Abstract

We present an investigation of the electromagnetic scattering from a three-dimensional (3-D) object above a two-dimensional (2-D) randomly rough surface. A Message Passing Interface-based parallel finite-difference time-domain (FDTD) approach is used, and the uniaxial perfectly matched layer (UPML) medium is adopted for truncation of the 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 number of processors is illustrated for one rough surface realization and shows that the computation time of our parallel FDTD algorithm is dramatically reduced relative to a single-processor implementation. Finally, the composite scattering coefficients versus scattered and azimuthal angle are presented and analyzed for different conditions, including the surface roughness, the dielectric constants, the polarization, and the size of the 3-D object.

© 2009 Optical Society of America

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  1. J. T. Johnson, “A study of the four-path model for scattering from a object above a half space,” Microwave Opt. Technol. Lett. 30, 130-134 (2001).
    [CrossRef]
  2. H. X. Ye and Y. Q. Jin, “A hybrid analytic-numerical algorithm of scattering from an object above a rough surface,” IEEE Trans. Geosci. Remote Sens. 45, 1174-1180 (2007).
    [CrossRef]
  3. M. R. Pino, J. L. Rodriguez, and F. Obelleiro, “Statistical description of the RCS of 2-D ship models on rough sea surfaces,” Microwave Opt. Technol. Lett. 32, 153-159 (2002).
    [CrossRef]
  4. N. Pinel, C. Bourlier, and J. Saillard, “Forward radar propagation over oil slicks on sea surfaces using the Ament model with shadowing effect,” Prog. Electromagn. Res. 76, 95-126 (2007).
    [CrossRef]
  5. Y. Zhang, J. Lu, J. Pacheo, Jr., C. D. Moss, C. O. Ao, T. M. Grzegorczyk, and J. A. Kong, “Mode-expansion method for calculating electromagnetic waves scattered by objects on rough ocean surfaces,” IEEE Trans. Antennas Propag. 53, 1631-1639 (2005).
    [CrossRef]
  6. L. P. Song, E. Simsek, and Q. H. Liu, “A fast 2-D volume integral equation solver for scattering from inhomogeneous objects in layered media,” Microwave Opt. Technol. Lett. 47, 128-134 (2005).
    [CrossRef]
  7. J. T. Johnson and R. J. Burkholder, “Coupled canonical grid/discrete dipole approach for computing scattering from objects above or below a rough interface,” IEEE Trans. Geosci. Remote Sens. 39, 1214-1220 (2001).
    [CrossRef]
  8. M. E. Shenawee, “Polarimetric scattering from two-layered two-dimensional random rough surfaces with and without buried objects,” IEEE Trans. Geosci. Remote Sens. 42, 67-76 (2004).
    [CrossRef]
  9. D. Colak, R. J. Burkholder, and E. H. Newman, “Multiple sweep method of moments analysis of electromagnetic scattering from 3D objects on ocean-like rough surfaces,” Microwave Opt. Technol. Lett. 49, 241-247 (2007).
    [CrossRef]
  10. L. X. Guo and C. Y. Kim, “Light scattering models for a spherical particle above a slightly dielectric rough surface,” Microwave Opt. Technol. Lett. 33, 142-146 (2002).
    [CrossRef]
  11. R. Wang and L. X. Guo, “Study on electromagnetic scattering from the time-varying lossy dielectric ocean and a moving conducting plate above it,” J. Opt. Soc. Am. A 26, 517-529 (2009).
    [CrossRef]
  12. J. Li, L. X. Guo, and H. Zeng, “FDTD investigation on bistatic scattering from an object above two-layered rough surfaces using UPML absorbing condition,” Prog. Electromagn. Res. 88, 197-211 (2008).
    [CrossRef]
  13. J. Li, L. X. Guo and H. Zeng, “FDTD investigation on the electromagnetic scattering from a object above a randomly rough a sea surface,” Waves Random Complex Media 18, 641-650 (2008).
    [CrossRef]
  14. L. X. Guo, A. Q. Wang, and J. Ma, “Study on EM scattering from 2-D object above 1-D large scale rough surface with low grazing incidence by parallel MOM based on PC clusters,” Prog. Electromagn. Res. 89, 149-166 (2009).
    [CrossRef]
  15. C. Guiffaut and K. Mahdjoubi, “A parallel FDTD algorithm using the MPI library,” IEEE Antennas Propag. Mag. 43, 94-103 (2001).
    [CrossRef]
  16. Y. Kuga and P. Phu, “Experimental studies of millimeter wave scattering in discrete random media and from rough surfaces,” Prog. Electromagn. Res. 14, 37-88 (1996).
  17. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).
  18. 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]
  19. 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, 986-994 (1994).
    [CrossRef]
  20. 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]
  21. 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]
  22. J. A. Kong, Electromagnetic Wave Theory (Wiley, 1986).
  23. 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]
  24. J. Z. Lei, C. H. Liang, W. Ding, and Y. Zhang, “Study on MPI-Based parallel modified conformal FDTD for 3-D electrically large coated objects by using effective parameters,” IEEE Antennas Wireless Propag. Lett. 7, 175-178 (2008).
    [CrossRef]
  25. J. R. Wang and T. J. Schmugge, “An empirical model for the complex dielectric permittivity of soils as function of water content,” IEEE Trans. Geosci. Remote Sens. 18, 288-295 (1980).
    [CrossRef]
  26. L. Tsang, J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves (Wiley, 2001).
  27. J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (IOP, 1991).

2009 (2)

L. X. Guo, A. Q. Wang, and J. Ma, “Study on EM scattering from 2-D object above 1-D large scale rough surface with low grazing incidence by parallel MOM based on PC clusters,” Prog. Electromagn. Res. 89, 149-166 (2009).
[CrossRef]

R. Wang and L. X. Guo, “Study on electromagnetic scattering from the time-varying lossy dielectric ocean and a moving conducting plate above it,” J. Opt. Soc. Am. A 26, 517-529 (2009).
[CrossRef]

2008 (3)

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

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

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

2007 (3)

D. Colak, R. J. Burkholder, and E. H. Newman, “Multiple sweep method of moments analysis of electromagnetic scattering from 3D objects on ocean-like rough surfaces,” Microwave Opt. Technol. Lett. 49, 241-247 (2007).
[CrossRef]

N. Pinel, C. Bourlier, and J. Saillard, “Forward radar propagation over oil slicks on sea surfaces using the Ament model with shadowing effect,” Prog. Electromagn. Res. 76, 95-126 (2007).
[CrossRef]

H. X. Ye and Y. Q. Jin, “A hybrid analytic-numerical algorithm of scattering from an object above a rough surface,” IEEE Trans. Geosci. Remote Sens. 45, 1174-1180 (2007).
[CrossRef]

2005 (3)

Y. Zhang, J. Lu, J. Pacheo, Jr., C. D. Moss, C. O. Ao, T. M. Grzegorczyk, and J. A. Kong, “Mode-expansion method for calculating electromagnetic waves scattered by objects on rough ocean surfaces,” IEEE Trans. Antennas Propag. 53, 1631-1639 (2005).
[CrossRef]

L. P. Song, E. Simsek, and Q. H. Liu, “A fast 2-D volume integral equation solver for scattering from inhomogeneous objects in layered media,” Microwave Opt. Technol. Lett. 47, 128-134 (2005).
[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]

2004 (1)

M. E. Shenawee, “Polarimetric scattering from two-layered two-dimensional random rough surfaces with and without buried objects,” IEEE Trans. Geosci. Remote Sens. 42, 67-76 (2004).
[CrossRef]

2002 (2)

M. R. Pino, J. L. Rodriguez, and F. Obelleiro, “Statistical description of the RCS of 2-D ship models on rough sea surfaces,” Microwave Opt. Technol. Lett. 32, 153-159 (2002).
[CrossRef]

L. X. Guo and C. Y. Kim, “Light scattering models for a spherical particle above a slightly dielectric rough surface,” Microwave Opt. Technol. Lett. 33, 142-146 (2002).
[CrossRef]

2001 (3)

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

J. T. Johnson, “A study of the four-path model for scattering from a object above a half space,” Microwave Opt. Technol. Lett. 30, 130-134 (2001).
[CrossRef]

J. T. Johnson and R. J. Burkholder, “Coupled canonical grid/discrete dipole approach for computing scattering from objects above or below a rough interface,” IEEE Trans. Geosci. Remote Sens. 39, 1214-1220 (2001).
[CrossRef]

2000 (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]

1996 (3)

Y. Kuga and P. Phu, “Experimental studies of millimeter wave scattering in discrete random media and from rough surfaces,” Prog. Electromagn. Res. 14, 37-88 (1996).

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]

1994 (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, 986-994 (1994).
[CrossRef]

1980 (1)

J. R. Wang and T. J. Schmugge, “An empirical model for the complex dielectric permittivity of soils as function of water content,” IEEE Trans. Geosci. Remote Sens. 18, 288-295 (1980).
[CrossRef]

Ao, C. O.

Y. Zhang, J. Lu, J. Pacheo, Jr., C. D. Moss, C. O. Ao, T. M. Grzegorczyk, and J. A. Kong, “Mode-expansion method for calculating electromagnetic waves scattered by objects on rough ocean surfaces,” IEEE Trans. Antennas Propag. 53, 1631-1639 (2005).
[CrossRef]

Bourlier, C.

N. Pinel, C. Bourlier, and J. Saillard, “Forward radar propagation over oil slicks on sea surfaces using the Ament model with shadowing effect,” Prog. Electromagn. Res. 76, 95-126 (2007).
[CrossRef]

Burkholder, R. J.

D. Colak, R. J. Burkholder, and E. H. Newman, “Multiple sweep method of moments analysis of electromagnetic scattering from 3D objects on ocean-like rough surfaces,” Microwave Opt. Technol. Lett. 49, 241-247 (2007).
[CrossRef]

J. T. Johnson and R. J. Burkholder, “Coupled canonical grid/discrete dipole approach for computing scattering from objects above or below a rough interface,” IEEE Trans. Geosci. Remote Sens. 39, 1214-1220 (2001).
[CrossRef]

Colak, D.

D. Colak, R. J. Burkholder, and E. H. Newman, “Multiple sweep method of moments analysis of electromagnetic scattering from 3D objects on ocean-like rough surfaces,” Microwave Opt. Technol. Lett. 49, 241-247 (2007).
[CrossRef]

Ding, K. H.

L. Tsang, J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves (Wiley, 2001).

Ding, W.

J. Z. Lei, C. H. Liang, W. Ding, and Y. Zhang, “Study on MPI-Based parallel modified conformal FDTD for 3-D electrically large coated objects by using effective parameters,” IEEE Antennas Wireless Propag. Lett. 7, 175-178 (2008).
[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, 986-994 (1994).
[CrossRef]

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]

Grzegorczyk, T. M.

Y. Zhang, J. Lu, J. Pacheo, Jr., C. D. Moss, C. O. Ao, T. M. Grzegorczyk, and J. A. Kong, “Mode-expansion method for calculating electromagnetic waves scattered by objects on rough ocean surfaces,” IEEE Trans. Antennas Propag. 53, 1631-1639 (2005).
[CrossRef]

Guiffaut, C.

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

Guo, L. X.

R. Wang and L. X. Guo, “Study on electromagnetic scattering from the time-varying lossy dielectric ocean and a moving conducting plate above it,” J. Opt. Soc. Am. A 26, 517-529 (2009).
[CrossRef]

L. X. Guo, A. Q. Wang, and J. Ma, “Study on EM scattering from 2-D object above 1-D large scale rough surface with low grazing incidence by parallel MOM based on PC clusters,” Prog. Electromagn. Res. 89, 149-166 (2009).
[CrossRef]

J. Li, L. X. Guo and H. Zeng, “FDTD investigation on the electromagnetic scattering from a object above a randomly rough a 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 an object above two-layered rough surfaces using UPML absorbing condition,” Prog. Electromagn. Res. 88, 197-211 (2008).
[CrossRef]

L. X. Guo and C. Y. Kim, “Light scattering models for a spherical particle above a slightly dielectric rough surface,” Microwave Opt. Technol. Lett. 33, 142-146 (2002).
[CrossRef]

Hagness, S. C.

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

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, “A hybrid analytic-numerical algorithm of scattering from an object above a rough surface,” IEEE Trans. Geosci. Remote Sens. 45, 1174-1180 (2007).
[CrossRef]

Johnson, J. T.

J. T. Johnson, “A study of the four-path model for scattering from a object above a half space,” Microwave Opt. Technol. Lett. 30, 130-134 (2001).
[CrossRef]

J. T. Johnson and R. J. Burkholder, “Coupled canonical grid/discrete dipole approach for computing scattering from objects above or below a rough interface,” IEEE Trans. Geosci. Remote Sens. 39, 1214-1220 (2001).
[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]

Kim, C. Y.

L. X. Guo and C. Y. Kim, “Light scattering models for a spherical particle above a slightly dielectric rough surface,” Microwave Opt. Technol. Lett. 33, 142-146 (2002).
[CrossRef]

Kong, J. A.

Y. Zhang, J. Lu, J. Pacheo, Jr., C. D. Moss, C. O. Ao, T. M. Grzegorczyk, and J. A. Kong, “Mode-expansion method for calculating electromagnetic waves scattered by objects on rough ocean surfaces,” IEEE Trans. Antennas Propag. 53, 1631-1639 (2005).
[CrossRef]

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

L. Tsang, J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves (Wiley, 2001).

Kuga, Y.

Y. Kuga and P. Phu, “Experimental studies of millimeter wave scattering in discrete random media and from rough surfaces,” Prog. Electromagn. Res. 14, 37-88 (1996).

Lei, J. Z.

J. Z. Lei, C. H. Liang, W. Ding, and Y. Zhang, “Study on MPI-Based parallel modified conformal FDTD for 3-D electrically large coated objects 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 the electromagnetic scattering from a object above a randomly rough a 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 an object above two-layered rough surfaces using UPML absorbing condition,” Prog. Electromagn. Res. 88, 197-211 (2008).
[CrossRef]

Liang, C. H.

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

Liu, Q. H.

L. P. Song, E. Simsek, and Q. H. Liu, “A fast 2-D volume integral equation solver for scattering from inhomogeneous objects in layered media,” Microwave Opt. Technol. Lett. 47, 128-134 (2005).
[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]

Lu, J.

Y. Zhang, J. Lu, J. Pacheo, Jr., C. D. Moss, C. O. Ao, T. M. Grzegorczyk, and J. A. Kong, “Mode-expansion method for calculating electromagnetic waves scattered by objects on rough ocean surfaces,” IEEE Trans. Antennas Propag. 53, 1631-1639 (2005).
[CrossRef]

Ma, J.

L. X. Guo, A. Q. Wang, and J. Ma, “Study on EM scattering from 2-D object above 1-D large scale rough surface with low grazing incidence by parallel MOM based on PC clusters,” Prog. Electromagn. Res. 89, 149-166 (2009).
[CrossRef]

Mahdjoubi, K.

C. Guiffaut and K. Mahdjoubi, “A parallel FDTD algorithm using the MPI 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]

Moss, C. D.

Y. Zhang, J. Lu, J. Pacheo, Jr., C. D. Moss, C. O. Ao, T. M. Grzegorczyk, and J. A. Kong, “Mode-expansion method for calculating electromagnetic waves scattered by objects on rough ocean surfaces,” IEEE Trans. Antennas Propag. 53, 1631-1639 (2005).
[CrossRef]

Newman, E. H.

D. Colak, R. J. Burkholder, and E. H. Newman, “Multiple sweep method of moments analysis of electromagnetic scattering from 3D objects on ocean-like rough surfaces,” Microwave Opt. Technol. Lett. 49, 241-247 (2007).
[CrossRef]

Obelleiro, F.

M. R. Pino, J. L. Rodriguez, and F. Obelleiro, “Statistical description of the RCS of 2-D ship models on rough sea surfaces,” Microwave Opt. Technol. Lett. 32, 153-159 (2002).
[CrossRef]

Ogilvy, J. A.

J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (IOP, 1991).

Pacheo, J.

Y. Zhang, J. Lu, J. Pacheo, Jr., C. D. Moss, C. O. Ao, T. M. Grzegorczyk, and J. A. Kong, “Mode-expansion method for calculating electromagnetic waves scattered by objects on rough ocean surfaces,” IEEE Trans. Antennas Propag. 53, 1631-1639 (2005).
[CrossRef]

Phu, P.

Y. Kuga and P. Phu, “Experimental studies of millimeter wave scattering in discrete random media and from rough surfaces,” Prog. Electromagn. Res. 14, 37-88 (1996).

Pinel, N.

N. Pinel, C. Bourlier, and J. Saillard, “Forward radar propagation over oil slicks on sea surfaces using the Ament model with shadowing effect,” Prog. Electromagn. Res. 76, 95-126 (2007).
[CrossRef]

Pino, M. R.

M. R. Pino, J. L. Rodriguez, and F. Obelleiro, “Statistical description of the RCS of 2-D ship models on rough sea surfaces,” Microwave Opt. Technol. Lett. 32, 153-159 (2002).
[CrossRef]

Rodriguez, J. L.

M. R. Pino, J. L. Rodriguez, and F. Obelleiro, “Statistical description of the RCS of 2-D ship models on rough sea surfaces,” Microwave Opt. Technol. Lett. 32, 153-159 (2002).
[CrossRef]

Saillard, J.

N. Pinel, C. Bourlier, and J. Saillard, “Forward radar propagation over oil slicks on sea surfaces using the Ament model with shadowing effect,” Prog. Electromagn. Res. 76, 95-126 (2007).
[CrossRef]

Schmugge, T. J.

J. R. Wang and T. J. Schmugge, “An empirical model for the complex dielectric permittivity of soils as function of water content,” IEEE Trans. Geosci. Remote Sens. 18, 288-295 (1980).
[CrossRef]

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, 986-994 (1994).
[CrossRef]

Shenawee, M. E.

M. E. Shenawee, “Polarimetric scattering from two-layered two-dimensional random rough surfaces with and without buried objects,” IEEE Trans. Geosci. Remote Sens. 42, 67-76 (2004).
[CrossRef]

Simsek, E.

L. P. Song, E. Simsek, and Q. H. Liu, “A fast 2-D volume integral equation solver for scattering from inhomogeneous objects in layered media,” Microwave Opt. Technol. Lett. 47, 128-134 (2005).
[CrossRef]

Song, L. P.

L. P. Song, E. Simsek, and Q. H. Liu, “A fast 2-D volume integral equation solver for scattering from inhomogeneous objects in layered media,” Microwave Opt. Technol. Lett. 47, 128-134 (2005).
[CrossRef]

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 (Artech House, 2005).

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, 986-994 (1994).
[CrossRef]

Tsang, L.

L. Tsang, J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves (Wiley, 2001).

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]

Wang, A. Q.

L. X. Guo, A. Q. Wang, and J. Ma, “Study on EM scattering from 2-D object above 1-D large scale rough surface with low grazing incidence by parallel MOM based on PC clusters,” Prog. Electromagn. Res. 89, 149-166 (2009).
[CrossRef]

Wang, J. R.

J. R. Wang and T. J. Schmugge, “An empirical model for the complex dielectric permittivity of soils as function of water content,” IEEE Trans. Geosci. Remote Sens. 18, 288-295 (1980).
[CrossRef]

Wang, R.

Ye, H. X.

H. X. Ye and Y. Q. Jin, “A hybrid analytic-numerical algorithm of scattering from an object above a rough surface,” IEEE Trans. Geosci. Remote Sens. 45, 1174-1180 (2007).
[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 bistatic scattering from an object above two-layered rough surfaces using UPML absorbing condition,” Prog. Electromagn. Res. 88, 197-211 (2008).
[CrossRef]

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

Zhang, Y.

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

Y. Zhang, J. Lu, J. Pacheo, Jr., C. D. Moss, C. O. Ao, T. M. Grzegorczyk, and J. A. Kong, “Mode-expansion method for calculating electromagnetic waves scattered by objects on rough ocean surfaces,” IEEE Trans. Antennas Propag. 53, 1631-1639 (2005).
[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)

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]

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

IEEE Antennas Wireless Propag. Lett. (1)

J. Z. Lei, C. H. Liang, W. Ding, and Y. Zhang, “Study on MPI-Based parallel modified conformal FDTD for 3-D electrically large coated objects by using effective parameters,” IEEE Antennas Wireless Propag. Lett. 7, 175-178 (2008).
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IEEE Trans. Geosci. Remote Sens. (5)

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IEEE Trans. Microwave Theory Tech. (1)

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J. Opt. Soc. Am. A (1)

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Figures (11)

Fig. 1
Fig. 1

Two-dimensional rough surface model l x = l y = 1.0 λ : (a) δ = 0.06 λ , (b) δ = 0.1 λ .

Fig. 2
Fig. 2

FDTD division of the composite model.

Fig. 3
Fig. 3

Geometry of the incident wave and scattered wave in the coordinate x y z .

Fig. 4
Fig. 4

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

Fig. 5
Fig. 5

Comparison of the two different methods for the bistatic scattering from a 2-D rough surface, θ i = 20 ° : (a) PEC (b) dielectric.

Fig. 6
Fig. 6

(a) Scattering coefficient from one composite model realization for different processors. (b) Scalability of parallel FDTD algorithm for different processors.

Fig. 7
Fig. 7

Bistatic scattering coefficient from the composite model for different polarizations. (a) HH, θ i = 20 ° . (b)VH, θ i = 20 ° . (c) VV, θ i = 50 ° . (d)HV, θ i = 50 ° .

Fig. 8
Fig. 8

Bistatic scattering coefficient for different water content, θ i = 30 ° : (a) HH polarization, (b) VH polarization.

Fig. 9
Fig. 9

Bistatic scattering coefficient for different surface roughness: (a) rough surface, (b) composite model.

Fig. 10
Fig. 10

Bistatic scattering coefficient from the composite model for differing radii r 0 : (a) HH polarization, (b) VH polarization.

Fig. 11
Fig. 11

Bistatic scattering from the composite model versus azimuthal angle, θ i = 50 ° and θ s = 50 ° : (a) co-polarized scattering, (b) cross-polarized scattering.

Tables (1)

Tables Icon

Table 1 Comparison of Computation Time with One Composite Model Realization for Different Numbers of Processors

Equations (23)

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f ( x , y ) = 1 L × L m = N 2 N 2 1 n = N 2 N 2 1 F ( K x m , K y n ) exp ( j K x m x + j K y n y ) ,
F ( K x m , K y n ) = 2 π L W ( K x m , K y n ) { N ( 0 , 1 ) + j N ( 0 , 1 ) 2 , m , n 0 and N 2 N ( 0 , 1 ) , m , n = 0 or N 2 } ,
F ( K x m , K y n ) = F * ( K x m , K y n ) , F ( K x m , K y n ) = F * ( K x m , K y n ) .
W ( K x m , K y n ) = l x l y δ 2 4 π exp ( K x m 2 l x 2 4 K y n 2 l y 2 4 ) ,
E x n + 1 ( i + 1 2 , j , k ) = C A ( i + 1 2 , j , k ) E x n ( i + 1 2 , j , k ) + C B ( i + 1 2 , j , k ) [ H z n + 1 2 ( i + 1 2 , j + 1 2 , k ) H z n + 1 2 ( i + 1 2 , j 1 2 , k ) Δ y H y n + 1 2 ( i + 1 2 , j , k + 1 2 ) H y n + 1 2 ( i + 1 2 , j , k 1 2 ) Δ z ] ,
H x n + 1 2 ( i , j + 1 2 , k + 1 2 ) = C P ( i , j + 1 2 , k + 1 2 ) H x n 1 2 ( i , j + 1 2 , k + 1 2 ) C Q ( i , j + 1 2 , k + 1 2 ) [ E z n ( i , j + 1 , k + 1 2 ) E z n ( i , j , k + 1 2 ) Δ y E y n ( i , j + 1 2 , k + 1 ) E y n ( i , j + 1 2 , k ) Δ z ] .
E x n + 1 ( i + 1 2 , j , k ) = E x n ( i + 1 2 , j , k ) + Δ t ϵ [ × H ] x n + 1 2 Δ t ϵ H y , i n + 1 2 ( i + 1 2 , j , k + 1 2 ) Δ z ,
E y n + 1 ( i , j + 1 2 , k ) = E y n ( i , j + 1 2 , k ) + Δ t ϵ [ × H ] y n + 1 2 + Δ t ϵ H x , i n + 1 2 ( i , j + 1 2 , k + 1 2 ) Δ z ,
H x n + 1 2 ( i , j + 1 2 , k + 1 2 ) = H x n 1 2 ( i , j + 1 2 , k + 1 2 ) Δ t ϵ [ × E ] x n + Δ t μ E y , i n ( i , j + 1 2 , k ) Δ z ,
H y n + 1 2 ( i + 1 2 , j , k + 1 2 ) = H y n 1 2 ( i + 1 2 , j , k + 1 2 ) Δ t ϵ [ × E ] y n Δ t μ E x , i n ( i + 1 2 , j , k ) Δ z ,
G ( x , y ) = exp { [ ( x x 0 ) 2 + ( y y 0 ) 2 ] ( cos θ i T ) 2 } ,
P x n + 1 ( i + 1 2 , j , k ) = ϵ 1 ( m ) Δ t 0.5 σ 1 ( m ) ϵ 1 ( m ) Δ t + 0.5 σ 1 ( m ) P x n ( i + 1 2 , j , k ) + 1 Δ ϵ 1 ( m ) Δ t + 0.5 σ 1 ( m ) [ H z n + 1 2 ( i + 1 2 , j + 1 2 , k ) H z n + 1 2 ( i + 1 2 , j 1 2 , k ) H y n + 1 2 ( i + 1 2 , j , k + 1 2 ) + H y n + 1 2 ( i + 1 2 , j , k 1 2 ) ] ,
P x n + 1 ( i + 1 2 , j , k ) = k y ( m ) Δ t σ y ( m ) ( 2 ϵ 0 ) k y ( m ) Δ t + σ y ( m ) ( 2 ϵ 0 ) P x n ( i + 1 2 , j , k ) + 1 Δ t k y ( m ) Δ t + σ y ( m ) ( 2 ϵ 0 ) [ P x n + 1 ( i + 1 2 , j , k ) P x n ( i + 1 2 , j , k ) ] ,
E x n + 1 ( i + 1 2 , j , k ) = k z ( m ) Δ t σ z ( m ) ( 2 ϵ 0 ) k z ( m ) Δ t + σ z ( m ) ( 2 ϵ 0 ) E x n ( i + 1 2 , j , k ) + k x ( m ) Δ t + σ x ( m ) ( 2 ϵ 0 ) k z ( m ) Δ t + σ z ( m ) ( 2 ϵ 0 ) P x n + 1 ( i + 1 2 , j , k ) k x ( m ) Δ t σ x ( m ) ( 2 ϵ 0 ) k z ( m ) Δ t + σ z ( m ) ( 2 ϵ 0 ) P x n ( i + 1 2 , j , k ) ,
B x n + 1 2 ( i , j + 1 2 , k + 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 , k + 1 2 ) 1 Δ k y ( m ) Δ t + σ y ( m ) ( 2 ϵ 0 ) [ E z n ( i , j + 1 , k + 1 2 ) E z n ( i , j , k + 1 2 ) E y n ( i , j + 1 2 , k + 1 ) + E y n ( i , j + 1 2 , k ) ] ,
H x n + 1 2 ( i , j + 1 2 , k + 1 2 ) = k z ( m ) Δ t σ z ( m ) ( 2 ϵ 0 ) k z ( m ) Δ t + σ z ( m ) ( 2 ϵ 0 ) H x n 1 2 ( i , j + 1 2 , k + 1 2 ) + 1 μ 1 k x ( m ) Δ t + σ x ( m ) ( 2 ϵ 0 ) k z ( m ) Δ t + σ z ( m ) ( 2 ϵ 0 ) B x n + 1 2 ( i , j + 1 2 , k + 1 2 ) 1 μ 1 k x ( m ) Δ t σ x ( m ) ( 2 ϵ 0 ) k z ( m ) Δ t + σ z ( m ) ( 2 ϵ 0 ) B x n 1 2 ( i , j + 1 2 , k + 1 2 ) ,
{ σ x ( x ) = ( x d ) M σ x , max , κ x ( x ) = 1 + ( κ x , max 1 ) ( x d ) M , } ( 0 x d ) .
E θ = θ ̂ ( j k ̃ exp ( j k ̃ r ) 4 π r ) [ z ( f x cos θ s cos ϕ s + f y cos θ s sin ϕ s ) + ( f m x sin ϕ s + f m y cos ϕ s ) ] ,
E ϕ = ϕ ̂ j k ̃ exp ( j k ̃ r ) 4 π r [ z ( f x sin ϕ s f y cos ϕ s ) + ( f m x cos θ s cos ϕ s + f m y cos θ s sin ϕ s ) ] ,
σ HH = lim r 4 π r 2 S | E θ | 2 | E i | 2 σ VH = lim r 4 π r 2 S | E ϕ | 2 | E i | 2 ( α = 0 o ) ,
σ HV = lim r 4 π r 2 S | E θ | 2 | E i | 2 σ VV = lim r 4 π r 2 S | E ϕ | 2 | E i | 2 ( α = 90 o ) .
S = T 1 T n ,
E = S n × 100 % .

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