Some Applications of the Boundary Element Method for Potential Problems

  • C. A. Brebbia
  • L. Wrobel


The boundary element method is now firmly established as an important alternative technique to the prevailing numerical methods of analysis in continuum mechanics [1][2]. One of the most important types of applications is for the solution of a range of problems such as temperature diffusion, some types of fluid flow motion, flow in porous media and many others which can be written in function of a potential and whose governing equation is the Laplacian type. All these potential cases can generally be efficiently and economically analysed using boundary elements.


Boundary Element Fundamental Solution Boundary Element Method Boundary Integral Equation Integral Equation Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    BREBBIA, C.A. “The Boundary Element Method for Engineers” Pentech Press, London and Halstead Press, New York, 1978. Second Edition, 1980.Google Scholar
  2. 2.
    BREBBIA, C.A. and S. WALKER “Boundary Element Techniques in Engineering”, Butterworths, London, 1980.MATHGoogle Scholar
  3. 3.
    FREDHOLM, I. “Sur une Classe d’equations fonctionelles”, Acta Meth., 27, 365–390, 1903.MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    KELLOGG, O.D. “Foundations of Potential Theory”. Springer-Verlag, Berlin, 1929.CrossRefGoogle Scholar
  5. 5.
    JASWON, M.A. “Integral Equation Methods in Potential Theory I”, Proc. Royal Society A, 275, 23–32, 1963.MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    SYMM, G.T. “Integral Equation Methods in Potential Theory II”, Proc. Royal Society A, 275, 33–46, 1963.MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    JASWON, M.A. and A.R. PONTER “An Integral Equation Solution of the Torsion Problem”, Proc. Royal Society A, 273, 237–246, 1963.MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    HESS, J.L. and A.M.O. SMITH “Calculation of Potential Flow about Arbitrary Bodies” Progress in Aeronautical Sciences, Vol. 8, D. Kilchemann (ed.) Pergamon Press, London, 1967.Google Scholar
  9. 9.
    HARRINGTON, R.F., K. PONTOPPIDAN, P. ABRAHAMSEN and N.C. ALBERTSEN, “Computation of Laplacian Potentials by an equivalent-source method”, Proc. IEE, Vol. 116, No. 10, 1715–1720, 1969.MathSciNetGoogle Scholar
  10. 10.
    MAUTZ, J.R. and R.F. HARRINGTON “Computation of Rotationally Symmetric Laplacian Potentials”, Proc. IEE, Vol. 117, No. 4, 850–852, 1970.Google Scholar
  11. 11.
    JASWON, M.A. and G.T. SYMM “Integral Equation Methods in Potential Theory and Elastostatics”, Academic Press, London, 1977.MATHGoogle Scholar
  12. 12.
    FAIRWEATHER, G., F.J. RIZZO, D.J. SHIPPY and Y.S. WU “On the Numerical Solution of Two-Dimensional Potential Problems by an Improved Boundary Integral Equation Method ” Journal of Computational Physics, Vol. 31, 96–112, 1979.MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    CHANG, Y.P., C.S. YANG and D.J. CHEN “The Use of Fundamental Green’s Functions for the Solution of Heat Conduction in Anisotropic Media”. Int. Journal of Heat and Mass Transfer, Vol. 16, 1905–1918, 1973.MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    BIALECKI, R. and A.J. NOWAK “Boundary Value Problems for Nonlinear Applied Mathematical Modelling, Vol. 5, December 1981.Google Scholar
  15. 15.
    SVELEK, P. and C. BREBBIA “Nonlinear Potential Problems”, Chapter 1 in “Progress in Boundary Element Methods. Vol.2”. Pentech Press, London, 1982Google Scholar
  16. 16.
    ABBOTT, I.H. and A.E. VON DOENHOFF “Theory of Wing Sections”, Dover, New York, 1959.Google Scholar
  17. 17.
    GOLDENBERG, H. “External Thermal Resistance of Two Buried Cables”, Proc. IEE, Vol. 116, No. 5, 822–826, 1969.Google Scholar
  18. 18.
    WOOD, W.L. “On the Finite Element Solution of the Exterior Boundary-Value Problem”, Int. Journal Num. Methods Engng, Vol. 10, 885–891, 1976.MATHCrossRefGoogle Scholar
  19. 19.
    SKERGET, P. Internal Report, Computational Mechanics Centre, Southampton, 1982.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1982

Authors and Affiliations

  • C. A. Brebbia
    • 1
    • 2
  • L. Wrobel
    • 1
    • 2
  1. 1.Computational Mechanics CentreSouthamptonUK
  2. 2.Federal University of Rio de JaneiroBrazil

Personalised recommendations