BibTex RIS Cite
Year 2015, Volume: 5 Issue: 2, 298 - 306, 01.12.2015

Abstract

References

  • Bayındır, C., (2009), Implementation of a Computational Model for Random Directional Seas and Underwater Acoustics, MS Thesis, University of Delaware.
  • Bayındır, C., (2015), Early detection of rogue waves by the wavelet transforms, Physics Letters A, 10.1016/j.physleta.2015.09.051.
  • Bayındır, C., (2015), Hesaplamalı akı¸skanlar mekani˘gi ¸calı¸smaları i¸cin sıkı¸stırılabilir Fourier tayfı y¨ontemi, 19. Mekanik Kongresi, Trabzon (In Turkish).
  • Bayındır, C., (2015), Okyanus dalgalarının sıkı¸stırılabilir Fourier tayfı y¨ontemiyle hızlı modellenmesi, 19. Mekanik Kongresi, Trabzon (In Turkish).
  • Bogomolov, Y. L. and Yunakovsky, A. D., (2006), Split-step Fourier method for nonlinear Schrodinger equation, Proceedings of the International Conference Day on Diffraction, pp. 34-42.
  • Candes, E. J., Romberg, J. and Tao, T., (2006), Robust uncertainty principles: Exact signal recon- struction from highly incomplete frequency information, IEEE Transactions on Information Theory, 52, pp. 489-509.
  • Canuto, C., Hussaini, M. Y., Quarteroni, A. and Zang, T. A. , (2006), Spectral Methods: Fundamen- tals in Single Domains, Springer-Verlag, Berlin.
  • Demiray, H. and Bayindir, C., (2015), A note on the cylindrical solitary waves in an electron-acoustic plasma with vortex electron distribution, Physics of Plasmas, 22, 092105; doi: 10.1063/1.4929863.
  • Hardin, R. H. and Tappert, F. D., (1973), Applications of the split-step Fourier method to the numerical solution of nonlinear and variable coefficient wave equation, SIAM Review Chronicles, 15, pp. 423-423.
  • Hirota, R., (1973), Exact envelope-soliton solutions of a nonlinear wave equation, The Journal of Mathematical Physics, 14, pp. 805-809.
  • Karjadi, E. A., Badiey, M. and Kirby, J. T., (2010), Impact of surface gravity waves on high-frequency acoustic propagation in shallow water, The Journal of the Acoustical Society of America, 127, pp. 1787-1787.
  • Karjadi, E. A., Badiey, M., Kirby, J. T. and Bayindir, C., (2012), The effects of surface gravity waves on high-frequency acoustic propagation in shallow water, IEEE Journal of Oceanic Engineering, 37, pp. 112-121.
  • Taha, T. R. and Ablowitz, M. J., (1984), Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical Nonlinear Schrodinger Equation, Journal of Computational Physics, 22, pp. 203-230.
  • Trefethen, L. N., (2000), Spectral Methods in MATLAB, SIAM, Philadelphia.
  • Zakharov, V. E., (1968), Stability of periodic waves of finite amplitude on the surface of a deep fluid, Soviet Physics JETP, 2, pp. 190-194.

Compressive Split-Step Fourier Method

Year 2015, Volume: 5 Issue: 2, 298 - 306, 01.12.2015

Abstract

In this paper an approach for decreasing the computational effort required for the split-step Fourier method SSFM is introduced. It is shown that using the sparsity property of the simulated signals, the compressive sampling algorithm can be used as a very efficient tool for the split-step spectral simulations of various phenomena which can be modeled by using differential equations. The proposed method depends on the idea of using a smaller number of spectral components compared to the classical split-step Fourier method with a high number of components. After performing the time integration with a smaller number of spectral components and using the compressive sampling technique with l1 minimization, it is shown that the sparse signal can be reconstructed with a significantly better efficiency compared to the classical split-step Fourier method. Proposed method can be named as compressive split-step Fourier method CSSFM . For testing of the proposed method the Nonlinear Schr¨odinger Equation and its one-soliton and two-soliton solutions are considered.

References

  • Bayındır, C., (2009), Implementation of a Computational Model for Random Directional Seas and Underwater Acoustics, MS Thesis, University of Delaware.
  • Bayındır, C., (2015), Early detection of rogue waves by the wavelet transforms, Physics Letters A, 10.1016/j.physleta.2015.09.051.
  • Bayındır, C., (2015), Hesaplamalı akı¸skanlar mekani˘gi ¸calı¸smaları i¸cin sıkı¸stırılabilir Fourier tayfı y¨ontemi, 19. Mekanik Kongresi, Trabzon (In Turkish).
  • Bayındır, C., (2015), Okyanus dalgalarının sıkı¸stırılabilir Fourier tayfı y¨ontemiyle hızlı modellenmesi, 19. Mekanik Kongresi, Trabzon (In Turkish).
  • Bogomolov, Y. L. and Yunakovsky, A. D., (2006), Split-step Fourier method for nonlinear Schrodinger equation, Proceedings of the International Conference Day on Diffraction, pp. 34-42.
  • Candes, E. J., Romberg, J. and Tao, T., (2006), Robust uncertainty principles: Exact signal recon- struction from highly incomplete frequency information, IEEE Transactions on Information Theory, 52, pp. 489-509.
  • Canuto, C., Hussaini, M. Y., Quarteroni, A. and Zang, T. A. , (2006), Spectral Methods: Fundamen- tals in Single Domains, Springer-Verlag, Berlin.
  • Demiray, H. and Bayindir, C., (2015), A note on the cylindrical solitary waves in an electron-acoustic plasma with vortex electron distribution, Physics of Plasmas, 22, 092105; doi: 10.1063/1.4929863.
  • Hardin, R. H. and Tappert, F. D., (1973), Applications of the split-step Fourier method to the numerical solution of nonlinear and variable coefficient wave equation, SIAM Review Chronicles, 15, pp. 423-423.
  • Hirota, R., (1973), Exact envelope-soliton solutions of a nonlinear wave equation, The Journal of Mathematical Physics, 14, pp. 805-809.
  • Karjadi, E. A., Badiey, M. and Kirby, J. T., (2010), Impact of surface gravity waves on high-frequency acoustic propagation in shallow water, The Journal of the Acoustical Society of America, 127, pp. 1787-1787.
  • Karjadi, E. A., Badiey, M., Kirby, J. T. and Bayindir, C., (2012), The effects of surface gravity waves on high-frequency acoustic propagation in shallow water, IEEE Journal of Oceanic Engineering, 37, pp. 112-121.
  • Taha, T. R. and Ablowitz, M. J., (1984), Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical Nonlinear Schrodinger Equation, Journal of Computational Physics, 22, pp. 203-230.
  • Trefethen, L. N., (2000), Spectral Methods in MATLAB, SIAM, Philadelphia.
  • Zakharov, V. E., (1968), Stability of periodic waves of finite amplitude on the surface of a deep fluid, Soviet Physics JETP, 2, pp. 190-194.
There are 15 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

C. Bayındır This is me

Publication Date December 1, 2015
Published in Issue Year 2015 Volume: 5 Issue: 2

Cite