Node-based Local Mesh Generation Algorithm

With widespread use of FEM in engineering and the rapid development of the parallel computing system, Parallel finite element method as well as its mesh generation techniques has drawn the unprecedented attention. The node-based local mesh generation algorithm (shorted for NLMG) is studied extensively in this paper, which is considered one of the core techniques in the parallel computing of the finite element method. The main results and conclusions are as follows:Comparing the FEM with meshless method in the process of generating approximate functions and interpolation.The rule that whether the shape functions depend on the topological relationships between nodes or not is proposed to distinguish FEM from meshless method in this paper.Aiming at solving the grid inconsistency problems which probably occurring in NLMG, the natural relationships between the searching circles and inconsistency problem are studied extensively. Moreover, the theorem of consistency is proposed in this paper, which any NLMGs satisfying the conditions of are able to circumvent the inconsistency phenomenon. In virtue of the uniqueness of the Delaunay triangulation, a new NLMG is proposed, which is free of the inconsistency phenomenon. Sufficient examples show that the NLMG proposed in this paper is reliable, efficient, and suitable for parallel computing.The application of the NLMG in Nature Element Method as well as the meshless local-petrov Galerkin method based on the Voronoi cells is discussed in this paper. In the virtue of NLMG, both of the methods are able to achieve the seamless connection naturally.A new 2D arbitrary domain partition algorithm by means of searching constrained Delaunay path is proposed, which keeps the distributed processors free of communication during the process of parallel mesh generation. Both the theory analysis and parallel numerical examples results show that the application of the domain partition technique using Constrained Delaunay Path (CDP) in the parallel local mesh generation is able to enhance the parallel efficiency of FEM mesh generation in the case of given nodes.Based on NLMG, A new parallel scheme of the finite element method wasproposed in this paper, which possessed three following prominent characteristics: easy to realize the workload balance of the different processes naturally, achieving synchronization of all the schedules naturally under complex parallel environment. Breaking through the serial characteristic of mesh generation first, global stiffness matrix computation second.