Local Regular Dual Reciprocity Method For 2D Convection-diffusion Equation
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N. Caruso1,2, M. Portapila1,2 & H. Power3
In this paper a new technique considering the dual reciprocity method (DRM) with only internal collocation points is considered along with local radial basis function interpolation. This approach gives rise to regular integral equations. Numerical results for the convection-diffusion equation are presented for different Peclet numbers. Comparisons with other numerical techniques are shown in order to illustrate the good solutions obtained by this method. Keywords: DRM, RBF, regular integral equations. 1 Introduction The basis of boundary element method (BEM) is to transform the original partial differential equation (PDE), into an equivalent integral equation. Several methods have been developed to take domain integrals to the boundary in order to eliminate the need for internal cells (boundary only BEM formulations). One of the most popular to date is the dual reciprocity method (DRM) introduced by Nardini and Brebbia , it converts the domain integrals into equivalent boundary integrals. Popov and Power  found that the DRM approach can be substantially improved by using domain decomposition to improve the accuracy of the DRM approach, this idea was inspired by the work of Kansa and Carlson  on the radial basis function (RBF) data approximations. Florez e t a l . [ 4] improved the performance of the DRM in the BEM numerical solution of the Navier- Stokes equations through a multidomain decomposition technique. Following those results, the performance the DRM-MD was investigated , implementing quadratic shape functions of the boundary elements for both the approximation of
DRM, RBF, regular integral equations.