Skip to main content
SpringerLink
Log in
Book cover

International Workshop on Numerical Analysis and Its Applications

WNAA 1996: Numerical Analysis and Its Applications pp 243–249Cite as

Numerical methods for computation of the double layer logarithmic potential

  • Conference paper
  • First Online:

  • 255 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1196))

Abstract

An approximation of the double layer logarithmic potential is obtained as a solution to a discrete Laplacian equation with a new right-hand side. The error is estimated under the assumption that the potential belongs to some Besov spaces. Since the right hand side includes evaluation of line integrals, we use appropriate quadratures for their computation. The well know scheme of A. Mayo, 1984, can be obtained as a partial case.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Friedman, A.: Mathematics in industrial problems. Springer (1992)

    Google Scholar 

  2. Gold J., Graham I.: Towards automatition of boundary integral methods for Laplace's equation. in ”Mathematics of finite elements and applications” Academic Press (1991) 349–360

    Google Scholar 

  3. Golovin G., Makarov M., Sablin M., Sukhachev D., Yakovlev V.: Comparison of various methods for solving the Dirichlet problem for the Laplace equation in complicated domains. Zh. Vychisl. Mat. Fiz. 27 (1987) 1662–1679 (in Russian)

    Google Scholar 

  4. Drenska, N.: Computation of potentials used in the boundary element method. Colloq. Math. Soc. Janos Bolyai 59 (1990) 157–163

    Google Scholar 

  5. Kolkovska, N.: Reconstruction of some potentials used in the boundary element method. J. of Integral Equations and Applications 5 (1993) 345–367

    Google Scholar 

  6. Kress, R.: Linear integral equations. Springer (1989) 298

    Google Scholar 

  7. Lazarov, R., Mokin Yu. On the computation of the logarithmic potential. Soviet Math. Dokl. 28 (1983) 320–323

    Google Scholar 

  8. Mayo A.: The fast solution of Poisson's and the biharmonic equation on irregular regions. SIAM J. Numer. Anal. 21 (1984) 285–299

    Google Scholar 

  9. Mayo A., Greenbaum A.: Fast parallel iterative solutions of Poisson's and the biharmonic equations on irregular domains. SIAM J. Sci. Stat. Comp. 13(1992) 101–118

    Google Scholar 

  10. Mokin, Yu.: Methods of calculating a logarithmic potential. Izd. Moskovsk. Gos. Univ., Moscow (1988) 124 (in Russian)

    Google Scholar 

  11. Yakovlev V. On the computation of the flaxere of the thin plate with leant edges Vestn. MGU, ser. 15 (1985) 19–22 (in Russian)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathemtics and Informatics, G. Bonchev str., bl 8, 1113, Sofia, Bulgaria

    Natalia Kolkovska

Authors
  1. Natalia Kolkovska
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Lubin Vulkov Jerzy Waśniewski Plamen Yalamov

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kolkovska, N. (1997). Numerical methods for computation of the double layer logarithmic potential. In: Vulkov, L., Waśniewski, J., Yalamov, P. (eds) Numerical Analysis and Its Applications. WNAA 1996. Lecture Notes in Computer Science, vol 1196. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62598-4_100

Download citation

  • DOI: https://doi.org/10.1007/3-540-62598-4_100

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62598-8

  • Online ISBN: 978-3-540-68326-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation