Node Placement Algorithm and Application Based on the Centroidal Voronoi Tessellation

JI Cuilian¹  ZHOU Shenjie²  TIAN Yun³  WANG Kai²

(1. Municipal Department, Shandong City Building Vocational College, Jinan 250014;
2. School of Mechanical Engineering, Shandong University, Jinan 250061;
3. School of Mechanical and Electronic Engineering, Shandong Jianzhu University, Jinan 250101)

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  Meshless methods  Centroidal  Voronoi tessellations

CLC No: TP301

国家自然科学基金资助项目(10572077). Received 20070225, received in revised form 20070709