Chinese Journal of Computers   Full Text
Title	A Reliable and Effective Tetrahedral Meshing Algorithm
Authors	SHAN Ju-Lin GUAN Zhen-Qun SONG Chao
Address	(State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics， Dalian University of Technology, Dalian, Liaoning 116024)
Year	2007
Issue	No.11(1989—1997)
Abstract &   Background	Abstract A reliable and effective tetrahedral meshing algorithm is proposed based on advancing front method. The detailed design of the data structure is given which representing a mesh topology connection. The operators such as insert, query and delete like a database are implemented by using hash table which accelerates the whole algorithm. Instead of preparing a background mesh for mesh spacing control, this information is estimated at the beginning of each layer at each node from the area of connecting triangles on the front and a user-specified stretching factor. A Cell Searcher is prepared to correct the mesh spacing information and to perform geometric search efficiently. During rolling back the advancing path is changed by changing preferential factor of front, as a result the times of rolling back is decreased significantly. Node inserting based on linear programming technique guarantees the convergence of the algorithm. At the end of the mesh generation process, unwanted node removing and angle-based smoothing are employed to enhance the resulting mesh quality. The examples demonstrate that high quality tetrahedral meshes can be generated within a reasonable time limit. keywords tetrahedral mesh generation; advancing front technique; finite element Background The automatic generation of unstructured meshes plays an important role in computational mechanics especially in the framework of the finite element analysis (FEA). For three-dimensional mesh generation, some useful methods have been developed, such as the advancing front technique (AFT), Delaunay triangulation and spatial decomposition or Octree techniques. It is noted that most of these methods have focused on tetrahedral elements since tetrahedral elements are easily adapted for discretization of a complex, three-dimensional region. Over the years, the advancing front technique has achieved considerable success in two and three-dimensional mesh generation .In this approach, elements and nodes are generated simultaneously starting from the boundary of the domain and proceeding into the interior. The boundary discretization is taken as the initial front, and a set of heuristics determines where a new element is to be created, where to place a new interior node, and how to reconnect the front. The algorithm terminates when the front is empty. The main objective of this study is to develop an automatic tetrahedral mesh generator for FEA. However, the performance of the conventional advancing technique in three dimensions is not always effective and stable. In this paper, topology based meshing data structures are implemented. A node inserting algorithm is proposed based on linear programming technique to solve the Schoenhardt polyhedron problem which is the main barrier of AFT in three-dimensional tetrahedral meshing. The algorithm of adaptive tetrahedral generation and the optimization of tetrahedral meshing are also given at the end of this paper.