Abstract

A fast numerical method has been proposed in this paper for calculating the electromagnetic scattering from a perfectly electric conducting object above a two-layered dielectric rough surface. The focus in this study is large incidence. The parallel fast multipole method is combined with the method of moments for fast implementation of the scattering from this composite model. The biconjugate gradient method is adopted to solve the unsymmetrical matrix equation and parallelized. The simulating time and parallel speedup ratio with different processors are provided. Several numerical results are shown and analyzed to discuss the influences of the parameters of the rough surface, the object, and the intermediate medium on the bistatic scattering.

© 2011 Optical Society of America

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  1. E. I. Thorsos, “The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum,” J. Acoust. Soc. Am. 83, 78–92 (1988).
    [CrossRef]
  2. Y. Zhang, Y. E. Yang, H. Braunisch, and J. A. Kong, “Electromagnetic wave interaction of conducting object with rough surface by hybrid SPM/MOM technique,” Prog. Electromagn. Res. 22, 315–335 (1999).
    [CrossRef]
  3. Z. X. Li, and Y. Q. Jin, “Bistatic scattering from a fractal dynamic rough sea surface with a ship presence at low grazing-angle incidence using the GFBM/SAA,” Microw. Opt. Technol. Lett. 31, 146–151 (2001).
    [CrossRef]
  4. 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]
  5. L. X. Guo, A. Q. Wang, and J. Ma, “Study on EM scattering from 2-D target 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]
  6. X. Wang, Y. B. Gan, and L. W. Li, “Electromagnetic scattering by partially buried PEC cylinder at the dielectric rough surface interface: TM case,” IEEE Antennas Wireless Propag. Lett. 2, 319–323 (2003).
    [CrossRef]
  7. X. Wang, C. F. Wang, Y. B. Gan, and L. W. Li, “Electromagnetic scattering from a circular target above or below rough surface,” Prog. Electromagn. Res. 40, 207–227 (2003).
    [CrossRef]
  8. X. Wang and L. W. Li, “Numerical characterization of bistatic scattering from PEC cylinder partially embedded in a dielectric rough surface interface: horizontal polarization,” Prog. Electromagn. Res. 91, 35–51 (2009).
    [CrossRef]
  9. N. T. Thành, H. Sahli, and D. N. Hào, “Finite-difference methods and validity of a thermal model for landmine detection with soil property estimation,” IEEE Trans. Geosci. Remote Sens. 45, 656–674 (2007).
    [CrossRef]
  10. P. G. Rodríguez and A. D. Kim, “Light propagation in two-layer tissues with an irregular interface,” J. Opt. Soc. Am. A 25, 64–73 (2008).
    [CrossRef]
  11. 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,” Prog. Electromagn. Res. 88, 197–211 (2008).
    [CrossRef]
  12. C. H. Kuo and M. Moghaddam, “Electromagnetic scattering from a buried cylinder in layered media with rough interfaces,” IEEE Trans. Antennas Propag. 54, 2392–2401(2006).
    [CrossRef]
  13. C. H. Kuo and M. Moghaddam, “A theoretical analysis of backscattering enhancement due to surface plasmons from multilayer structures with rough interfaces,” IEEE Trans. Antennas Propagat. 56, 1133–1143 (2008).
    [CrossRef]
  14. R. F. Harrington, Filed Computation by Moment Method (IEEE, 1993).
    [CrossRef]
  15. C. D. Moss, T. M. Grzegorczyk, H. C. Han, and J. A. Kong, “Forward-backward method with spectral acceleration for scattering from layered rough surfaces,” IEEE Trans. Antennas Propag. 54, 1006–1016 (2006).
    [CrossRef]
  16. N. Déchamps, N. de Beaucoudrey, C. Bourlier, and S. Toutain, “Fast numerical method for electromagnetic scattering by rough layered interfaces: propagation-inside-layer expansion method,” J. Opt. Soc. Am. A 23, 359–369 (2006).
    [CrossRef]
  17. 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]
  18. L. Tsang, J. A. Kong, K. H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley, 2001).
    [CrossRef]
  19. C. T. Kelley, Iterative Methods for Linear and Nonlinear Equations (Society for Industrial and Applied Mathematics, 1995).
    [CrossRef]
  20. A. Q. Wang, L. X. Guo, and C. Chai, “Numerical simulations of electromagnetic scattering from 2D rough surface: geometric modeling by NURBS surface,” J. Electromagn. Waves Appl. 24, 1315–1328 (2010).
    [CrossRef]
  21. R. Wang and L. X. Guo, “Study on EM 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]
  22. L. X. Guo, J. Li, and H. Zeng, “Bistatic scattering from a three-dimensional object above a two- dimensional randomly rough surface modeled with the parallel FDTD approach,” J. Opt. Soc. Am. A 26, 2383–2392 (2009).
    [CrossRef]
  23. J. Li, L. X. Guo, H. Zeng, and X. B. Han, “Message-passing-interface-based parallel FDTD investigation on the EM scattering from a 1-D rough sea surface using uniaxial perfectly matched layer absorbing boundary,” J. Opt. Soc. Am. A 26, 1494–1502 (2009).
    [CrossRef]
  24. C. C. Lu and W. C. Chew, “Fast algorithm for solving hybrid integral equations,” IEE Proc. H, Microw. Antennas Propag. 140, 455–460 (1993).
    [CrossRef]
  25. W. C. Chew, J. M. Jin, E. Michielssen, and J. Song, Fast and Efficient Algorithms in Computational Electromagnetics(Artech House, 2001).
  26. J. Curtis, “Dielectric properties of soils: various sites in Bosnia,” Waterways Experiment, Station Data Rep. (U. S. Army Corps of Engineers, 1996).

2010 (1)

A. Q. Wang, L. X. Guo, and C. Chai, “Numerical simulations of electromagnetic scattering from 2D rough surface: geometric modeling by NURBS surface,” J. Electromagn. Waves Appl. 24, 1315–1328 (2010).
[CrossRef]

2009 (5)

2008 (3)

C. H. Kuo and M. Moghaddam, “A theoretical analysis of backscattering enhancement due to surface plasmons from multilayer structures with rough interfaces,” IEEE Trans. Antennas Propagat. 56, 1133–1143 (2008).
[CrossRef]

P. G. Rodríguez and A. D. Kim, “Light propagation in two-layer tissues with an irregular interface,” J. Opt. Soc. Am. A 25, 64–73 (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,” Prog. Electromagn. Res. 88, 197–211 (2008).
[CrossRef]

2007 (1)

N. T. Thành, H. Sahli, and D. N. Hào, “Finite-difference methods and validity of a thermal model for landmine detection with soil property estimation,” IEEE Trans. Geosci. Remote Sens. 45, 656–674 (2007).
[CrossRef]

2006 (3)

C. D. Moss, T. M. Grzegorczyk, H. C. Han, and J. A. Kong, “Forward-backward method with spectral acceleration for scattering from layered rough surfaces,” IEEE Trans. Antennas Propag. 54, 1006–1016 (2006).
[CrossRef]

N. Déchamps, N. de Beaucoudrey, C. Bourlier, and S. Toutain, “Fast numerical method for electromagnetic scattering by rough layered interfaces: propagation-inside-layer expansion method,” J. Opt. Soc. Am. A 23, 359–369 (2006).
[CrossRef]

C. H. Kuo and M. Moghaddam, “Electromagnetic scattering from a buried cylinder in layered media with rough interfaces,” IEEE Trans. Antennas Propag. 54, 2392–2401(2006).
[CrossRef]

2004 (2)

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]

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 (2)

X. Wang, Y. B. Gan, and L. W. Li, “Electromagnetic scattering by partially buried PEC cylinder at the dielectric rough surface interface: TM case,” IEEE Antennas Wireless Propag. Lett. 2, 319–323 (2003).
[CrossRef]

X. Wang, C. F. Wang, Y. B. Gan, and L. W. Li, “Electromagnetic scattering from a circular target above or below rough surface,” Prog. Electromagn. Res. 40, 207–227 (2003).
[CrossRef]

2001 (1)

Z. X. Li, and Y. Q. Jin, “Bistatic scattering from a fractal dynamic rough sea surface with a ship presence at low grazing-angle incidence using the GFBM/SAA,” Microw. Opt. Technol. Lett. 31, 146–151 (2001).
[CrossRef]

1999 (1)

Y. Zhang, Y. E. Yang, H. Braunisch, and J. A. Kong, “Electromagnetic wave interaction of conducting object with rough surface by hybrid SPM/MOM technique,” Prog. Electromagn. Res. 22, 315–335 (1999).
[CrossRef]

1993 (1)

C. C. Lu and W. C. Chew, “Fast algorithm for solving hybrid integral equations,” IEE Proc. H, Microw. Antennas Propag. 140, 455–460 (1993).
[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, 78–92 (1988).
[CrossRef]

Ao, C. O.

L. Tsang, J. A. Kong, K. H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley, 2001).
[CrossRef]

Bourlier, C.

Braunisch, H.

Y. Zhang, Y. E. Yang, H. Braunisch, and J. A. Kong, “Electromagnetic wave interaction of conducting object with rough surface by hybrid SPM/MOM technique,” Prog. Electromagn. Res. 22, 315–335 (1999).
[CrossRef]

Chai, C.

A. Q. Wang, L. X. Guo, and C. Chai, “Numerical simulations of electromagnetic scattering from 2D rough surface: geometric modeling by NURBS surface,” J. Electromagn. Waves Appl. 24, 1315–1328 (2010).
[CrossRef]

Chew, W. C.

C. C. Lu and W. C. Chew, “Fast algorithm for solving hybrid integral equations,” IEE Proc. H, Microw. Antennas Propag. 140, 455–460 (1993).
[CrossRef]

W. C. Chew, J. M. Jin, E. Michielssen, and J. Song, Fast and Efficient Algorithms in Computational Electromagnetics(Artech House, 2001).

Curtis, J.

J. Curtis, “Dielectric properties of soils: various sites in Bosnia,” Waterways Experiment, Station Data Rep. (U. S. Army Corps of Engineers, 1996).

de Beaucoudrey, N.

Déchamps, N.

Ding, K. H.

L. Tsang, J. A. Kong, K. H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley, 2001).
[CrossRef]

Gan, Y. B.

X. Wang, Y. B. Gan, and L. W. Li, “Electromagnetic scattering by partially buried PEC cylinder at the dielectric rough surface interface: TM case,” IEEE Antennas Wireless Propag. Lett. 2, 319–323 (2003).
[CrossRef]

X. Wang, C. F. Wang, Y. B. Gan, and L. W. Li, “Electromagnetic scattering from a circular target above or below rough surface,” Prog. Electromagn. Res. 40, 207–227 (2003).
[CrossRef]

Grzegorczyk, T. M.

C. D. Moss, T. M. Grzegorczyk, H. C. Han, and J. A. Kong, “Forward-backward method with spectral acceleration for scattering from layered rough surfaces,” IEEE Trans. Antennas Propag. 54, 1006–1016 (2006).
[CrossRef]

Guo, L. X.

A. Q. Wang, L. X. Guo, and C. Chai, “Numerical simulations of electromagnetic scattering from 2D rough surface: geometric modeling by NURBS surface,” J. Electromagn. Waves Appl. 24, 1315–1328 (2010).
[CrossRef]

J. Li, L. X. Guo, H. Zeng, and X. B. Han, “Message-passing-interface-based parallel FDTD investigation on the EM scattering from a 1-D rough sea surface using uniaxial perfectly matched layer absorbing boundary,” J. Opt. Soc. Am. A 26, 1494–1502 (2009).
[CrossRef]

R. Wang and L. X. Guo, “Study on EM 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, J. Li, and H. Zeng, “Bistatic scattering from a three-dimensional object above a two- dimensional randomly rough surface modeled with the parallel FDTD approach,” J. Opt. Soc. Am. A 26, 2383–2392 (2009).
[CrossRef]

L. X. Guo, A. Q. Wang, and J. Ma, “Study on EM scattering from 2-D target 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 bistatic scattering from a target above two-layered rough surfaces using UPML absorbing condition,” Prog. Electromagn. Res. 88, 197–211 (2008).
[CrossRef]

Han, H. C.

C. D. Moss, T. M. Grzegorczyk, H. C. Han, and J. A. Kong, “Forward-backward method with spectral acceleration for scattering from layered rough surfaces,” IEEE Trans. Antennas Propag. 54, 1006–1016 (2006).
[CrossRef]

Han, X. B.

Hào, D. N.

N. T. Thành, H. Sahli, and D. N. Hào, “Finite-difference methods and validity of a thermal model for landmine detection with soil property estimation,” IEEE Trans. Geosci. Remote Sens. 45, 656–674 (2007).
[CrossRef]

Harrington, R. F.

R. F. Harrington, Filed Computation by Moment Method (IEEE, 1993).
[CrossRef]

Jin, J. M.

W. C. Chew, J. M. Jin, E. Michielssen, and J. Song, Fast and Efficient Algorithms in Computational Electromagnetics(Artech House, 2001).

Jin, Y. Q.

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]

Z. X. Li, and Y. Q. Jin, “Bistatic scattering from a fractal dynamic rough sea surface with a ship presence at low grazing-angle incidence using the GFBM/SAA,” Microw. Opt. Technol. Lett. 31, 146–151 (2001).
[CrossRef]

Kelley, C. T.

C. T. Kelley, Iterative Methods for Linear and Nonlinear Equations (Society for Industrial and Applied Mathematics, 1995).
[CrossRef]

Kim, A. D.

Kong, J. A.

C. D. Moss, T. M. Grzegorczyk, H. C. Han, and J. A. Kong, “Forward-backward method with spectral acceleration for scattering from layered rough surfaces,” IEEE Trans. Antennas Propag. 54, 1006–1016 (2006).
[CrossRef]

Y. Zhang, Y. E. Yang, H. Braunisch, and J. A. Kong, “Electromagnetic wave interaction of conducting object with rough surface by hybrid SPM/MOM technique,” Prog. Electromagn. Res. 22, 315–335 (1999).
[CrossRef]

L. Tsang, J. A. Kong, K. H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley, 2001).
[CrossRef]

Kuo, C. H.

C. H. Kuo and M. Moghaddam, “A theoretical analysis of backscattering enhancement due to surface plasmons from multilayer structures with rough interfaces,” IEEE Trans. Antennas Propagat. 56, 1133–1143 (2008).
[CrossRef]

C. H. Kuo and M. Moghaddam, “Electromagnetic scattering from a buried cylinder in layered media with rough interfaces,” IEEE Trans. Antennas Propag. 54, 2392–2401(2006).
[CrossRef]

Li, J.

Li, L. W.

X. Wang and L. W. Li, “Numerical characterization of bistatic scattering from PEC cylinder partially embedded in a dielectric rough surface interface: horizontal polarization,” Prog. Electromagn. Res. 91, 35–51 (2009).
[CrossRef]

X. Wang, C. F. Wang, Y. B. Gan, and L. W. Li, “Electromagnetic scattering from a circular target above or below rough surface,” Prog. Electromagn. Res. 40, 207–227 (2003).
[CrossRef]

X. Wang, Y. B. Gan, and L. W. Li, “Electromagnetic scattering by partially buried PEC cylinder at the dielectric rough surface interface: TM case,” IEEE Antennas Wireless Propag. Lett. 2, 319–323 (2003).
[CrossRef]

Li, Z. X.

Z. X. Li, and Y. Q. Jin, “Bistatic scattering from a fractal dynamic rough sea surface with a ship presence at low grazing-angle incidence using the GFBM/SAA,” Microw. Opt. Technol. Lett. 31, 146–151 (2001).
[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]

Lu, C. C.

C. C. Lu and W. C. Chew, “Fast algorithm for solving hybrid integral equations,” IEE Proc. H, Microw. Antennas Propag. 140, 455–460 (1993).
[CrossRef]

Ma, J.

L. X. Guo, A. Q. Wang, and J. Ma, “Study on EM scattering from 2-D target 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]

Michielssen, E.

W. C. Chew, J. M. Jin, E. Michielssen, and J. Song, Fast and Efficient Algorithms in Computational Electromagnetics(Artech House, 2001).

Moghaddam, M.

C. H. Kuo and M. Moghaddam, “A theoretical analysis of backscattering enhancement due to surface plasmons from multilayer structures with rough interfaces,” IEEE Trans. Antennas Propagat. 56, 1133–1143 (2008).
[CrossRef]

C. H. Kuo and M. Moghaddam, “Electromagnetic scattering from a buried cylinder in layered media with rough interfaces,” IEEE Trans. Antennas Propag. 54, 2392–2401(2006).
[CrossRef]

Moss, C. D.

C. D. Moss, T. M. Grzegorczyk, H. C. Han, and J. A. Kong, “Forward-backward method with spectral acceleration for scattering from layered rough surfaces,” IEEE Trans. Antennas Propag. 54, 1006–1016 (2006).
[CrossRef]

Rodríguez, P. G.

Sahli, H.

N. T. Thành, H. Sahli, and D. N. Hào, “Finite-difference methods and validity of a thermal model for landmine detection with soil property estimation,” IEEE Trans. Geosci. Remote Sens. 45, 656–674 (2007).
[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]

Song, J.

W. C. Chew, J. M. Jin, E. Michielssen, and J. Song, Fast and Efficient Algorithms in Computational Electromagnetics(Artech House, 2001).

Thành, N. T.

N. T. Thành, H. Sahli, and D. N. Hào, “Finite-difference methods and validity of a thermal model for landmine detection with soil property estimation,” IEEE Trans. Geosci. Remote Sens. 45, 656–674 (2007).
[CrossRef]

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, 78–92 (1988).
[CrossRef]

Toutain, S.

Tsang, L.

L. Tsang, J. A. Kong, K. H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley, 2001).
[CrossRef]

Wang, A. Q.

A. Q. Wang, L. X. Guo, and C. Chai, “Numerical simulations of electromagnetic scattering from 2D rough surface: geometric modeling by NURBS surface,” J. Electromagn. Waves Appl. 24, 1315–1328 (2010).
[CrossRef]

L. X. Guo, A. Q. Wang, and J. Ma, “Study on EM scattering from 2-D target 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, C. F.

X. Wang, C. F. Wang, Y. B. Gan, and L. W. Li, “Electromagnetic scattering from a circular target above or below rough surface,” Prog. Electromagn. Res. 40, 207–227 (2003).
[CrossRef]

Wang, R.

Wang, X.

X. Wang and L. W. Li, “Numerical characterization of bistatic scattering from PEC cylinder partially embedded in a dielectric rough surface interface: horizontal polarization,” Prog. Electromagn. Res. 91, 35–51 (2009).
[CrossRef]

X. Wang, C. F. Wang, Y. B. Gan, and L. W. Li, “Electromagnetic scattering from a circular target above or below rough surface,” Prog. Electromagn. Res. 40, 207–227 (2003).
[CrossRef]

X. Wang, Y. B. Gan, and L. W. Li, “Electromagnetic scattering by partially buried PEC cylinder at the dielectric rough surface interface: TM case,” IEEE Antennas Wireless Propag. Lett. 2, 319–323 (2003).
[CrossRef]

Yang, Y. E.

Y. Zhang, Y. E. Yang, H. Braunisch, and J. A. Kong, “Electromagnetic wave interaction of conducting object with rough surface by hybrid SPM/MOM technique,” Prog. Electromagn. Res. 22, 315–335 (1999).
[CrossRef]

Zeng, H.

Zhang, Y.

Y. Zhang, Y. E. Yang, H. Braunisch, and J. A. Kong, “Electromagnetic wave interaction of conducting object with rough surface by hybrid SPM/MOM technique,” Prog. Electromagn. Res. 22, 315–335 (1999).
[CrossRef]

IEE Proc. H, Microw. Antennas Propag. (1)

C. C. Lu and W. C. Chew, “Fast algorithm for solving hybrid integral equations,” IEE Proc. H, Microw. Antennas Propag. 140, 455–460 (1993).
[CrossRef]

IEEE Antennas Wireless Propag. Lett. (1)

X. Wang, Y. B. Gan, and L. W. Li, “Electromagnetic scattering by partially buried PEC cylinder at the dielectric rough surface interface: TM case,” IEEE Antennas Wireless Propag. Lett. 2, 319–323 (2003).
[CrossRef]

IEEE Trans. Antennas Propag. (3)

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]

C. H. Kuo and M. Moghaddam, “Electromagnetic scattering from a buried cylinder in layered media with rough interfaces,” IEEE Trans. Antennas Propag. 54, 2392–2401(2006).
[CrossRef]

C. D. Moss, T. M. Grzegorczyk, H. C. Han, and J. A. Kong, “Forward-backward method with spectral acceleration for scattering from layered rough surfaces,” IEEE Trans. Antennas Propag. 54, 1006–1016 (2006).
[CrossRef]

IEEE Trans. Antennas Propagat. (1)

C. H. Kuo and M. Moghaddam, “A theoretical analysis of backscattering enhancement due to surface plasmons from multilayer structures with rough interfaces,” IEEE Trans. Antennas Propagat. 56, 1133–1143 (2008).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (2)

N. T. Thành, H. Sahli, and D. N. Hào, “Finite-difference methods and validity of a thermal model for landmine detection with soil property estimation,” IEEE Trans. Geosci. Remote Sens. 45, 656–674 (2007).
[CrossRef]

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]

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, 78–92 (1988).
[CrossRef]

J. Electromagn. Waves Appl. (1)

A. Q. Wang, L. X. Guo, and C. Chai, “Numerical simulations of electromagnetic scattering from 2D rough surface: geometric modeling by NURBS surface,” J. Electromagn. Waves Appl. 24, 1315–1328 (2010).
[CrossRef]

J. Opt. Soc. Am. A (5)

Microw. Opt. Technol. Lett. (1)

Z. X. Li, and Y. Q. Jin, “Bistatic scattering from a fractal dynamic rough sea surface with a ship presence at low grazing-angle incidence using the GFBM/SAA,” Microw. Opt. Technol. Lett. 31, 146–151 (2001).
[CrossRef]

Prog. Electromagn. Res. (5)

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,” Prog. Electromagn. Res. 88, 197–211 (2008).
[CrossRef]

X. Wang, C. F. Wang, Y. B. Gan, and L. W. Li, “Electromagnetic scattering from a circular target above or below rough surface,” Prog. Electromagn. Res. 40, 207–227 (2003).
[CrossRef]

X. Wang and L. W. Li, “Numerical characterization of bistatic scattering from PEC cylinder partially embedded in a dielectric rough surface interface: horizontal polarization,” Prog. Electromagn. Res. 91, 35–51 (2009).
[CrossRef]

Y. Zhang, Y. E. Yang, H. Braunisch, and J. A. Kong, “Electromagnetic wave interaction of conducting object with rough surface by hybrid SPM/MOM technique,” Prog. Electromagn. Res. 22, 315–335 (1999).
[CrossRef]

L. X. Guo, A. Q. Wang, and J. Ma, “Study on EM scattering from 2-D target 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]

Other (5)

R. F. Harrington, Filed Computation by Moment Method (IEEE, 1993).
[CrossRef]

L. Tsang, J. A. Kong, K. H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley, 2001).
[CrossRef]

C. T. Kelley, Iterative Methods for Linear and Nonlinear Equations (Society for Industrial and Applied Mathematics, 1995).
[CrossRef]

W. C. Chew, J. M. Jin, E. Michielssen, and J. Song, Fast and Efficient Algorithms in Computational Electromagnetics(Artech House, 2001).

J. Curtis, “Dielectric properties of soils: various sites in Bosnia,” Waterways Experiment, Station Data Rep. (U. S. Army Corps of Engineers, 1996).

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Figures (10)

Fig. 1
Fig. 1

Geometry for EM scattering from an object above a two-layered rough surface at a large incident angle.

Fig. 2
Fig. 2

Assignment of the impedance matrices to the corresponding processor.

Fig. 3
Fig. 3

Simulating time and parallel speedup ratio of different processors.

Fig. 4
Fig. 4

BSC from a two-layered rough surface with or without an object above it.

Fig. 5
Fig. 5

BSC from an object above a two-layered rough surface with different radii.

Fig. 6
Fig. 6

BSC from an object above a two-layered rough surface with different altitudes.

Fig. 7
Fig. 7

BSC from an object above a two-layered rough surface with different rms heights.

Fig. 8
Fig. 8

BSC from an object above a two-layered rough surface with different correlation lengths.

Fig. 9
Fig. 9

BSC from an object above a two-layered lossy or lossless rough surface.

Fig. 10
Fig. 10

BSC from an object above a two-layered rough surface with different average heights.

Equations (26)

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f ± ( x n ) = 1 L m = N / 2 + 1 N / 2 f ˜ ± ( K m ) exp ( i K m x n ) ,
f ˜ ± ( K m ) = 2 π L W ± ( K m ) { [ N ( 0 , 1 ) + i N ( 0 , 1 ) ] / 2 m 0 , N / 2 N ( 0 , 1 ) m = 0 , N / 2 .
W ± ( K m ) = δ ± 2 l ± 2 π exp ( K m 2 l ± 2 4 ) ,
1 2 ψ 0 ( r ) = ψ inc ( r ) + S + [ ψ 0 ( r ) G 0 ( r , r ) n + G 0 ( r , r ) ψ 0 ( r ) n + ] d S + S 0 ψ 0 ( r ) G 0 ( r , r ) n 0 d S , r Ω 0 ,
1 2 ψ 1 ( r ) = S + [ ψ 1 ( r ) G 1 ( r , r ) n + G 1 ( r , r ) ψ 1 ( r ) n + ] d S + S [ ψ 1 ( r ) G 1 ( r , r ) n G 1 ( r , r ) ψ 1 ( r ) n ] d S , r Ω 1 ,
1 2 ψ 2 ( r ) = S [ ψ 2 ( r ) G 2 ( r , r ) n G 2 ( r , r ) ψ 2 ( r ) n ] d S , r Ω 2 ,
ψ 0 ( r ) = ψ 1 ( r ) , ψ 0 ( r ) n + = 1 ρ 10 ψ 1 ( r ) n + , r S + ,
ψ 1 ( r ) = ψ 2 ( r ) , ψ 1 ( r ) n = 1 ρ 21 ψ 2 ( r ) n , r S ,
[ A ¯ ¯ t B ¯ ¯ t C ¯ t 0 ¯ ¯ 0 ¯ ¯ D ¯ ¯ t A ¯ ¯ B ¯ ¯ 0 ¯ ¯ 0 ¯ ¯ 0 ¯ ¯ C ¯ ¯ ρ 10 D ¯ ¯ E ¯ ¯ F ¯ ¯ 0 ¯ ¯ G ¯ ¯ ρ 10 H ¯ ¯ I ¯ ¯ J ¯ ¯ 0 ¯ ¯ 0 ¯ ¯ 0 ¯ ¯ K ¯ ¯ ρ 21 L ¯ ¯ ] [ V ¯ 0 V ¯ 1 V ¯ 2 V ¯ 3 V ¯ 4 ] = [ ψ ¯ inc ψ ¯ inc 0 ¯ 0 ¯ 0 ¯ ] ,
A s t t = { Δ l t i k 0 4 ( n ^ 0 · R 0 ) H 1 ( 1 ) ( k 0 | r s r t | ) s t 1 2 Z 0 ( x t ) Δ x t 4 π [ 1 + Z 0 2 ( x t ) ] s = t ,
B s n t = Δ l n i k 0 4 ( n ^ + · R 1 ) H 1 ( 1 ) ( k 0 | r s r n | ) ,
C s n t = Δ l n i 4 H 0 ( 1 ) ( k 0 | r s r n | ) ,
D m t t = Δ l t i k 0 4 ( n ^ 0 · R 2 ) H 1 ( 1 ) ( k 0 | r m r t | ) ,
Δ l t = Δ x t 1 + [ Z 0 ( x t ) ] 2 , Δ l n = Δ x 1 + [ f + ( x n ) ] 2 ,
n ^ 0 = Z 0 ( x t ) x ^ + z ^ 1 + [ Z 0 ( x t ) ] 2 , n ^ + = f + ( x n ) x ^ + z ^ 1 + [ f + ( x n ) ] 2 ,
R 0 = r s r t | r s r t | , R 1 = r s r n | r s r n | , R 2 = r m r t | r m r t | ,
ψ inc ( r ) = y ^ ψ inc ( r ) = y ^ exp [ i k 0 ( x sin θ i z cos θ i ) [ 1 + w ( r ) ] ] exp ( ( x + z tan θ i ) 2 g 2 ) ,
ψ s ( r ) = i 4 2 π k 0 r exp ( i k 0 r i π 4 ) ψ s N ( θ s , θ i ) , r Ω 0 ,
ψ s N ( θ s , θ i ) = S + [ i ( n ^ + · k s ) V 1 ( x ) V 2 ( x ) ] exp ( i k s · r ) 1 + [ f + ( x ) ] 2 d x + S 0 [ i ( n ^ + · k s ) V 0 ( x ) ] exp ( i k s · r 0 ) 1 + [ Z 0 ( x ) ] 2 d x ,
σ ( θ s ) = | ψ s N ( θ s , θ i ) | 2 8 π k 0 g π 2 cos θ i ( 1 1 + 2 tan 2 θ i 2 k 0 2 g 2 cos 2 θ i ) .
H 0 ( 1 ) ( k r m n ) = 1 2 π 0 2 π d α β ¯ m l t ( α ) α ¯ ¯ l l ( α ) β ¯ l n ( α ) ,
n n H 0 ( 1 ) ( k r m n ) = 1 2 π 0 2 π d α β ¯ m l t ( α ) α ¯ ¯ l l ( α ) [ i k ( n x n cos α + n z n sin α ) ] β ¯ l n ( α ) ,
[ α ¯ ¯ l l ( α ) ] = p = P P H p ( 1 ) ( k r l l ) exp [ i p ( φ l l α + π / 2 ) ] ,
[ β ¯ m l ( α ) ] = exp [ i k r m l cos ( α φ m l ) ] , [ β ¯ l n ( α ) ] = exp [ i k r l n cos ( α φ l n ) ] .
A ¯ ¯ x ¯ = b ¯ .
S p = t 1 t p .

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