An effective boundary element method for inhomogeneous partial differential equations

  • C. J. Coleman
  • D. L. Tullock
  • N. Phan-Thien
Original Papers


A method for removing the domain or volume integral arising in boundary integral formulations for linear inhomogeneous partial differential equations is presented. The technique removes the integral by considering a particular solution to the homogeneous partial differential equation which approximates the inhomogeneity in terms of radial basis functions. The remainder of the solution will then satisfy a homogeneous partial differential equation and hence lead to an integral equation with only boundary contributions. Some results for the inhomogeneous Poisson equation and for linear elastostatics with known body forces are presented.


Differential Equation Integral Equation Basis Function Partial Differential Equation Mathematical Method 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    C. A. Brebbia (Ed.),Boundary Elements X, Vol. 3. Computational Mechanics Publications, Southampton 1989.Google Scholar
  2. [2]
    B. L. Buzbee, F. W. Dorr, J. A. George and G. H. Golub,The direct solution of the discrete Poisson equation on irregular regions. SIAM J. Numer. Anal.8, 722–738 (1971).Google Scholar
  3. [3]
    C. J. Coleman.A boundary element approach to some nonlinear equations from fluid mechanics. Computational Mechanics, in press.Google Scholar
  4. [4]
    W. Horchers and F. K. Hebeker,The boundary element spectral method and applications in 3D viscous hydrodynamics. In: C. A. Brebbia et al. (Eds.),Boundary Elements VIII, Vol. 3. Springer-Verlag, Berlin 1986.Google Scholar
  5. [5]
    D. Nardini and C. A. Brebbia,A new approach to free vibration analysis using boundary elements. In: C. A. Brebbia (Ed.),Boundary element methods in engineering. Springer-Verlag, Berlin and New York 1982.Google Scholar
  6. [6]
    P. K. Banerjee, S. Ahmad and H. C. Wang,A new BEM formulation for the acoustic eigenfrequency analysis. Int. J. Num. Meth. Engng.26, 1299–1309 (1988).Google Scholar
  7. [7]
    D. P. Henry Jr. and P. K. Banerjee,A new BEM formulation for two- and three-dimensional elastoplasticity using particular integrals. Int. J. Numer. Meth. Engng.26, 2079–2098 (1988).Google Scholar
  8. [8]
    S. Saigal, A. Gupta and J. Cheng,Stepwise linear regression particular integrals for uncoupled thermoelasticity with boundary elements. Int. J. Solids Struct.26, 471–482 (1990).Google Scholar
  9. [9]
    R. B. Wilson, N. M. Miller and P. K. Banerjee,Free-vibration analysis of three-dimensional solids by BEM. Int. J. Numer. Meth. Engng.29, 1737–1757 (1990).Google Scholar
  10. [10]
    R. Zheng, N. Phan-Thien and C. J. Coleman,A Boundary Element approach for non-linear boundary-value problems. Computational Mechanics, in press.Google Scholar
  11. [11]
    M. J. D. Powell,Radial basis functions for multivariate interpolation. In: J. C. Mason and M. G. Cox (Eds),Algorithms for Approximation. Clarendon Press, Oxford 1987.Google Scholar
  12. [12]
    C. E. Pearson,Theoretical Elasticity. Harvard University Press, Cambridge, Mass. 1959.Google Scholar
  13. [13]
    P. K. Banerjee and R. Butterfield,Boundary Element Method in Engineering Science. McGraw-Hill, London 1981.Google Scholar
  14. [14]
    C. A. Brebbia, J. C. F. Telles and L. C. Wrobel,Boundary Element Technique. Springer-Verlag, Berlin 1984.Google Scholar
  15. [15]
    R. V. Southwell,An Introduction to the Theory of Elasticity. Clarendon Press, Oxford 1936.Google Scholar

Copyright information

© Birkhäuser Verlag 1991

Authors and Affiliations

  • C. J. Coleman
    • 1
  • D. L. Tullock
    • 1
  • N. Phan-Thien
    • 1
  1. 1.Dept of Mechanical EngineeringThe University of SydneyAustralia

Personalised recommendations