【摘要】 在有限元分析中,四边网格比三角网格更难以生成,特别是在具有复杂形状和拓扑结构的平面域上.为此,基于几何迭代算法,提出一种在形状复杂和高亏格的n边平面域上生成高质量四边网格的方法,并保证生成的四边网格不自交.该方法以自适应像素化离散技术生成的四边网格作为初始网格,网格边界迭代拟合至给定的平面区域边界,其中每次边界迭代后,通过分层的Laplace算子改变内部顶点的位置;在迭代过程中,网格顶点的移动都受到限制,保证生成的网格严格不自交.最后通过实验验证了文中算法的效率和有效性.更多还原

【Abstract】 In finite element analysis, the generation of quadrilateral(quad) meshes is harder than that of triangular meshes, especially on planar regions with complicated shape and topology structure. In this paper, we developed an iterative method to produce quad meshes on n-sided connected planar regions with complicated geometric shape and high genus, and the generated quad mesh is guaranteed to be non-self-overlapping. Starting with an initial quad mesh, which is constructed by adaptive pixelization, the boundary of the quad mesh is iteratively fitted to the boundary of the given planar region. After each iteration of the boundary, the positions of inner vertices are changed by the layered Laplace operation. Finally, the quad mesh is generated by further optimizations. In the iterations, the movements of the mesh vertices are restricted so that the produced quad mesh is guaranteed to be strictly non-self-overlapping. Lots of examples presented in this paper show the efficiency and effectiveness of the developed method.更多还原