Zhang, “Study on mpi-based parallel modified conformal FDTD for 3-D electrically large coated targets by using effective parameters,” IEEE Antennas Wireless Propag. Lett. 7, 175-178 (2008).
[CrossRef]

Liu, P.

P. Liu and Y. Q. Jin, “Numerical simulation of bistatic scattering from a target at low altitude above rough sea surface under an EM-wave incidence at low grazing angle by using the finite element method,” IEEE Trans. Antennas Propag. 52, 1205-1210 (2004).
[CrossRef]

Liu, Y. J.

W. H. Yu, Y. J. Liu, T. Su, N. T. Hunag, and R. Mittra, “A robust parallel conformal finite-difference time-domain processing package using the MPI library,” IEEE Antennas Propag. Mag. 47, 39-59 (2005).
[CrossRef]

Mahdjoubi, K.

C. Guiffaut and K. Mahdjoubi, “A parallel FDTD algorithm using the MP/Library,” IEEE Antennas Propag. Mag. 43, 94-103 (2001).
[CrossRef]

Mittra, R.

W. H. Yu, Y. J. Liu, T. Su, N. T. Hunag, and R. Mittra, “A robust parallel conformal finite-difference time-domain processing package using the MPI library,” IEEE Antennas Propag. Mag. 47, 39-59 (2005).
[CrossRef]

Moore, R. K.

F. T. Ulaby, R. K. Moore, and A. K. Fung, Microwave Remote Sensing (Academic, 1982).

Oliveira, R. D.

R. Dusséaux and R. D. Oliveira, “Scattering of a plane wave by a 1-dimensional rough surface study in a nonorthogonal coordinate system,” Electromagn. Waves 34, 63-88 (2001).
[CrossRef]

Ruck, G.

G. Ruck, D. E. Barrick, W. D. Stuart, and C. K. Krichbaum, Radar Cross Section Handbook (Academic, 1970).

Shah, M. R.

A. K. Fung, M. R. Shah, and S. Tjuatja, “Numerical simulation of scattering from three-dimensional randomly rough surfaces,” IEEE Trans. Geosci. Remote Sens. 32, 986-995 (1995).
[CrossRef]

Stuart, W. D.

G. Ruck, D. E. Barrick, W. D. Stuart, and C. K. Krichbaum, Radar Cross Section Handbook (Academic, 1970).

Su, T.

W. H. Yu, Y. J. Liu, T. Su, N. T. Hunag, and R. Mittra, “A robust parallel conformal finite-difference time-domain processing package using the MPI library,” IEEE Antennas Propag. Mag. 47, 39-59 (2005).
[CrossRef]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Academic, 2005).

Thorsos, E. I.

E. I. Thorsos, “The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum,” J. Acoust. Soc. Am. 83, 78-91 (1988).
[CrossRef]

Tjuatja, S.

A. K. Fung, M. R. Shah, and S. Tjuatja, “Numerical simulation of scattering from three-dimensional randomly rough surfaces,” IEEE Trans. Geosci. Remote Sens. 32, 986-995 (1995).
[CrossRef]

Toporkov, J. V.

J. V. Toporkov and G. S. Brown, “Numerical simulations of scattering from time-varying randomly rough surfaces,” IEEE Trans. Geosci. Remote Sens. 38, 1616-1625 (2001).
[CrossRef]

Torrungrueng, D.

D. Torrungrueng, H. T. Chou, and J. T. Johnson, “A novel acceleration algorithm for the computation of scattering from two-dimensional large-scale perfectly conducting random rough surfaces with the forward-backward method,” IEEE Trans. Geosci. Remote Sens. 38, 1656-1667 (2000).
[CrossRef]

Tsang, L.

M. Y. Xia, C. H. Chan, S. Q. Li, B. Zhang, and L. Tsang, “An efficient algorithm for electromagnetic scattering from rough surfaces using a single integral equation and multilevel sparse-matrix canonical-grid method,” IEEE Trans. Antennas Propag. 51, 1142-1149 (2003).
[CrossRef]

L. Tsang and J. A. Kong, Scattering of Electromagnetic Waves: Numerical Simulations (Academic, 1982).

Tsiboukis, T. D.

J. S. Juntunen and T. D. Tsiboukis, “Reduction of numerical dispersion in FDTD method through artificial anisotropy,” IEEE Trans. Microwave Theory Tech. 58, 582-588 (2000).
[CrossRef]

Ulaby, F. T.

F. T. Ulaby, R. K. Moore, and A. K. Fung, Microwave Remote Sensing (Academic, 1982).

Wallace, A. R.

G. P. Harrison and A. R. Wallace, “Climate sensitivity of marine energy,” Renewable Energy 30, 1801-1817 (2005).
[CrossRef]

Xia, M. Y.

M. Y. Xia, C. H. Chan, S. Q. Li, B. Zhang, and L. Tsang, “An efficient algorithm for electromagnetic scattering from rough surfaces using a single integral equation and multilevel sparse-matrix canonical-grid method,” IEEE Trans. Antennas Propag. 51, 1142-1149 (2003).
[CrossRef]

Ye, H. X.

H. X. Ye and Y. Q. Jin, “Parametrization of the tapered incident wave for numerical simulation of electromagnetic scattering from rough surface,” IEEE Trans. Antennas Propag. 53, 1234-1237 (2005).
[CrossRef]

Yu, W. H.

W. H. Yu, Y. J. Liu, T. Su, N. T. Hunag, and R. Mittra, “A robust parallel conformal finite-difference time-domain processing package using the MPI library,” IEEE Antennas Propag. Mag. 47, 39-59 (2005).
[CrossRef]

Zeng, H.

J. Li, L.-X. Guo, and H. Zeng, “FDTD investigation on the electromagnetic scattering from a target above a randomly rough sea surface,” Waves Random Complex Media 18, 641-650 (2008).
[CrossRef]

J. Li, L.-X. Guo, and H. Zeng, “FDTD investigation on bistatic scattering from a target above two-layered rough surfaces using upml absorbing condition,” Electromagn. Waves 88, 197-211 (2008).
[CrossRef]

Zhang, B.

M. Y. Xia, C. H. Chan, S. Q. Li, B. Zhang, and L. Tsang, “An efficient algorithm for electromagnetic scattering from rough surfaces using a single integral equation and multilevel sparse-matrix canonical-grid method,” IEEE Trans. Antennas Propag. 51, 1142-1149 (2003).
[CrossRef]

Zhang, W. D.

J. Z. Lei, C. H. Liang, W. D. Zhang, and Y. Zhang, “Study on mpi-based parallel modified conformal FDTD for 3-D electrically large coated targets by using effective parameters,” IEEE Antennas Wireless Propag. Lett. 7, 175-178 (2008).
[CrossRef]

Zhang, Y.

J. Z. Lei, C. H. Liang, W. D. Zhang, and Y. Zhang, “Study on mpi-based parallel modified conformal FDTD for 3-D electrically large coated targets by using effective parameters,” IEEE Antennas Wireless Propag. Lett. 7, 175-178 (2008).
[CrossRef]

Electromagn. Waves (2)

R. Dusséaux and R. D. Oliveira, “Scattering of a plane wave by a 1-dimensional rough surface study in a nonorthogonal coordinate system,” Electromagn. Waves 34, 63-88 (2001).
[CrossRef]

J. Li, L.-X. Guo, and H. Zeng, “FDTD investigation on bistatic scattering from a target above two-layered rough surfaces using upml absorbing condition,” Electromagn. Waves 88, 197-211 (2008).
[CrossRef]

Electromagnetics (1)

S. D. Gedney, “An anisotropic PML absorbing media for the FDTD simulation for fields in lossy and dispersive media,” Electromagnetics 16, 425-449 (1996).
[CrossRef]

IEEE Antennas Propag. Mag. (2)

C. Guiffaut and K. Mahdjoubi, “A parallel FDTD algorithm using the MP/Library,” IEEE Antennas Propag. Mag. 43, 94-103 (2001).
[CrossRef]

W. H. Yu, Y. J. Liu, T. Su, N. T. Hunag, and R. Mittra, “A robust parallel conformal finite-difference time-domain processing package using the MPI library,” IEEE Antennas Propag. Mag. 47, 39-59 (2005).
[CrossRef]

IEEE Antennas Wireless Propag. Lett. (1)

J. Z. Lei, C. H. Liang, W. D. Zhang, and Y. Zhang, “Study on mpi-based parallel modified conformal FDTD for 3-D electrically large coated targets by using effective parameters,” IEEE Antennas Wireless Propag. Lett. 7, 175-178 (2008).
[CrossRef]

IEEE Trans. Antennas Propag. (5)

M. Y. Xia, C. H. Chan, S. Q. Li, B. Zhang, and L. Tsang, “An efficient algorithm for electromagnetic scattering from rough surfaces using a single integral equation and multilevel sparse-matrix canonical-grid method,” IEEE Trans. Antennas Propag. 51, 1142-1149 (2003).
[CrossRef]

P. Liu and Y. Q. Jin, “Numerical simulation of bistatic scattering from a target at low altitude above rough sea surface under an EM-wave incidence at low grazing angle by using the finite element method,” IEEE Trans. Antennas Propag. 52, 1205-1210 (2004).
[CrossRef]

D. Holliday, “Resolution of a controversy surrounding the Kirchhoff approach and the small perturbation method in rough surface scattering theory,” IEEE Trans. Antennas Propag. 35, 120-122 (1987).
[CrossRef]

H. X. Ye and Y. Q. Jin, “Parametrization of the tapered incident wave for numerical simulation of electromagnetic scattering from rough surface,” IEEE Trans. Antennas Propag. 53, 1234-1237 (2005).
[CrossRef]

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630-1639 (1996).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (3)

J. V. Toporkov and G. S. Brown, “Numerical simulations of scattering from time-varying randomly rough surfaces,” IEEE Trans. Geosci. Remote Sens. 38, 1616-1625 (2001).
[CrossRef]

A. K. Fung, M. R. Shah, and S. Tjuatja, “Numerical simulation of scattering from three-dimensional randomly rough surfaces,” IEEE Trans. Geosci. Remote Sens. 32, 986-995 (1995).
[CrossRef]

D. Torrungrueng, H. T. Chou, and J. T. Johnson, “A novel acceleration algorithm for the computation of scattering from two-dimensional large-scale perfectly conducting random rough surfaces with the forward-backward method,” IEEE Trans. Geosci. Remote Sens. 38, 1656-1667 (2000).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

J. S. Juntunen and T. D. Tsiboukis, “Reduction of numerical dispersion in FDTD method through artificial anisotropy,” IEEE Trans. Microwave Theory Tech. 58, 582-588 (2000).
[CrossRef]

J. Acoust. Soc. Am. (1)

E. I. Thorsos, “The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum,” J. Acoust. Soc. Am. 83, 78-91 (1988).
[CrossRef]

Renewable Energy (1)

G. P. Harrison and A. R. Wallace, “Climate sensitivity of marine energy,” Renewable Energy 30, 1801-1817 (2005).
[CrossRef]

Waves Random Complex Media (1)

J. Li, L.-X. Guo, and H. Zeng, “FDTD investigation on the electromagnetic scattering from a target above a randomly rough sea surface,” Waves Random Complex Media 18, 641-650 (2008).
[CrossRef]

Other (5)

J. A. Kong, Electromagnetic Wave Theory (Academic, 1986).

G. Ruck, D. E. Barrick, W. D. Stuart, and C. K. Krichbaum, Radar Cross Section Handbook (Academic, 1970).

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Academic, 2005).

F. T. Ulaby, R. K. Moore, and A. K. Fung, Microwave Remote Sensing (Academic, 1982).

L. Tsang and J. A. Kong, Scattering of Electromagnetic Waves: Numerical Simulations (Academic, 1982).

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Figures (9)

Fig. 1
Fig. 1

Geometry for 1-D rough sea surface.

Fig. 2
Fig. 2

FDTD model of rough sea surface.

Fig. 3
Fig. 3

Domain decomposition of parallel FDTD.

Fig. 4
Fig. 4

Exchange of the tangential magnetic field H y with overlapping area.

Fig. 5
Fig. 5

Comparison of the two different methods for the bistatic scattering from a dielectric sea surface. (a) θ i = 30 ° , (b) θ i = 50 ° .

Fig. 6
Fig. 6

(a) Different decomposition of parallel FDTD in 2-D rectangular coordinate. (b) Scattering from one dielectric sea surface realization for different decomposition. (c) Scalability of parallel FDTD algorithm for different decomposition.

Fig. 7
Fig. 7

Bistatic scattering from a dielectric sea surface for different polarization with large incident angle: (a) θ i = 70 ° , (b) θ i = 75 ° .

Fig. 8
Fig. 8

Backscattering from a dielectric sea surface for different wind speed: (a) U 19.5 = 3 m s , (b) U 19.5 = 5 m s .

Fig. 9
Fig. 9

(a) Profile of randomly rough sea surface with U 19.5 = 10 m s and U 19.5 = 15 m s . (b) Bistatic scattering from a dielectric sea surface with U 19.5 = 10 m s and U 19.5 = 15 m s .

Tables (1)

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Table 1 Comparison of Time (in s) with One Sea Surface Realization for Different Divisions

Equations (38)

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ζ ( x m ) = 1 L i = M 2 M 2 1 F ( k i ) e j 0 k i x m ,
F ( k i ) = [ 2 π L W ( k i ) ] 1 2 { [ N ( 0 , 1 ) + j 0 N ( 0 , 1 ) ] 2 , i 0 , M 2 N ( 0 , 1 ) , i = 0 , M 2 } .
W ( k ) = { α 4 k 3 exp ( β g 2 k 2 U 19.5 4 ) k i 0 0 k i < 0 } ,
h = ( ζ ( x ) ) 2 = + W ( k ) d k = 2 0 W ( k ) d k = α U 19.5 4 4 β g 2 ,
l = 1.0 ( C ( 0 ) ) 2 + ( C ( x ) ) 2 d x ,
C ( 0 ) = ( ζ ( x ) ) 2 , then
+ ( C ( x ) ) 2 d x = + d x ( + W ( k ) exp ( j 0 k x ) d k ) 2 = + d x ( + W ( k ) exp ( j 0 k x ) d k + W ( k ) exp ( j 0 k x ) d k ) .
+ ( C ( x ) ) 2 d x = 4 π 0 ( W ( k ) ) 2 d k = π α 2 4 0 k 6 exp ( 2 β g 2 k 2 U 19.5 4 ) d k .
l = 3 π U 19.5 2 8 g π 2 β 0.175 U 19.5 2 .
{ E z y = j 0 w μ 1 s y s x H x E z x = j 0 w μ 1 s x s y H y } .
H y x H x y = ( j 0 w ϵ 1 + σ 1 ) s x s y E z ,
B x = μ 1 s x H x , B y = μ 1 s y H y .
P z = s y s x E z , P z = P z s x .
E z y = k y B x t σ y ϵ 0 B x ,
k x B x t + σ x ϵ 0 B x = μ 1 H x t .
E z x = k x B y t + σ x ϵ 0 B y ,
k y B y t + σ y ϵ 0 B y = μ 1 H y t .
H y x H x y = ϵ 1 P z t + σ 1 P z ,
P z t = k x P z t + σ x ϵ 0 P z ,
P z t = k y E z t + σ y ϵ 0 E z ,
B x n + 1 2 ( i , j + 1 2 ) = k y ( m ) Δ t σ y ( m ) 2 ϵ 0 k y ( m ) Δ t + σ y ( m ) 2 ϵ 0 B x n 1 2 ( i , j + 1 2 ) 1 Δ y k y ( m ) Δ t + σ y ( m ) 2 ϵ 0 ( E z n ( i , j + 1 ) E z n ( i , j ) ) ,
H x n + 1 2 ( i , j + 1 2 ) = H x n 1 2 ( i , j + 1 2 ) + k x ( m ) Δ t + σ x ( m ) 2 ϵ 0 μ 1 Δ t B x n + 1 2 ( i , j + 1 2 ) k x ( m ) Δ t σ x ( m ) 2 ϵ 0 μ 1 Δ t B x n 1 2 ( i , j + 1 2 ) ,
B y n + 1 2 ( i + 1 2 , j ) = k x ( m ) Δ t σ x ( m ) 2 ϵ 0 k x ( m ) Δ t + σ x ( m ) 2 ϵ 0 B y n 1 2 ( i + 1 2 , j ) + 1 Δ x k x ( m ) Δ t + σ x ( m ) 2 ϵ 0 ( E z n ( i + 1 , j ) E z n ( i , j ) ) ,
H y n + 1 2 ( i + 1 2 , j ) = H y n 1 2 ( i + 1 2 , j ) + k y ( m ) Δ t + σ y ( m ) 2 ϵ 0 μ 1 Δ t B y n + 1 2 ( i + 1 2 , j ) k y ( m ) Δ t σ y ( m ) 2 ϵ 0 μ 1 Δ t B y n 1 2 ( i + 1 2 , j ) ,
P z n + 1 ( i , j ) = ϵ 1 ( m ) Δ t 0.5 σ 1 ( m ) ϵ 1 ( m ) Δ t + 0.5 σ 1 ( m ) P z n ( i , j ) + 1 ϵ 1 ( m ) Δ t + 0.5 σ 1 ( m ) × [ 1 Δ x ( H y n + 1 2 ( i + 1 2 , j ) H y n + 1 2 ( i 1 2 , j ) ) 1 Δ y ( H x n + 1 2 ( i , j + 1 2 ) H x n + 1 2 ( i , j 1 2 ) ) ] ,
P z n + 1 ( i , j ) = k x ( m ) Δ t σ x ( m ) ( 2 ϵ 0 ) k x ( m ) Δ t + σ x ( m ) ( 2 ϵ 0 ) P z n ( i , j ) + 1 Δ t k x ( m ) Δ t + σ x ( m ) ( 2 ϵ 0 ) [ P z n + 1 ( i , j ) P z n ( i , j ) ] ,
E z n + 1 ( i , j ) = k y ( m ) Δ t σ y ( m ) ( 2 ϵ 0 ) k y ( m ) Δ t + σ y ( m ) ( 2 ϵ 0 ) E z n ( i , j ) + 1 Δ t k y ( m ) Δ t + σ y ( m ) ( 2 ϵ 0 ) ( P z n + 1 ( i , j ) P z n ( i , j ) ) ,
y 1 = i Δ x sin θ i j Δ y cos θ i .
E z = ( 1 w ) E i n ( p ) + w E i n ( p + 1 ) .
H x = ( 1 w ) H i n ( p ) + w H i n ( p + 1 ) .
{ E z , i ( i , j ) = E z H x , i ( i , j + 1 2 ) = H x cos θ i } .
E z n + 1 ( i , j ) = E z n ( i , j ) + Δ t ϵ [ × H ] z n + 1 2 Δ t ϵ H x , i n + 1 2 ( i , j + 1 2 ) Δ y ,
H x n + 1 2 ( i , j + 1 2 ) = H x n 1 2 ( i , j + 1 2 ) Δ t μ [ × E ] x n Δ t μ E z , i n ( i , j ) Δ y .
G ( x , y ) = exp { [ ( x x 0 ) 2 + ( y y 0 ) 2 ] ( cos θ i T ) 2 } ,
E s = z ̂ 1 2 j 0 k i 2 π r exp ( j 0 k i r ) ( z f z f m x sin ϕ ) ,
σ = lim r 2 π r L E s 2 E i 2 .
S = T 1 T n ,
E = S n × 100 % .

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