Radial basis function approximation in the dual reciprocity method

  • Authors:

  • S. R. Karur;P. A. Ramachandran

  • Affiliations:

  • Department of Chemical Engineering, Washington University One Brookings Drive, Campus Box 1198, St. Louis, MO 63130, U.S.A.;Department of Chemical Engineering, Washington University One Brookings Drive, Campus Box 1198, St. Louis, MO 63130, U.S.A.

  • Venue:
  • Mathematical and Computer Modelling: An International Journal
  • Year:
  • 1994

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Abstract

The Dual Reciprocity Method (DRM) is a class of boundary element techniques wherein, the domain integral resulting from the nonhomogeneous terms in Poisson type equations is transferred to an equivalent boundary integral by using suitable approximation functions. The use of radial basis functions (RBF) as approximating functions for this purpose has several advantages over conventional interpolation techniques. In this work, the convergence property of RBF for two dimensional problems is examined numerically. The interpolation error is quantified for a particular test function and the local behavior of the RBF is illustrated. The RBF are then used for approximation in DRM to solve nonlinear Poisson type equations and the results are compared with known exact solutions. The close agreement of the numerical solution to the exact solution, for a uniform mesh refinement, demonstrates the convergence properties of the RBF and the accuracy of their use in DRM.