Parallel node-based local tetrahedral mesh generation

In this paper, we introduce the parallel Node-based Local FEM (NLFEM)-a novel version of FEM with natural parallel performances and adaptivity to various complex parallel environments. As a crucial part of 3D NLFEM, the Node-based Local Tetrahedron Mesh Generation (NLTMG) algorithm is presented, where guaranteeing the global conformity of local meshes is a strategy of ensuring the validity of the NLFEM and decoupling the NLFEM. In order to generate conforming local mesh, we search the neighbor nodes by the neighborhood of a corresponding multilevel bucket and then those nodes are Delaunay tetrahedralized by the TetGen. Accordingly, we prove that the global conformity of local mesh should be guaranteed if the maximum of nodes' numerical in a bucket, denoted by P, meets the following condition: P >λ * V _max, where V _max is the maximum of nodes' number connected with a node in the Delaunay tetrahedralization of the overall nodes set. Based on our experiments, estimates of l are provided.