A dual reciprocity hybrid radial boundary node method based on radial point interpolation method

Abstract

A novel truly meshless method called dual reciprocity hybrid radial boundary node method (DHRBNM) is developed in present, which combines dual reciprocity method (DRM), hybrid boundary node method (HBNM) and radial point interpolation method (RPIM). Compared to the dual reciprocity hybrid boundary node method (DHBNM), RPIM is exploited to replace the moving least square in DHRBNM, unlike HBNM, the shape function obtained by present method has the delta function property, so the boundary conditions can be applied directly and easily, and computational expense is greatly reduced. In order to get the interpolation property of different basis function in DRM, different approximate functions are applied in DRM for comparison, and the accuracy and efficiency of them are discussed. Besides, RPIM is also exploited in DRM, which can greatly improve the accuracy of present method. Moreover, the accuracy of DRM is greatly influenced by the nodes number and their location, hence, some examples are investigated to show that the internal node number is equal to boundary node number and they are arranged parallel to the high gradient direction of the problem are the best choice. Finally, DHBNM is applied for comparison and some selected numerical examples are given to illustrate that the present method is efficient and less computational expense than that of DHBNM.