Research On Quadrilateral Mesh Generation Technology

In the field of Engineering Technology,the finite element method(FEM)is widely used.And mesh generation,as an important preprocessing step in FEM analysis,is directly related to the reliability of numerical simulation results.Comparing with the traditional triangular element,the quadrilateral element has higher calculation accuracy and efficiency.But the automatic quadrilateral mesh generation of complex two-dimensional domain and threedimensional domain is still a difficult problem,which needs our continuous research and exploration.In this paper,the basic knowledge of grid and the research status of quadrilateral mesh are introduced firstly.Subsequently,this paper made a detailed study of the SubMapping method and improved it.Several typical template are given for the vertex classification step,and the linear integer programming equation which adjust the result of vertex classification is optimized.By the way,the trinational soft and hard settings are abandoned in the boundary discretization step,and a new method is given.The test results of a large number examples show that the improvement of the SubMapping method in this paper is successful,the application scope of the original algorithm is extended and the reliability is improved.Subsequently,a new quadrilateral mesh generation algorithm based on subdomain decomposition is proposed by using the ideas of the median axis method and the SubMapping method.Firstly,the algorithm generates a background mesh by constrained Delaunay Triangulation(CDT),and uses geometric and topological information in the background mesh to achieve a rough segmentation of the region,and continues to decompose the region into several quadrilateral regions through subsequent algorithms.Finally,an improved template method is applied to generate mesh in each subregion.Since the common edges of each subregion are discretized only once,the meshes of each subregion can be merged directly.Finally,the post-processing steps of quadrilateral meshes are introduced and studied.Some common mesh smoothing algorithms,such as Laplacian algorithm and T_Base algorithm,are implemented.At the same time,the method of topology optimization for quadrilateral meshes is also studied,and the strategy of topology optimization for transition elements in the template is given.