Abstract

The three-dimensional biorthogonal multiresolution time-domain (Bi-MRTD) method is presented for both free-space and half-space scattering problems. The perfectly matched layer (PML) is used as an absorbing boundary condition. It has been shown that improved numerical-dispersion properties can be obtained with the use of smooth, compactly supported wavelet functions as the basis, whereas we employ the Cohen–Daubechies–Fouveau (CDF) biorthogonal wavelets. When a CDF-wavelet expansion is used, the spatial-sampling rate can be reduced considerably compared with that of the conventional finite-difference time-domain (FDTD) method, implying that larger targets can be simulated without sacrificing accuracy. We implement the Bi-MRTD on a cluster of allocated-memory machines, using the message-passing interface (MPI), such that very large targets can be modeled. Numerical results are compared with analytical ones and with those obtained by use of the traditional FDTD method.

© 2003 Optical Society of America

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  1. A. Taflove, S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Boston, Mass., 2000).
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  3. G. S. Smith, W. R. Scott, “A scale model for studying ground penetrating radars,” IEEE Trans. Geosci. Remote Sens. 27, 358–363 (1989).
    [CrossRef]
  4. J. M. Bourgeois, G. S. Smith, “A fully three-dimensional simulation of ground penetrating radar: FDTD theory compared with experiment,” IEEE Trans. Geosci. Remote Sens. 34, 36–44 (1996).
    [CrossRef]
  5. C. T. Schroder, W. R. Scott, “A finite-difference model to study the elastic-wave interactions with buried land mines,” IEEE Trans. Geosci. Remote Sens. 38, 1505–1512 (2000).
    [CrossRef]
  6. S. B. Kumar, C. K. Aanandan, K. T. Mathew, “Buried-object detection using free-space time-domain near-field measurements,” Microwave Opt. Technol. Lett. 30, 45–47 (2001).
    [CrossRef]
  7. P. B. Johns, K. Akhtarzad, “Time domain approximations in the solution of fields by time domain diakoptics,” Int. J. Numer. Methods Eng. 18, 1361–1373 (1982).
    [CrossRef]
  8. D. Su, J. Park, Y. Qian, B. Houshmand, T. Itoh, “Waveguide bandpass filter analysis and design using multimode parallel FDTD diakoptics,” IEEE Trans. Microwave Theory Tech. 47, 867–876 (1999).
    [CrossRef]
  9. S. D. Gedney, “Finite-difference time-domain analysis of microwave circuit devices on high performance vector/parallel computers,” IEEE Trans. Microwave Theory Tech. 43, 2510–2514 (1995).
    [CrossRef]
  10. W. J. Buchanan, N. K. Gupta, “A novel parallel processoring synchronization method for observing electric fields in and around PCBs,” Int. J. Electron. 82, 61–76 (1997).
    [CrossRef]
  11. M. A. Alsunaidi, S. M. Hammadi, S. M. El-Ghazaly, “A parallel implementation of a two-dimensional hydrodynamic model for microwave semiconductor device including inertia effects in momentum relaxation,” Int. J. Numer. Model. Electron. Network Devices Fields 10, 107–119 (1997).
  12. Z. M. Liu, A. S. Mohan, T. A. Aubrey, W. R. Belcher, “Techniques for implementation of the FDTD method on a CM-5 parallel computer,” IEEE Antennas Propag. Mag. 37, 64–71 (1995).
    [CrossRef]
  13. K. C. Chew, V. F. Fusco, “A parallel implementation of the finite-difference time-domain algorithm,” Int. J. Numer. Model. Electron. Networks Devices and Fields 8, 293–299 (1995).
  14. C. Guiffaut, K. Mahdjoubi, “A parallel FDTD algorithm using the MPI library,” IEEE Antennas Propag. Mag. 43, 94–103 (2001).
    [CrossRef]
  15. G. A. Geist, M. T. Heath, B. W. Peyton, P. H. Worley, “PICL: a portable instrumented communications library, C reference manual,” (Oak Ridge National Laboratory, Oak Ridge, Tenn., 1990).
  16. A. Beguelin, J. Dongarra, G. A. Geist, R. Manchek, V. Sunderam, “A user’s guide to PVM: parallel virtual machine,” (Oak Ridge National Laboratory, Oak Ridge, Tenn., 1991).
  17. W. Gropp, E. Lusk, A. Skjellum, Using MPI. Portable Parallel Programming with the Message Passing Interface (MIT Press, Boston, Mass., 1994).
  18. T. Dogaru, L. Carin, “Multiresolution time-domain using biorthogonal wavelets,” IEEE Trans. Microwave Theory Tech. 49, 902–912 (2001).
    [CrossRef]
  19. X. Zhu, T. Dogaru, L. Carin, “Three-dimensional biorthogonal multi-resolution time-domain method and its application to electromagnetic scattering problems,” IEEE Trans. Antennas Propag. (to be published).
  20. M. Krumpholz, L. P. B. Katehi, “MRTD: New time domain schemes based on multiresolution analysis,” IEEE Trans. Microwave Theory Tech. 44, 555–561 (1996).
    [CrossRef]
  21. E. Tentzeris, R. Robertson, J. Harvey, L. P. B. Katehi, “Stability and dispersion analysis of Battle-Lemarie based MRTD schemes,” IEEE Trans. Microwave Theory Tech. 47, 1004–1013 (1999).
    [CrossRef]
  22. R. L. Robertson, E. Tentzeris, L. P. B. Katehi, “Modeling of dielectric-loaded cavities using MRTD,” Int. J. Numer. Model. Electron. Netw. Devices Fields 11, 55–68 (1998).
    [CrossRef]
  23. E. M. Tentzeris, A. Cangellaris, L. P. B. Katehi, “Multiresolution time-domain (MRTD) adaptive schemes using arbitrary resolutions of wavelets,” IEEE Trans. Microwave Theory Tech. 50, 501–516 (2002).
    [CrossRef]
  24. T. Dogaru, L. Carin, “Multiresolution time-domain analysis of scattering from a rough dielectric surface,” Radio Sci. 35, 1279–1292 (2000).
    [CrossRef]
  25. X. Zhu, L. Carin, “Multi-resolution time-domain analysis of plane-wave scattering from general three-dimensional surface and subsurface dielectric targets,” IEEE Trans. Antennas Propag. 49, 1568–1578 (2001).
    [CrossRef]
  26. I. Daubechies, Ten Lectures on Wavelets (SIAM ReviewPhiladelphia, Pa., 1992).
  27. Y. W. Cheong, Y. M. Lee, K. H. Ra, J. G. Kang, C. C. Shin, “Wavelet-Galerkin scheme of time-dependent inhomogeneous electromagnetic problems,” IEEE Microwave Guid. Wave Lett. 9, 297–299 (1999).
    [CrossRef]
  28. M. Fujii, W. J. R. Hoefer, “Dispersion of time domain wavelet Galerkin method based on Daubechies’ compactly supported scaling functions with three and four vanishing moments,” IEEE Microwave Guid. Wave Lett. 10, 125–127 (2000).
    [CrossRef]
  29. 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]
  30. E. M. Tentzeris, R. L. Robertson, J. F. Harvey, L. P. B. Katehi, “PML absorbing boundary conditions for the characterization of open microwave circuit components using multiresolution time-domain techniques (MRTD),” IEEE Trans. Antennas Propag. 47, 1709–1715 (1999).
    [CrossRef]
  31. T. Dogaru, L. Carin, “Application of Haar-wavelet based multi-resolution time-domain schemes to electromagnetic scattering problems,” IEEE Trans. Antennas Propag. 50, 774–784 (2002).
    [CrossRef]
  32. P. Hubral, M. Tygel, “Analysis of the Rayleigh pulse,” Geophysics 54, 654–658 (1989).
    [CrossRef]
  33. C. A. Balanis, Engineering Electromagnetics (Wiley, New York, 1989).
  34. L. Carin, L. B. Felsen, “Time-harmonic and transient scattering by finite periodic flat strip arrays: hybrid (ray)-(floquet Mode)-(MOM) algorithm and its GTD interpretation,” IEEE Trans. Antennas Propag. 41, 412–421 (1993).
    [CrossRef]

2002 (2)

E. M. Tentzeris, A. Cangellaris, L. P. B. Katehi, “Multiresolution time-domain (MRTD) adaptive schemes using arbitrary resolutions of wavelets,” IEEE Trans. Microwave Theory Tech. 50, 501–516 (2002).
[CrossRef]

T. Dogaru, L. Carin, “Application of Haar-wavelet based multi-resolution time-domain schemes to electromagnetic scattering problems,” IEEE Trans. Antennas Propag. 50, 774–784 (2002).
[CrossRef]

2001 (4)

X. Zhu, L. Carin, “Multi-resolution time-domain analysis of plane-wave scattering from general three-dimensional surface and subsurface dielectric targets,” IEEE Trans. Antennas Propag. 49, 1568–1578 (2001).
[CrossRef]

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

T. Dogaru, L. Carin, “Multiresolution time-domain using biorthogonal wavelets,” IEEE Trans. Microwave Theory Tech. 49, 902–912 (2001).
[CrossRef]

S. B. Kumar, C. K. Aanandan, K. T. Mathew, “Buried-object detection using free-space time-domain near-field measurements,” Microwave Opt. Technol. Lett. 30, 45–47 (2001).
[CrossRef]

2000 (3)

T. Dogaru, L. Carin, “Multiresolution time-domain analysis of scattering from a rough dielectric surface,” Radio Sci. 35, 1279–1292 (2000).
[CrossRef]

M. Fujii, W. J. R. Hoefer, “Dispersion of time domain wavelet Galerkin method based on Daubechies’ compactly supported scaling functions with three and four vanishing moments,” IEEE Microwave Guid. Wave Lett. 10, 125–127 (2000).
[CrossRef]

C. T. Schroder, W. R. Scott, “A finite-difference model to study the elastic-wave interactions with buried land mines,” IEEE Trans. Geosci. Remote Sens. 38, 1505–1512 (2000).
[CrossRef]

1999 (4)

E. M. Tentzeris, R. L. Robertson, J. F. Harvey, L. P. B. Katehi, “PML absorbing boundary conditions for the characterization of open microwave circuit components using multiresolution time-domain techniques (MRTD),” IEEE Trans. Antennas Propag. 47, 1709–1715 (1999).
[CrossRef]

Y. W. Cheong, Y. M. Lee, K. H. Ra, J. G. Kang, C. C. Shin, “Wavelet-Galerkin scheme of time-dependent inhomogeneous electromagnetic problems,” IEEE Microwave Guid. Wave Lett. 9, 297–299 (1999).
[CrossRef]

E. Tentzeris, R. Robertson, J. Harvey, L. P. B. Katehi, “Stability and dispersion analysis of Battle-Lemarie based MRTD schemes,” IEEE Trans. Microwave Theory Tech. 47, 1004–1013 (1999).
[CrossRef]

D. Su, J. Park, Y. Qian, B. Houshmand, T. Itoh, “Waveguide bandpass filter analysis and design using multimode parallel FDTD diakoptics,” IEEE Trans. Microwave Theory Tech. 47, 867–876 (1999).
[CrossRef]

1998 (1)

R. L. Robertson, E. Tentzeris, L. P. B. Katehi, “Modeling of dielectric-loaded cavities using MRTD,” Int. J. Numer. Model. Electron. Netw. Devices Fields 11, 55–68 (1998).
[CrossRef]

1997 (2)

W. J. Buchanan, N. K. Gupta, “A novel parallel processoring synchronization method for observing electric fields in and around PCBs,” Int. J. Electron. 82, 61–76 (1997).
[CrossRef]

M. A. Alsunaidi, S. M. Hammadi, S. M. El-Ghazaly, “A parallel implementation of a two-dimensional hydrodynamic model for microwave semiconductor device including inertia effects in momentum relaxation,” Int. J. Numer. Model. Electron. Network Devices Fields 10, 107–119 (1997).

1996 (3)

J. M. Bourgeois, G. S. Smith, “A fully three-dimensional simulation of ground penetrating radar: FDTD theory compared with experiment,” IEEE Trans. Geosci. Remote Sens. 34, 36–44 (1996).
[CrossRef]

M. Krumpholz, L. P. B. Katehi, “MRTD: New time domain schemes based on multiresolution analysis,” IEEE Trans. Microwave Theory Tech. 44, 555–561 (1996).
[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]

1995 (3)

S. D. Gedney, “Finite-difference time-domain analysis of microwave circuit devices on high performance vector/parallel computers,” IEEE Trans. Microwave Theory Tech. 43, 2510–2514 (1995).
[CrossRef]

Z. M. Liu, A. S. Mohan, T. A. Aubrey, W. R. Belcher, “Techniques for implementation of the FDTD method on a CM-5 parallel computer,” IEEE Antennas Propag. Mag. 37, 64–71 (1995).
[CrossRef]

K. C. Chew, V. F. Fusco, “A parallel implementation of the finite-difference time-domain algorithm,” Int. J. Numer. Model. Electron. Networks Devices and Fields 8, 293–299 (1995).

1993 (1)

L. Carin, L. B. Felsen, “Time-harmonic and transient scattering by finite periodic flat strip arrays: hybrid (ray)-(floquet Mode)-(MOM) algorithm and its GTD interpretation,” IEEE Trans. Antennas Propag. 41, 412–421 (1993).
[CrossRef]

1989 (2)

P. Hubral, M. Tygel, “Analysis of the Rayleigh pulse,” Geophysics 54, 654–658 (1989).
[CrossRef]

G. S. Smith, W. R. Scott, “A scale model for studying ground penetrating radars,” IEEE Trans. Geosci. Remote Sens. 27, 358–363 (1989).
[CrossRef]

1982 (1)

P. B. Johns, K. Akhtarzad, “Time domain approximations in the solution of fields by time domain diakoptics,” Int. J. Numer. Methods Eng. 18, 1361–1373 (1982).
[CrossRef]

Aanandan, C. K.

S. B. Kumar, C. K. Aanandan, K. T. Mathew, “Buried-object detection using free-space time-domain near-field measurements,” Microwave Opt. Technol. Lett. 30, 45–47 (2001).
[CrossRef]

Akhtarzad, K.

P. B. Johns, K. Akhtarzad, “Time domain approximations in the solution of fields by time domain diakoptics,” Int. J. Numer. Methods Eng. 18, 1361–1373 (1982).
[CrossRef]

Alsunaidi, M. A.

M. A. Alsunaidi, S. M. Hammadi, S. M. El-Ghazaly, “A parallel implementation of a two-dimensional hydrodynamic model for microwave semiconductor device including inertia effects in momentum relaxation,” Int. J. Numer. Model. Electron. Network Devices Fields 10, 107–119 (1997).

Aubrey, T. A.

Z. M. Liu, A. S. Mohan, T. A. Aubrey, W. R. Belcher, “Techniques for implementation of the FDTD method on a CM-5 parallel computer,” IEEE Antennas Propag. Mag. 37, 64–71 (1995).
[CrossRef]

Balanis, C. A.

C. A. Balanis, Engineering Electromagnetics (Wiley, New York, 1989).

Beguelin, A.

A. Beguelin, J. Dongarra, G. A. Geist, R. Manchek, V. Sunderam, “A user’s guide to PVM: parallel virtual machine,” (Oak Ridge National Laboratory, Oak Ridge, Tenn., 1991).

Belcher, W. R.

Z. M. Liu, A. S. Mohan, T. A. Aubrey, W. R. Belcher, “Techniques for implementation of the FDTD method on a CM-5 parallel computer,” IEEE Antennas Propag. Mag. 37, 64–71 (1995).
[CrossRef]

Bourgeois, J. M.

J. M. Bourgeois, G. S. Smith, “A fully three-dimensional simulation of ground penetrating radar: FDTD theory compared with experiment,” IEEE Trans. Geosci. Remote Sens. 34, 36–44 (1996).
[CrossRef]

Buchanan, W. J.

W. J. Buchanan, N. K. Gupta, “A novel parallel processoring synchronization method for observing electric fields in and around PCBs,” Int. J. Electron. 82, 61–76 (1997).
[CrossRef]

Cangellaris, A.

E. M. Tentzeris, A. Cangellaris, L. P. B. Katehi, “Multiresolution time-domain (MRTD) adaptive schemes using arbitrary resolutions of wavelets,” IEEE Trans. Microwave Theory Tech. 50, 501–516 (2002).
[CrossRef]

Carin, L.

T. Dogaru, L. Carin, “Application of Haar-wavelet based multi-resolution time-domain schemes to electromagnetic scattering problems,” IEEE Trans. Antennas Propag. 50, 774–784 (2002).
[CrossRef]

T. Dogaru, L. Carin, “Multiresolution time-domain using biorthogonal wavelets,” IEEE Trans. Microwave Theory Tech. 49, 902–912 (2001).
[CrossRef]

X. Zhu, L. Carin, “Multi-resolution time-domain analysis of plane-wave scattering from general three-dimensional surface and subsurface dielectric targets,” IEEE Trans. Antennas Propag. 49, 1568–1578 (2001).
[CrossRef]

T. Dogaru, L. Carin, “Multiresolution time-domain analysis of scattering from a rough dielectric surface,” Radio Sci. 35, 1279–1292 (2000).
[CrossRef]

L. Carin, L. B. Felsen, “Time-harmonic and transient scattering by finite periodic flat strip arrays: hybrid (ray)-(floquet Mode)-(MOM) algorithm and its GTD interpretation,” IEEE Trans. Antennas Propag. 41, 412–421 (1993).
[CrossRef]

X. Zhu, T. Dogaru, L. Carin, “Three-dimensional biorthogonal multi-resolution time-domain method and its application to electromagnetic scattering problems,” IEEE Trans. Antennas Propag. (to be published).

Cheong, Y. W.

Y. W. Cheong, Y. M. Lee, K. H. Ra, J. G. Kang, C. C. Shin, “Wavelet-Galerkin scheme of time-dependent inhomogeneous electromagnetic problems,” IEEE Microwave Guid. Wave Lett. 9, 297–299 (1999).
[CrossRef]

Chew, K. C.

K. C. Chew, V. F. Fusco, “A parallel implementation of the finite-difference time-domain algorithm,” Int. J. Numer. Model. Electron. Networks Devices and Fields 8, 293–299 (1995).

Daubechies, I.

I. Daubechies, Ten Lectures on Wavelets (SIAM ReviewPhiladelphia, Pa., 1992).

Dogaru, T.

T. Dogaru, L. Carin, “Application of Haar-wavelet based multi-resolution time-domain schemes to electromagnetic scattering problems,” IEEE Trans. Antennas Propag. 50, 774–784 (2002).
[CrossRef]

T. Dogaru, L. Carin, “Multiresolution time-domain using biorthogonal wavelets,” IEEE Trans. Microwave Theory Tech. 49, 902–912 (2001).
[CrossRef]

T. Dogaru, L. Carin, “Multiresolution time-domain analysis of scattering from a rough dielectric surface,” Radio Sci. 35, 1279–1292 (2000).
[CrossRef]

X. Zhu, T. Dogaru, L. Carin, “Three-dimensional biorthogonal multi-resolution time-domain method and its application to electromagnetic scattering problems,” IEEE Trans. Antennas Propag. (to be published).

Dongarra, J.

A. Beguelin, J. Dongarra, G. A. Geist, R. Manchek, V. Sunderam, “A user’s guide to PVM: parallel virtual machine,” (Oak Ridge National Laboratory, Oak Ridge, Tenn., 1991).

El-Ghazaly, S. M.

M. A. Alsunaidi, S. M. Hammadi, S. M. El-Ghazaly, “A parallel implementation of a two-dimensional hydrodynamic model for microwave semiconductor device including inertia effects in momentum relaxation,” Int. J. Numer. Model. Electron. Network Devices Fields 10, 107–119 (1997).

Felsen, L. B.

L. Carin, L. B. Felsen, “Time-harmonic and transient scattering by finite periodic flat strip arrays: hybrid (ray)-(floquet Mode)-(MOM) algorithm and its GTD interpretation,” IEEE Trans. Antennas Propag. 41, 412–421 (1993).
[CrossRef]

Fujii, M.

M. Fujii, W. J. R. Hoefer, “Dispersion of time domain wavelet Galerkin method based on Daubechies’ compactly supported scaling functions with three and four vanishing moments,” IEEE Microwave Guid. Wave Lett. 10, 125–127 (2000).
[CrossRef]

Fusco, V. F.

K. C. Chew, V. F. Fusco, “A parallel implementation of the finite-difference time-domain algorithm,” Int. J. Numer. Model. Electron. Networks Devices and Fields 8, 293–299 (1995).

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, “Finite-difference time-domain analysis of microwave circuit devices on high performance vector/parallel computers,” IEEE Trans. Microwave Theory Tech. 43, 2510–2514 (1995).
[CrossRef]

Geist, G. A.

G. A. Geist, M. T. Heath, B. W. Peyton, P. H. Worley, “PICL: a portable instrumented communications library, C reference manual,” (Oak Ridge National Laboratory, Oak Ridge, Tenn., 1990).

A. Beguelin, J. Dongarra, G. A. Geist, R. Manchek, V. Sunderam, “A user’s guide to PVM: parallel virtual machine,” (Oak Ridge National Laboratory, Oak Ridge, Tenn., 1991).

Gropp, W.

W. Gropp, E. Lusk, A. Skjellum, Using MPI. Portable Parallel Programming with the Message Passing Interface (MIT Press, Boston, Mass., 1994).

Guiffaut, C.

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

Gupta, N. K.

W. J. Buchanan, N. K. Gupta, “A novel parallel processoring synchronization method for observing electric fields in and around PCBs,” Int. J. Electron. 82, 61–76 (1997).
[CrossRef]

Hagness, S.

A. Taflove, S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Boston, Mass., 2000).

Hammadi, S. M.

M. A. Alsunaidi, S. M. Hammadi, S. M. El-Ghazaly, “A parallel implementation of a two-dimensional hydrodynamic model for microwave semiconductor device including inertia effects in momentum relaxation,” Int. J. Numer. Model. Electron. Network Devices Fields 10, 107–119 (1997).

Harvey, J.

E. Tentzeris, R. Robertson, J. Harvey, L. P. B. Katehi, “Stability and dispersion analysis of Battle-Lemarie based MRTD schemes,” IEEE Trans. Microwave Theory Tech. 47, 1004–1013 (1999).
[CrossRef]

Harvey, J. F.

E. M. Tentzeris, R. L. Robertson, J. F. Harvey, L. P. B. Katehi, “PML absorbing boundary conditions for the characterization of open microwave circuit components using multiresolution time-domain techniques (MRTD),” IEEE Trans. Antennas Propag. 47, 1709–1715 (1999).
[CrossRef]

Heath, M. T.

G. A. Geist, M. T. Heath, B. W. Peyton, P. H. Worley, “PICL: a portable instrumented communications library, C reference manual,” (Oak Ridge National Laboratory, Oak Ridge, Tenn., 1990).

Hoefer, W. J. R.

M. Fujii, W. J. R. Hoefer, “Dispersion of time domain wavelet Galerkin method based on Daubechies’ compactly supported scaling functions with three and four vanishing moments,” IEEE Microwave Guid. Wave Lett. 10, 125–127 (2000).
[CrossRef]

Houshmand, B.

D. Su, J. Park, Y. Qian, B. Houshmand, T. Itoh, “Waveguide bandpass filter analysis and design using multimode parallel FDTD diakoptics,” IEEE Trans. Microwave Theory Tech. 47, 867–876 (1999).
[CrossRef]

Hubral, P.

P. Hubral, M. Tygel, “Analysis of the Rayleigh pulse,” Geophysics 54, 654–658 (1989).
[CrossRef]

Itoh, T.

D. Su, J. Park, Y. Qian, B. Houshmand, T. Itoh, “Waveguide bandpass filter analysis and design using multimode parallel FDTD diakoptics,” IEEE Trans. Microwave Theory Tech. 47, 867–876 (1999).
[CrossRef]

Johns, P. B.

P. B. Johns, K. Akhtarzad, “Time domain approximations in the solution of fields by time domain diakoptics,” Int. J. Numer. Methods Eng. 18, 1361–1373 (1982).
[CrossRef]

Kang, J. G.

Y. W. Cheong, Y. M. Lee, K. H. Ra, J. G. Kang, C. C. Shin, “Wavelet-Galerkin scheme of time-dependent inhomogeneous electromagnetic problems,” IEEE Microwave Guid. Wave Lett. 9, 297–299 (1999).
[CrossRef]

Katehi, L. P. B.

E. M. Tentzeris, A. Cangellaris, L. P. B. Katehi, “Multiresolution time-domain (MRTD) adaptive schemes using arbitrary resolutions of wavelets,” IEEE Trans. Microwave Theory Tech. 50, 501–516 (2002).
[CrossRef]

E. M. Tentzeris, R. L. Robertson, J. F. Harvey, L. P. B. Katehi, “PML absorbing boundary conditions for the characterization of open microwave circuit components using multiresolution time-domain techniques (MRTD),” IEEE Trans. Antennas Propag. 47, 1709–1715 (1999).
[CrossRef]

E. Tentzeris, R. Robertson, J. Harvey, L. P. B. Katehi, “Stability and dispersion analysis of Battle-Lemarie based MRTD schemes,” IEEE Trans. Microwave Theory Tech. 47, 1004–1013 (1999).
[CrossRef]

R. L. Robertson, E. Tentzeris, L. P. B. Katehi, “Modeling of dielectric-loaded cavities using MRTD,” Int. J. Numer. Model. Electron. Netw. Devices Fields 11, 55–68 (1998).
[CrossRef]

M. Krumpholz, L. P. B. Katehi, “MRTD: New time domain schemes based on multiresolution analysis,” IEEE Trans. Microwave Theory Tech. 44, 555–561 (1996).
[CrossRef]

Krumpholz, M.

M. Krumpholz, L. P. B. Katehi, “MRTD: New time domain schemes based on multiresolution analysis,” IEEE Trans. Microwave Theory Tech. 44, 555–561 (1996).
[CrossRef]

Kumar, S. B.

S. B. Kumar, C. K. Aanandan, K. T. Mathew, “Buried-object detection using free-space time-domain near-field measurements,” Microwave Opt. Technol. Lett. 30, 45–47 (2001).
[CrossRef]

Lee, Y. M.

Y. W. Cheong, Y. M. Lee, K. H. Ra, J. G. Kang, C. C. Shin, “Wavelet-Galerkin scheme of time-dependent inhomogeneous electromagnetic problems,” IEEE Microwave Guid. Wave Lett. 9, 297–299 (1999).
[CrossRef]

Liu, Z. M.

Z. M. Liu, A. S. Mohan, T. A. Aubrey, W. R. Belcher, “Techniques for implementation of the FDTD method on a CM-5 parallel computer,” IEEE Antennas Propag. Mag. 37, 64–71 (1995).
[CrossRef]

Lusk, E.

W. Gropp, E. Lusk, A. Skjellum, Using MPI. Portable Parallel Programming with the Message Passing Interface (MIT Press, Boston, Mass., 1994).

Mahdjoubi, K.

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

Manchek, R.

A. Beguelin, J. Dongarra, G. A. Geist, R. Manchek, V. Sunderam, “A user’s guide to PVM: parallel virtual machine,” (Oak Ridge National Laboratory, Oak Ridge, Tenn., 1991).

Mathew, K. T.

S. B. Kumar, C. K. Aanandan, K. T. Mathew, “Buried-object detection using free-space time-domain near-field measurements,” Microwave Opt. Technol. Lett. 30, 45–47 (2001).
[CrossRef]

Mohan, A. S.

Z. M. Liu, A. S. Mohan, T. A. Aubrey, W. R. Belcher, “Techniques for implementation of the FDTD method on a CM-5 parallel computer,” IEEE Antennas Propag. Mag. 37, 64–71 (1995).
[CrossRef]

Park, J.

D. Su, J. Park, Y. Qian, B. Houshmand, T. Itoh, “Waveguide bandpass filter analysis and design using multimode parallel FDTD diakoptics,” IEEE Trans. Microwave Theory Tech. 47, 867–876 (1999).
[CrossRef]

Peyton, B. W.

G. A. Geist, M. T. Heath, B. W. Peyton, P. H. Worley, “PICL: a portable instrumented communications library, C reference manual,” (Oak Ridge National Laboratory, Oak Ridge, Tenn., 1990).

Qian, Y.

D. Su, J. Park, Y. Qian, B. Houshmand, T. Itoh, “Waveguide bandpass filter analysis and design using multimode parallel FDTD diakoptics,” IEEE Trans. Microwave Theory Tech. 47, 867–876 (1999).
[CrossRef]

Ra, K. H.

Y. W. Cheong, Y. M. Lee, K. H. Ra, J. G. Kang, C. C. Shin, “Wavelet-Galerkin scheme of time-dependent inhomogeneous electromagnetic problems,” IEEE Microwave Guid. Wave Lett. 9, 297–299 (1999).
[CrossRef]

Robertson, R.

E. Tentzeris, R. Robertson, J. Harvey, L. P. B. Katehi, “Stability and dispersion analysis of Battle-Lemarie based MRTD schemes,” IEEE Trans. Microwave Theory Tech. 47, 1004–1013 (1999).
[CrossRef]

Robertson, R. L.

E. M. Tentzeris, R. L. Robertson, J. F. Harvey, L. P. B. Katehi, “PML absorbing boundary conditions for the characterization of open microwave circuit components using multiresolution time-domain techniques (MRTD),” IEEE Trans. Antennas Propag. 47, 1709–1715 (1999).
[CrossRef]

R. L. Robertson, E. Tentzeris, L. P. B. Katehi, “Modeling of dielectric-loaded cavities using MRTD,” Int. J. Numer. Model. Electron. Netw. Devices Fields 11, 55–68 (1998).
[CrossRef]

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C. T. Schroder, W. R. Scott, “A finite-difference model to study the elastic-wave interactions with buried land mines,” IEEE Trans. Geosci. Remote Sens. 38, 1505–1512 (2000).
[CrossRef]

Scott, W. R.

C. T. Schroder, W. R. Scott, “A finite-difference model to study the elastic-wave interactions with buried land mines,” IEEE Trans. Geosci. Remote Sens. 38, 1505–1512 (2000).
[CrossRef]

G. S. Smith, W. R. Scott, “A scale model for studying ground penetrating radars,” IEEE Trans. Geosci. Remote Sens. 27, 358–363 (1989).
[CrossRef]

Shin, C. C.

Y. W. Cheong, Y. M. Lee, K. H. Ra, J. G. Kang, C. C. Shin, “Wavelet-Galerkin scheme of time-dependent inhomogeneous electromagnetic problems,” IEEE Microwave Guid. Wave Lett. 9, 297–299 (1999).
[CrossRef]

Skjellum, A.

W. Gropp, E. Lusk, A. Skjellum, Using MPI. Portable Parallel Programming with the Message Passing Interface (MIT Press, Boston, Mass., 1994).

Smith, G. S.

J. M. Bourgeois, G. S. Smith, “A fully three-dimensional simulation of ground penetrating radar: FDTD theory compared with experiment,” IEEE Trans. Geosci. Remote Sens. 34, 36–44 (1996).
[CrossRef]

G. S. Smith, W. R. Scott, “A scale model for studying ground penetrating radars,” IEEE Trans. Geosci. Remote Sens. 27, 358–363 (1989).
[CrossRef]

Su, D.

D. Su, J. Park, Y. Qian, B. Houshmand, T. Itoh, “Waveguide bandpass filter analysis and design using multimode parallel FDTD diakoptics,” IEEE Trans. Microwave Theory Tech. 47, 867–876 (1999).
[CrossRef]

Sunderam, V.

A. Beguelin, J. Dongarra, G. A. Geist, R. Manchek, V. Sunderam, “A user’s guide to PVM: parallel virtual machine,” (Oak Ridge National Laboratory, Oak Ridge, Tenn., 1991).

Taflove, A.

A. Taflove, S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Boston, Mass., 2000).

Tentzeris, E.

E. Tentzeris, R. Robertson, J. Harvey, L. P. B. Katehi, “Stability and dispersion analysis of Battle-Lemarie based MRTD schemes,” IEEE Trans. Microwave Theory Tech. 47, 1004–1013 (1999).
[CrossRef]

R. L. Robertson, E. Tentzeris, L. P. B. Katehi, “Modeling of dielectric-loaded cavities using MRTD,” Int. J. Numer. Model. Electron. Netw. Devices Fields 11, 55–68 (1998).
[CrossRef]

Tentzeris, E. M.

E. M. Tentzeris, A. Cangellaris, L. P. B. Katehi, “Multiresolution time-domain (MRTD) adaptive schemes using arbitrary resolutions of wavelets,” IEEE Trans. Microwave Theory Tech. 50, 501–516 (2002).
[CrossRef]

E. M. Tentzeris, R. L. Robertson, J. F. Harvey, L. P. B. Katehi, “PML absorbing boundary conditions for the characterization of open microwave circuit components using multiresolution time-domain techniques (MRTD),” IEEE Trans. Antennas Propag. 47, 1709–1715 (1999).
[CrossRef]

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P. Hubral, M. Tygel, “Analysis of the Rayleigh pulse,” Geophysics 54, 654–658 (1989).
[CrossRef]

Worley, P. H.

G. A. Geist, M. T. Heath, B. W. Peyton, P. H. Worley, “PICL: a portable instrumented communications library, C reference manual,” (Oak Ridge National Laboratory, Oak Ridge, Tenn., 1990).

Zhu, X.

X. Zhu, L. Carin, “Multi-resolution time-domain analysis of plane-wave scattering from general three-dimensional surface and subsurface dielectric targets,” IEEE Trans. Antennas Propag. 49, 1568–1578 (2001).
[CrossRef]

X. Zhu, T. Dogaru, L. Carin, “Three-dimensional biorthogonal multi-resolution time-domain method and its application to electromagnetic scattering problems,” IEEE Trans. Antennas Propag. (to be published).

Geophysics (1)

P. Hubral, M. Tygel, “Analysis of the Rayleigh pulse,” Geophysics 54, 654–658 (1989).
[CrossRef]

IEEE Antennas Propag. Mag. (2)

Z. M. Liu, A. S. Mohan, T. A. Aubrey, W. R. Belcher, “Techniques for implementation of the FDTD method on a CM-5 parallel computer,” IEEE Antennas Propag. Mag. 37, 64–71 (1995).
[CrossRef]

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

IEEE Microwave Guid. Wave Lett. (2)

Y. W. Cheong, Y. M. Lee, K. H. Ra, J. G. Kang, C. C. Shin, “Wavelet-Galerkin scheme of time-dependent inhomogeneous electromagnetic problems,” IEEE Microwave Guid. Wave Lett. 9, 297–299 (1999).
[CrossRef]

M. Fujii, W. J. R. Hoefer, “Dispersion of time domain wavelet Galerkin method based on Daubechies’ compactly supported scaling functions with three and four vanishing moments,” IEEE Microwave Guid. Wave Lett. 10, 125–127 (2000).
[CrossRef]

IEEE Trans. Antennas Propag. (5)

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]

E. M. Tentzeris, R. L. Robertson, J. F. Harvey, L. P. B. Katehi, “PML absorbing boundary conditions for the characterization of open microwave circuit components using multiresolution time-domain techniques (MRTD),” IEEE Trans. Antennas Propag. 47, 1709–1715 (1999).
[CrossRef]

T. Dogaru, L. Carin, “Application of Haar-wavelet based multi-resolution time-domain schemes to electromagnetic scattering problems,” IEEE Trans. Antennas Propag. 50, 774–784 (2002).
[CrossRef]

L. Carin, L. B. Felsen, “Time-harmonic and transient scattering by finite periodic flat strip arrays: hybrid (ray)-(floquet Mode)-(MOM) algorithm and its GTD interpretation,” IEEE Trans. Antennas Propag. 41, 412–421 (1993).
[CrossRef]

X. Zhu, L. Carin, “Multi-resolution time-domain analysis of plane-wave scattering from general three-dimensional surface and subsurface dielectric targets,” IEEE Trans. Antennas Propag. 49, 1568–1578 (2001).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (3)

G. S. Smith, W. R. Scott, “A scale model for studying ground penetrating radars,” IEEE Trans. Geosci. Remote Sens. 27, 358–363 (1989).
[CrossRef]

J. M. Bourgeois, G. S. Smith, “A fully three-dimensional simulation of ground penetrating radar: FDTD theory compared with experiment,” IEEE Trans. Geosci. Remote Sens. 34, 36–44 (1996).
[CrossRef]

C. T. Schroder, W. R. Scott, “A finite-difference model to study the elastic-wave interactions with buried land mines,” IEEE Trans. Geosci. Remote Sens. 38, 1505–1512 (2000).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (6)

D. Su, J. Park, Y. Qian, B. Houshmand, T. Itoh, “Waveguide bandpass filter analysis and design using multimode parallel FDTD diakoptics,” IEEE Trans. Microwave Theory Tech. 47, 867–876 (1999).
[CrossRef]

S. D. Gedney, “Finite-difference time-domain analysis of microwave circuit devices on high performance vector/parallel computers,” IEEE Trans. Microwave Theory Tech. 43, 2510–2514 (1995).
[CrossRef]

E. M. Tentzeris, A. Cangellaris, L. P. B. Katehi, “Multiresolution time-domain (MRTD) adaptive schemes using arbitrary resolutions of wavelets,” IEEE Trans. Microwave Theory Tech. 50, 501–516 (2002).
[CrossRef]

T. Dogaru, L. Carin, “Multiresolution time-domain using biorthogonal wavelets,” IEEE Trans. Microwave Theory Tech. 49, 902–912 (2001).
[CrossRef]

M. Krumpholz, L. P. B. Katehi, “MRTD: New time domain schemes based on multiresolution analysis,” IEEE Trans. Microwave Theory Tech. 44, 555–561 (1996).
[CrossRef]

E. Tentzeris, R. Robertson, J. Harvey, L. P. B. Katehi, “Stability and dispersion analysis of Battle-Lemarie based MRTD schemes,” IEEE Trans. Microwave Theory Tech. 47, 1004–1013 (1999).
[CrossRef]

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W. J. Buchanan, N. K. Gupta, “A novel parallel processoring synchronization method for observing electric fields in and around PCBs,” Int. J. Electron. 82, 61–76 (1997).
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[CrossRef]

Int. J. Numer. Model. Electron. Netw. Devices Fields (1)

R. L. Robertson, E. Tentzeris, L. P. B. Katehi, “Modeling of dielectric-loaded cavities using MRTD,” Int. J. Numer. Model. Electron. Netw. Devices Fields 11, 55–68 (1998).
[CrossRef]

Int. J. Numer. Model. Electron. Network Devices Fields (1)

M. A. Alsunaidi, S. M. Hammadi, S. M. El-Ghazaly, “A parallel implementation of a two-dimensional hydrodynamic model for microwave semiconductor device including inertia effects in momentum relaxation,” Int. J. Numer. Model. Electron. Network Devices Fields 10, 107–119 (1997).

Int. J. Numer. Model. Electron. Networks Devices and Fields (1)

K. C. Chew, V. F. Fusco, “A parallel implementation of the finite-difference time-domain algorithm,” Int. J. Numer. Model. Electron. Networks Devices and Fields 8, 293–299 (1995).

Microwave Opt. Technol. Lett. (1)

S. B. Kumar, C. K. Aanandan, K. T. Mathew, “Buried-object detection using free-space time-domain near-field measurements,” Microwave Opt. Technol. Lett. 30, 45–47 (2001).
[CrossRef]

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T. Dogaru, L. Carin, “Multiresolution time-domain analysis of scattering from a rough dielectric surface,” Radio Sci. 35, 1279–1292 (2000).
[CrossRef]

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I. Daubechies, Ten Lectures on Wavelets (SIAM ReviewPhiladelphia, Pa., 1992).

X. Zhu, T. Dogaru, L. Carin, “Three-dimensional biorthogonal multi-resolution time-domain method and its application to electromagnetic scattering problems,” IEEE Trans. Antennas Propag. (to be published).

C. A. Balanis, Engineering Electromagnetics (Wiley, New York, 1989).

A. Taflove, S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Boston, Mass., 2000).

A. Taflove, ed., Advances in Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Boston, Mass., 1998).

G. A. Geist, M. T. Heath, B. W. Peyton, P. H. Worley, “PICL: a portable instrumented communications library, C reference manual,” (Oak Ridge National Laboratory, Oak Ridge, Tenn., 1990).

A. Beguelin, J. Dongarra, G. A. Geist, R. Manchek, V. Sunderam, “A user’s guide to PVM: parallel virtual machine,” (Oak Ridge National Laboratory, Oak Ridge, Tenn., 1991).

W. Gropp, E. Lusk, A. Skjellum, Using MPI. Portable Parallel Programming with the Message Passing Interface (MIT Press, Boston, Mass., 1994).

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Figures (9)

Fig. 1
Fig. 1

Time-domain far-zone field backscattered by a dielectric sphere of dielectric constant r = 3 and diameter 1 m. The excitation is provided by a fourth-order Rayleigh pulse with a maximum frequency of approximately 1.5 GHz. (a) Far-field scattered fields from 0 to 64 ns, (b) far-field scattered fields from 56 to 64 ns.

Fig. 2
Fig. 2

As in Fig. 1, but in this case the maximum frequency of the incident wave is approximately 3.0 GHz. (a) Far-field scattered fields from 0 to 64 ns, (b) far-field scattered fields from 36 to 47 ns, (c) far-field scattered fields from 56 to 64 ns.

Fig. 3
Fig. 3

As in Fig. 1, but in this case the maximum frequency of the incident wave is approximately 4.5 GHz. (a) Far-field scattered fields from 0 to 64 ns, (b) far-field scattered fields from 24 to 35 ns, (c) far-field scattered fields from 39 to 48 ns, (d) far-field scattered fields from 56 to 64 ns.

Fig. 4
Fig. 4

Time-domain far-zone field backscattered by a dielectric cube of dielectric constant r = 3 with sides of 0.75 m. The excitation is provided by a fourth-order Rayleigh pulse with a maximum frequency of approximately 4.5 GHz. (a) Comparison of far-field scattered fields produced with fine-grid FDTD (40 ppcw) and coarse-grid Bi-MRTD (20 ppcw) sampling. (b) Comparison of far-field scattered fields produced with fine-grid FDTD (40 ppcw) and coarse-grid FDTD (20 ppcw) sampling. (c) Comparison of far-field scattered fields produced with a FDTD (20 and 40 ppcw) and Bi-MRTD (20 ppcw) sampling from 25 to 45 ns.

Fig. 5
Fig. 5

Dielectric sinusoidal surface embedded in a half-space

Fig. 6
Fig. 6

Bistatic RCS of a sinusoidal dielectric surface embedded in a half-space. (a) Bistatic RCS at 1.5 GHz, (b) bistatic RCS at 3.0 GHz.

Fig. 7
Fig. 7

Schematic of the 24-cylinder problem considered in Fig. 8. The rods have a radius of 0.333 a , where a = 1.8   mm is the lattice spacing and the host medium has a dielectric constant of r = 4 . Each cylinder is 15 mm long.

Fig. 8
Fig. 8

Transmitted x component of the electric field for the example in Fig. 7. The transmitted fields are observed in the midpoint of the array (see Fig. 7), 0.2 mm from the end of the array layer. The Bi-MRTD results are shown for sampling at 30 points per free-space wavelength at the central frequency in free space, and the FDTD results are shown for 30 and 60 points per wavelength. The central frequency of the incident pulse is 100 GHz.

Fig. 9
Fig. 9

CPU-time performance of the parallel algorithm. T1 represents the time required by the serial code, whereas T n represents the time required by the parallel code employing n processors.

Tables (1)

Tables Icon

Table 1 Displacements for Different Field Components

Equations (8)

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  E x t + σ E x = H z y - H y z .
F ( x ,   y ,   z ,   t ) = i , j , k , m = - h m + δ t ( t ) × [ F i , j , k ϕ ˜ , ϕ ˜ , ϕ ˜ ϕ ˜ i + δ x ( x ) ϕ ˜ j + δ y ( y ) ϕ ˜ k + δ z ( z ) + F i , j , k ϕ ˜ , ϕ ˜ , ψ ˜ ϕ ˜ i + δ x ( x ) ϕ ˜ j + δ y ( y ) ψ ˜ k + δ z ( z ) + F i , j , k ϕ ˜ , ψ ˜ , ϕ ˜ ϕ ˜ i + δ x ( x ) ψ ˜ j + δ y ( y ) ϕ ˜ k + δ x ( z ) + F i , j , k ϕ ˜ , ψ ˜ , ψ ˜ ϕ ˜ i + δ x ( x ) ψ ˜ j + δ y ( y ) ψ ˜ k + δ z ( z ) + F i , j , k ψ ˜ , ϕ ˜ , ϕ ˜ ψ ˜ i + δ x ( x ) ϕ ˜ j + δ y ( y ) ϕ ˜ k + δ z ( z ) + F i , j , k ψ ˜ , ϕ ˜ , ψ ˜ ψ ˜ i + δ x ( x ) ϕ ˜ j + δ y ( y ) ψ ˜ k + δ z ( z ) + F i , j , k ψ ˜ , ψ ˜ , ϕ ˜ ψ ˜ i + δ x ( x ) ψ ˜ j + δ y ( y ) ϕ ˜ k + δ z ( z ) + F i , j , k ψ ˜ , ψ ˜ , ψ ˜ ψ ˜ i + δ x ( x ) ψ ˜ j + δ y ( y ) ψ ˜ k + δ z ( z ) ] ,
E xi , j , k , m + 1 ϕ , ϕ , ϕ = α E xi , j , k , m ϕ , ϕ , ϕ + β n = 1 n a a ( n ) × ( H z i , j + n - 1 , k , m + 1 / 2 ϕ , ϕ , ϕ - H z i , j - n , k , m + 1 / 2 ϕ , ϕ , ϕ ) + n = 1 n c c ( n ) ( H z i , j + n - 1 , k , m + 1 / 2 ϕ , ψ , ϕ - H z i , j - n - 1 , k , m + 1 / 2 ϕ , ψ , ϕ ) - n = 1 n a a ( n ) ( H y i , j , k + n - 1 , m + 1 / 2 ϕ , ϕ , ϕ - H y i , j , k - n , m + 1 / 2 ϕ , ϕ , ϕ ) - n = 1 n c c ( n ) ( H y i , j , k + n - 1 , m + 1 / 2 ϕ , ϕ , ψ - H y i , j , k - n - 1 , m + 1 / 2 ϕ , ϕ , ψ ) ,
α = 1 - σ Δ t / 2 1 + σ Δ t / 2 , β = Δ t Δ x ( 1 + σ Δ t / 2 ) ,
a ( n ) = ϕ ˜ n + 1 / 2 ( x ) x   ϕ n ( x ) d x ,
c ( n ) = ψ ˜ n + 1 ( x ) x   ϕ n ( x ) d x .
z ( x ,   y ) = A   sin ( k x x ) sin ( k y y ) ,
sin ( θ ) = - sin ( θ i ) + m ( λ 0 / 2 d ) ,

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