The Research On Quadrilateral Mesh Generation Algorithm

Finite element method has been developing and becoming more and more mature in the past decades,which plays an important role in the field of engineering technology.And as a core step of the finite element calculation,mesh generation is also a research hotspot in recent years,the triangle(tetrahedral)mesh generation algorithm now is relatively mature,while quadrilateral(hexahedron)mesh generation algorithm is deeply researched,but manual intervention is inevitable while deal with complex industrial models.The quadrilateral mesh generation is still unable to realize full automation,so more deep research is necessary.Together with many scholars' efforts,quadrilateral mesh generation algorithm based on thought of division has developed into one of the mainstream algorithms,the basic idea of this algorithm is to divide the region recursively until it was decomposed into a series of subregions which are shaped like quadrilateral,usually it stops when the number of subdomain's nodes reachs 4 or 6,then accomplish the mesh generation on the subregions.In this paper,a quadrilateral mesh generation algorithm which combines Delaunay triangulation and thought of divide-and-conquer is presented.The Delaunay triangulation results of regions are used as background grid to select the optimal cutting lines,the efficiency of the region division is greatly improved,the grid template is improved,and it could deal subregions with different number of nodes,satisfy the requirement of the grid pattern transition,also reduce the frequency of regional recursive decomposition.In general,for arbitrary discreted two-dimensional regoins,if it is multi-connected,firstly it will be transformed into a simply connected topology sphere by the topological decomposition,then the simply connected topology circle will be divided recursively until its subregions reached the standard of mesh generation,secondly the transition mesh template combined with mapping method are applied to accomplish the mesh generation of the subregions.Finally,through the splicing and optimize,mesh generation of the whole multi-connected domain is accomplished.The results show that the proposed algorithm can automatically generate quadrilateral meshes with high quality for any two-dimensional region.In addition,the geometric engine OpenCascade is researched and developed in this paper.With the help of its surface parameterization system and other functions,the algorithm is also used to generate the quadrilateral mesh over 3d surfaces,and the fine results are obtained.