A new implementation of DRM with dual interpolation boundary face method for Poisson equation

Abstract

We present a new numerical algorithm combining the dual reciprocity method with the dual interpolation boundary face method for solving the two-dimensional Poisson equations. In this new combined approach, the boundary physical variables and particular solutions are approximated by dual interpolation elements which include source and virtual points. Additionally, this algorithm is implemented by employing the augmented thin plate spline interpolation function to approximate non-homogeneous term and the Hermite-type moving-least-square approximation to approximate physical variables for virtual nodes. Compared with the traditional dual reciprocity boundary element method, this combined method possesses higher accuracy and efficiency and is better suited for structures with small feature sizes. Several numerical examples are given to illustrate the superiority of the proposed method for solving Poisson equations.