Abstract: Based on the Voronoi tessellation of initial points, an algorithm with centroidal Voronoi tessellation for construction of nodes used in meshless discretization is proposed. Voronoi tessellations are constructed corresponding to a given set of initial points on the domain. By using natural coordinates of triangles, the centroids of Voronoi tessellations are determined, and the cost function is used as convergence theorem. If the centroids of Voronoi tessellations meet the convergence theorem, those centroids are final obtained nodes placed in the domain and on the boundary. Then by cutting boundary technique, points can be placed in arbitrary domains. Uniform and non-uniform nodal arrangements can be realized by this algorithm. A numerical example of cylinder with hole subjected to uniform internal pressure is presented by using the natural neighbour Petrov-Galerkin method and the proposed algorithm. The numerical results are in great agreement with the exact solutions, which indicates that the proposed algorithm is very accurate and reliable in meshless methods.

Key words: Algorithm of points displacement, Centroidal Voronoi tessellations, Meshless methods