Design And Realization Of Delaunay Mesh Generation Method

The finite element method which has important applications in the field of science and engineering is an approximate method for solving the complex problems. The finite element mesh including structured mesh and unstructured mesh is an important part of the finite element method. In unstructured mesh adaptive mesh is very important. Delaunay mesh generation algorithm is an important adaptive meshing method, which not only has a strong theoretical foundation of mathematics, but also was applied in various engineering fields. Delaunay meshing algorithm can generate high-quality triangular mesh in curve meshing, plane meshing and surface meshing. Delaunay mesh generation algorithm is fit for complex space curves and surfaces, which has simpler algorithm, higher efficiency.This paper further studies and improves Delaunay mesh generation method for curves, planes and surfaces. On the basis of Alpha which is the finite element analysis software of the independent development in Key Laboratory of Integrated Automation of Process Industry at Northeastern University. This paper designs and implements Delaunay mesh generation algorithm, the main work is as follow:At the theoretical level, this paper evaluates and summarizes the most popular Delaunay mesh generation algorithms, and defined a basic process and the input and the output. This paper divides Delaunay meshing methods into three parts, namely:curve meshing, plane meshing, and surface meshing. In the curve meshing section, this paper cited Riemann metric and details the relevant theoretical knowledge of Riemannian metric. In the plane meshing section, this paper applies the coloring algorithm to solve the problem of regional recognition and to improve the efficiency of the algorithm. In the surface meshing section, this paper cleverly combines the curve meshing algorithm and the plane meshing algorithm to form a surface meshing algorithm based mapping method, and to get satisfactory results.At the practice level, the generator system is developed with Visual Studio 2010 and implemented by standard C++language. The three key classes of Delaunay meshing algorithm is designed by using object-oriented programming. These classes are meshing class, geometry class and meshing data class. This paper designs and implements curve Delaunay meshing algorithm, plane Delaunay meshing algorithm and surface Delaunay meshing algorithm. The structure of program is not only independent but also has encapsulation. The code runs in the higher efficiency and has good efficiency of time and space complexity.