Some Issues Of Surface Meshing For Engineering And Scientific Computation

Mesh generation is the pre-process of various numerical methods such as Finite Element Method (FEM), and one of the universal supporting techniques of Computer Aided Engineering (CAE). The ability to generate high-qualified meshes in an efficient way is vital to the success of these numerical methods. In this field, surface meshes play a special and important role. They are the input of volume mesh generators and the boundary conditions will be attached on them, thus they will significantly influence the quality of volume meshes and further the numerical results. High-quality surface meshes are also needed for the analysis of shell structures, and their generation is directly related to geometric modelling. Surface meshes also have many other applications in various fields.To satisfy the requirements for high-quality surface meshes oriented to engineering and scientific computation, this thesis systematically studies the related problems such as surface meshing, remeshing and optimization with corresponding algorithms implemented. Besides, with the fast development of supercomputers and the ever larger problems arising in such areas as Computational Fluid Dynamics (CFD) and Computational Electro-Magnetics (CEM), close attention has been paid to parallel mesh generation to overcome the bottlenecks of serial mesh generation in terms of time and memory consuming. Thus we also have developed a general framework for parallel planar mesh generation. Concretely, the contents of the thesis are arranged as follows.The background, significance and framework of the thesis are briefly introduced in the first chapter. Then comes the review of finite element mesh generation methods, with the emphasis on closely related topics, such as mesh quality control and mesh gradation, parallel mesh generation, surface meshing and remeshing, and mesh optimization.Chapter 3 presents several procedures for improving the topology of unstructured quadrilateral meshes. Based on the local topological structures of the meshes, these procedures are organized in the form of "case-operation". A case is a kind of local meshed region, which satisfies some pre-defined constrained conditions, and its topology or the degrees of its vertices can be optimized by means of topological transformation.The general framework for parallel planar mesh generation is given in Chapter 4, which includes several modules, i.e. serial or parallel geometry decomposer, SubDomain Graph (SDG) Manager, parallel planar mesh generator and an optional mesh repartitioner. Besides the basic features required by parallel algorithms such as scalability, stability and high parallel efficiency, this framework also possesses some other good traits: It can reuse the existed codes of serial geometry decomposition and mesh generation algorithms; With the help of SDG and its static or dynamic partitioning, the parallel generated distributed mesh is of high partitioning quality, thereby the cost of mesh repartitioning, which is required by traditional methods, can be eliminated or reduced, consequently, the efficiency of the whole parallel simulation will be improved; A parallel planar Delaunay mesh generator PDMG-2D, which is integrated in this framework, can generate hundreds of millions of elements in minutes with medium sized parallel resources.Chapter 5 presents a system for complex composite parametric surface mesh generation. From the perspective of system, it has its own geometric definition oriented to mesh generation and the ability to generate such geometric objects, which reveals the effort to bridge the gap between the CAD and mesh generation systems. Meanwhile it also has the functions of CAD/CAE conversion and CAD repair, which brings it the capability of generating meshes on a mass of CAD models. From the perspective of algorithm, it includes two indirect surface mesh generation algorithms. One is an existed Advancing Front Technique (AFT) based on the transformation matrix, and the other a new Delaunay method based on Riemannian metric. The surface meshes generated by them are of high quality. The chapter introduces these algorithms and the framework in detail.Chapter 6 gives an improved Laplacian smoothing approach for surface meshes. The geometric features are first detected by a simple procedure and then treated carefully to prevent them from disappearing. All the nodes of smoothed meshes are guaranteed to be on the original discrete surface by a projection algorithm, thus the shrinkage problem of Laplacian smoothing is avoided. What's more important, the fatal flaw of Laplacian smoothing for generating extremely abnormal or even inverted elements is settled by solving a constrained optimization problem, which is based on the principle of minimum surface in differential geometry.Chapter 7 presents a surface remeshing method with feature preservation. According to the specified density, different regions on a mesh are coarsened or refined by topological transformations, which operate directly on the discrete surface without a continuous supporting surface. Thus it is easy to implement and of high efficiency. The mesh is finally optimized by methods of edge swapping and the improved Laplacian smoothing approach given in Chapter 6.Finally, Chapter 8 concludes the thesis and suggests the directions for future research work.