论文标题:一类非结构任意四边形网格自动生成
An Unstructured Automatic Quadrilateral Mesh Generation on Arbitrary Geometry
论文作者 王龙
论文导师 傅凯新；舒适,论文学位 硕士,论文专业 计算数学
论文单位 湘潭大学,点击次数 135,论文页数 74页File Size2069k
2001-04-01论文网 http://www.lw23.com/lunwen_862501737/ 有限元，非结构化，网格自动生成，四边形，铺砖法。
Finite Element, Unstructured, Automatic Mesh Generation, Quadrilateral, Paving.
在二维非结构化网格自动生成的研究中，四边形网格和三角形网格是当前应用最为广泛的两类网格。目前，三角形网格的自动生成技术已趋成熟，但关于任意四边形网格自动生成技术还不完善，因此，关于任意四边形网格自动生成的研究成为现在二维非结构化网格自动生成研究的热点和难点。铺砖法因为具有边界吻合度好，拓扑变换不变，不规则点少的优点而备受研究者青睐。但它存在交叉检验效率低和网格尺寸的光滑过渡差（特别是在单元尺寸相差很大时）等缺陷。我们对铺砖法做了以下改进： （1）首先对离散边界节点进行Delaunay三角形剖分，利用这一网格建立尺寸空间和邻居空间；然后借助这两个铺助的工具和规范边长概念来生成单元新边，从而将单元生成与整体尺寸控制很好地结合起来。 （2）利用尺寸空间和邻居网格把铺砖法中的相交检验化为局部性的工作：即高效的局部查找。 （3）引入Q-Morph方法中的铺砖边状态函数概念及当前铺砖回路和当前铺砖边的选取方法，并且实行每次生成一个单元而非一层，且每生成一个新四边形单元便进行局部光滑。 这样，经改善的铺砖法便能高效地生成高质量的任意四边形网格。此外，通过多种光滑及预处理技巧的综合使用，对区域尺寸分布复杂的情况也有很好的结果。实验证明：算法是有效、稳定和健壮的。
Abstract Quadrilateral mesh and triangular mesh are the most widely used mesh recently in two-dimensional mesh generations. At present, the technique for the automatic generation of triangular element mesh has been developed perfectiy. By the contrast, the technique for the automatic generation of quadrilateral element mesh in arbitraiy geometries is not so satisfactory. Therefore, most research on creating fully automatic unstructured mesh generators focus on the automatic generation of quadrilateral element mesh in arbitraiy geometries. Many researchers prefer employing Paving as automatic quadrilateral mesh generators to the other techniques for the three reasons: boundary sensitive, orientation insensitive and few irregular nodes. However; Paving suffered from a lack of low e1~ciency in intersecfion check and bad mesh transition (especially in the region with a large gradation of element sizes). In this paper we present an improved Paving algorithm based on the following aspect1. Firstly by the initial Delaunay mesh obtained on the discrete boundary, we construct a background mesh, which is then used to create Control Space and Neighborhood Space. AlInrwanl on the edge generation of quadrilateral element, by the tools of Control Space, Neighborhood Space and the idea of norm edge, we associate a step size all over the domain easily.2. The tool of Control Space and Neighborhood Space localize the intersection check into a fast local check.3. By the idea of Paving edge condition function and the choice of departure Paving loop and Paving edge in Q-Morph method, we generate a quadrilateral element every time but not a row of elements. And that, we process smooth after the element generation. Then, we can use the improved Paving algorithm to rapidly generate high-quality quadrilateral mesh for an arbitrary planar area. In addition, combined with many smooth and pre-adjustment skills, we can mesh the large graded region effectively. Numerical test shows that the algorithm is efficient, stable and robust
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