| The finite element mesh generation is a very important process. It need consider a lot of question, and the workload we spent on it also very big. The form of mesh generation directly influences compute precision and compute scope. With the finite element method developed, the finite element mesh generation has a great deal of development. The earliest finite element mesh generation appeared in early 1970's.The mesh auto-generation straight is the focus of the finite element research not only in country but also in oversea. And much different arithmetic is produced. The application of the finite element method needs two processes: pro-process and post-process. A question must be conquered is that the whole geometry shape defined efficiency the finite element mesh. With finite element methods widely application recently years, mesh generation technology has been deeply researched and developed. And many mesh generation methods was appeared. In this article, author will introduce a simple and efficiency quadrangle finite element mesh generation method. Because automatic method for the generation of all-quadrangle mesh is more difficult than triangle mesh. So most of automatic generation methods generated triangle mesh. Except automatic generation quadtree method and interaction mapping method, few methods could generate quadrangle mesh. It can offset this gap by research triangle mesh turn to quadrangle mesh. Most of results will turn to triangle mesh and quadrangle mesh. In this article, author take plane paving method generates triangle mesh. Paving algorithm is a kind of broad-based grid generation algorithm. The step of the method is that generating the mesh form the boundary to interior region line upon line till the region is filled. In my paper I improved some conditions on the original algorithm, such as the generation of the new node, sewing the grids and fairing of the mesh. When produce the new node, two ways of grid generation are presented according to different angle, when, the new node is ; when , the new node is , the processing advantage of this step ensure that the paving border will become more fairing and the grid generation is evener. In the step of sewing the grids, two kinds of things need solving. One is that the new element exist the known node, the other is that the new generated node enter into the existent element. According as different angle, selecting different sewing ways can ensure that the paving algorithm process successfully. The interior boundary with the difference of fairing power being 2 replaced the paving boundary in the fairing step. The quality of grids with the improved paving algorithm is higher and time of gird generation will be shortened.The method of triangle mesh translated to quadrangle mesh is that delete common side of two adjacent triangle mesh. Thus it can be translated to quadrangle element. It is easy to implement. If three side of a triangle mesh has adjacent element, which side was selected canGenerated good quality quadrangle or the surface generated meshes more appropriate. In the paper, the author takes an algorithm: classification method. It can measure triangular quality dimension (area/sum of squares of three sides) from triangle angle. As for quadrilateral, a new distortion coefficient has to be introduced. Pass through all the elements. All the nodes and sides were checked. The side's list was based. It included each side's start point, end point, and adjacent element. The side can be consider the common side of the two adjacent elements and computed its value. Computing all the side except border edges. Giving out the quadrilateral value which user can accept and classification number. Checking all the interior sides. Deleting all the sides if the sides' value were not smaller and transforming a quadrangle. Value is . For a single triangular mesh, inserting a node. Computing each side's midpoint, linking the four points. Transforming this element to three elements. At last, smoothing the meshes. Comparin...
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