Research On Tetrahedral Mesh Generation Algorithm Based On Surface Model

In recent years, with the rapid development of science and technology, tetrahedral meshhas been widely used in the field of finite element analysis and scientific visualization andbecomes the hotspot of current researches. Continuous region is partitioned into discreteelements in the process of mesh triangulation. Delaunay triangulation and advancing frontalgorithm are currently two most widely used methods for generating tetrahedral mesh. Witha rigorous mathematical basis，delaunay triangulation algorithm can generate high qualitytetrahedral mesh which meets the condition of topology conformity automatically. Buttetrahedral mesh generated by delaunay triangulation can not maintain the boundary of theregion, so a boundary recover algorithm is needed which is complex and not fit the surfacemodel which has complex shape. The advancing front algorithm generates tetrahedron towardthe interior which takes the surface model as the initial front and boundary recovery isunnecessary. This method can control the position of the inserted node flexibly. But themethod required to construct the background or size control function which are used tocalculate the size of the generated tetrahedron, reduce the degree of automation of thealgorithm. It is necessary to ensure the topology conformity between the new generatedtetrahedron and the existed tetrahedrons. This thesis uses the advancing front algorithm togenerate the tetrahedral mesh of the surface model, the main content of this thesis is:(1) To address the issue that background mesh is constructed and size control functionis specified manually in the process of mesh generation, which reduces the degree ofautomation of the algorithm, a method that calculates the mesh size automatically is proposed.Though tetrahedral mesh generation by each layer, based on the surrounding front and normalinformation, the size of tetrahedron is calculated and smooth mesh is generated.(2) A detailed analysis is given for all situations that may destroy the condition oftopology conformity in the advancing front algorithm. Though simultaneous parameterequations of the line and plane, the relationship between a segment and a triangle is judged,the intersection condition is given in detail, which is implemented easily in programming.(3) The connection between the node and the triangle is used frequently, the connectioninformation of geometry elements is simplified, which can reduce the memory consumption, at the same time, the complexly of the algorithm is not influenced. The search algorithmbetween the geometry elements is given.(4) Based on the advancing front method, tetrahedral mesh is generated for the adjacentlayer contour lines.The algorithm of this thesis is used to generate to tetrahedral mesh of some surfacemodels, the results show that this algorithm could generate high quality mesh.