Acoustical Physics

, Volume 64, Issue 2, pp 252–259 | Cite as

A New Numerical Method for Solving the Acoustic Radiation Problem

  • J. Poblet-Puig
  • A. V. Shanin
Acoustic Signal Processing and Computer Simulation


A numerical method of solving the problem of acoustic wave radiation in the presence of a rigid scatterer is described. It combines the finite element method and the boundary algebraic equation one. In the proposed method, the exterior domain around the scatterer is discretized, so that there appear an infinite domain with regular discretization and a relatively small layer with irregular mesh. For the infinite regular mesh, the boundary algebraic equation method is used with spurious resonance suppression according to Burton and Miller. In the thin layer with irregular mesh, the finite element method is used. The proposed method is characterized by simple implementation, fair accuracy, and absence of spurious resonances.


finite element method boundary element method boundary algebraic equations discrete Green’s function 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    B. A. Voinov, Akust. Zh. 40, 935 (1994).Google Scholar
  2. 2.
    I. P. Getman and N. V. Kurbatova, Akust. Zh. 40, 581 (1994).Google Scholar
  3. 3.
    C. Saltzer, Discrete Potential Theory for Two-Dimensional Laplace and Poisson Difference Equations, Technical Report No. 4086 (National Advisory Committee on Aeronautics, 1958).Google Scholar
  4. 4.
    V. S. Ryaben’kii, Math. Nachr. 177, 251 (1996).MathSciNetCrossRefGoogle Scholar
  5. 5.
    P.-G. Martinsson and G. J. Rodin, Proc. R. Soc. A 465, 2489 (2009).ADSCrossRefGoogle Scholar
  6. 6.
    S. V. Tsynkov, J. Sci. Comput. 18, 155 (2003).MathSciNetCrossRefGoogle Scholar
  7. 7.
    J. Poblet-Puig and A. V. Shanin, J. Integr. Equations Appl. 27, 233 (2016).CrossRefGoogle Scholar
  8. 8.
    A. J. Burton and G. F. Miller, Proc. R. Soc. London, Ser. A 323, 201 (1971).ADSCrossRefGoogle Scholar
  9. 9.
    S. Katsura and S. Inawashi, J. Math. Phys. 12, 1622 (1971).ADSCrossRefGoogle Scholar
  10. 10.
    P. A. Martin, Wave Motion 43, 619 (2006).MathSciNetCrossRefGoogle Scholar
  11. 11.
    O. C. Zienkiewicz, The Finite Element Method in Engineering Science, 2nd ed. (McGraw-Hill, London, New York, 1971).zbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Polytechnic University of CataloniaBarcelonaSpain
  2. 2.Department of PhysicsMoscow State UniversityMoscowRussia

Personalised recommendations