The dual reciprocity hybrid radial boundary node method for Generalized Poisson Equation ∇2u=b(x,y,u)

The dual reciprocity hybrid radial boundary node method (DRHRBNM) combines the hybrid radial boundary node method (HRBND) and the dual reciprocity method (DRM). In the HRBND, since the radial basis point interpolation is used to construct the shape function with delta function property, the boundary conditions can be imposed directly and easily. The DRM is used to avoid the domain integral. In this way, it is a truly meshless method, i.e. absolutely no meshes are required neither for interpolation nor for integration. However, this method has been used only for solving the inhomogeneous problems in which the inhomogeneous term is a given functon. This paper applied this method for solving Generalized Poisson Equation. In this paper, the solution is composed of two parts, the homogeneous solution and the particular solution. The homogeneous one is solved by the HRBND. By expressing the right-hand term and the unknown function of the governing equation as a combination of radial basis functions (RBF), the inhomogeneous solution is gained by the DRM. Numerical examples show that high convergence rates and high accuracy are achievable.