Skip to main content
Log in

Solution of wave diffraction problems by the null-field method

  • Classical Problems of Linear Acoustics and Wave Theory
  • Published:
Acoustical Physics Aims and scope Submit manuscript

Abstract

Numerical realization of the null-field method for solving wave diffraction problems is investigated. It is shown that this method provides correct and stable algorithms only when the null-field surface encloses the set of singularities of the analytic continuation of the wave field inside the scatterer. Considering specific examples of diffraction problems, it is demonstrated that the null-field surface is best constructed by analytic deformation of the scatterer’s boundary.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. E. L. Shenderov, Emission and Scattering of Sound (Sudostroenie, Leningrad, 1989) [in Russian].

    Google Scholar 

  2. V. D. Kupradze and M. A. Aleksidze, Zh. Vychisl. Mat. Mat. Fiz. 4, 683 (1963).

    MathSciNet  Google Scholar 

  3. A. G. Kyurkchan, Radiotekh. Elektron. (Moscow) 29, 2129 (1984).

    ADS  Google Scholar 

  4. Yu. I. Bobrovnitski and T. T. Tomilina, Akust. Zh. 41, 737 (1995) [Acoust. Phys. 41, 649 (1995)].

    Google Scholar 

  5. A. G. Kyurkchan, S. A. Minaev, and A. L. Soloveichik, Radiotekh. Elektron. (Moscow) 46, 666 (2001).

    Google Scholar 

  6. A. G. Kyurkchan and N. I. Smirnova, Akust. Zh. 53, 490 (2007) [Acoust. Phys. 53, 426 (2007)].

    Google Scholar 

  7. P. C. Waterman, J. Acoust. Soc. Am. 45, 1417 (1969).

    Article  MATH  ADS  Google Scholar 

  8. D. Colton and R. Kress, Integral Equations Methods in Scattering Theory (Wiley, New York, 1983; Mir, Moscow, 1987).

    Google Scholar 

  9. Generalized Multipole Techniques for Electromagnetic and Light Scattering, Ed. by T. Wriedt (Elsevier, 1999).

  10. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge Univ., Cambridge, 2002).

    Google Scholar 

  11. T. Wriedt, J. Quantitative Spectrosc. Radiat. Transfer 106, 535 (2007).

    Article  ADS  Google Scholar 

  12. V. G. Farafonov, A. A. Vinokurov, and V. B. Il’in, Opt. Spektrosk. 102, 1006 (2007) [Opt. Spectrosc. 102, 927 (2007)].

    Article  Google Scholar 

  13. V. F. Apel’tsin and A. G. Kyurkchan, Analytical Properties of Wave Fields (Mosk. Gos. Univ., Moscow, 1990) [in Russian].

    Google Scholar 

  14. A. G. Kyurkchan, B. Yu. Sternin, and V. E. Shatalov, Usp. Fiz. Nauk 166, 1285 (1996) [Phys. Usp. 39, 1221 (1996)].

    Article  Google Scholar 

  15. N. B. Konyukhova and T. V. Pak, Diffraction of a Plane Sound Wave by a Rigid Prolate Spheroid (Vychisl. Tsentr Akad. Nauk SSSR, Moscow, 1985) [in Russian].

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. G. Kyurkchan.

Additional information

Original Russian Text © A.G. Kyurkchan, N.I. Smirnova, 2009, published in Akusticheskiĭ Zhurnal, 2009, Vol. 55, No. 6, pp. 691–697.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kyurkchan, A.G., Smirnova, N.I. Solution of wave diffraction problems by the null-field method. Acoust. Phys. 55, 691–697 (2009). https://doi.org/10.1134/S1063771009060013

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063771009060013

PACS numbers

Navigation