Advertisement

On Numerical Solution of Integral Equations for Three-Dimensional Diffraction Problems

  • A. A. Kashirin
  • S. I. Smagin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6083)

Abstract

Questions of solution of three-dimensional diffraction problems are considered. The problems are formulated as weakly singular integral equations of 1 kind with alone unknown density. Discretization of these equations is realized by means of special smoothing method of fit integral operators. Numerical solutions of systems of linear algebraic equations, approximating integral equations of diffraction problems, were found by using of the variational iterative method and parallel computing technology. We gave the numerical experiment results.

Keywords

diffraction numerical method boundary integral equations variational iterative method parallel computing 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Kashirin, A.A., Smagin, S.I.: Generalized Solutions of the Integral Equations of a Scalar Diffraction Problem. Differential Equations 42(1), 79–90 (2006) (in Russian)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Smagin, S.I.: Numerical Solution of Integral Equation of the 1st Kind with a Weak Singularity on a Closed Surface. FAS USSR 303(5), 1048–1051 (1988) (in Russian)Google Scholar
  3. 3.
    Kashirin, A.A.: Research and Numerical Solution of Integral Equations of Three-dimensional Stationary Problems of Diffraction of Acoustic Waves: Thesis... of the candidate of physical and mathematical sciences. Khabarovsk (2006) (in Russian)Google Scholar
  4. 4.
    Ershov, N.E., Smagin, S.I.: Numerical Solution of a Three-dimensional Stationary Problem of Diffraction of Acoustic Waves on Three-dimensional Elastic Inclusion. Vladivostok (1989) (in Russian)Google Scholar
  5. 5.
    Saad, Y.: Iterative Methods for Sparse Linear Systems. PWS Publ. Co., Boston (2000)Google Scholar
  6. 6.
    Colton, D., Kress, R.: Integral Equation Method in Scattering Theory: Translated from English. Mir, Moscow (1987) (in Russian)Google Scholar
  7. 7.
    Selezov, I.T., Krivonos, Y.G., Jakovlev, V.V.: Scattering of Waves by Local Heterogeneities in Continuous Media. Naukova dumka, Kiev (1985) (in Russian)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • A. A. Kashirin
    • 1
  • S. I. Smagin
    • 1
  1. 1.Computing Center FEB RASKhabarovsk

Personalised recommendations