基于离散微分方法的体网格生成研究

项目名称： 基于离散微分方法的体网格生成研究

项目编号： No.60873126

项目类型： 面上项目

立项/批准年度： 2009

项目学科： 建筑科学

项目作者： 童若锋

作者单位： 浙江大学

项目金额： 28万元

中文摘要： 能对任意实体生成质量理想的六面体网格一直是三维仿真领域的瓶颈问题，具有极大的应用价值。本项目利用体网格上的离散微分技术，对高质量的六面体网格划分方法进行了研究。首先，我们通过体网格上拉普拉斯方程构造了给定约束条件下的体域调和场及其梯度向量场。然后，本项目采用两种不同的思路生成六面体网格：一方面，通过三个互相共轭的调和向量场构造体网格上的准保角参数化映射，进而利用体映射生成六面体网格；另一方面，我们研究了调和向量场引导下的扫掠法和表面前进法来建立高质量正交各向异性六面体网格。最后，通过将复杂体域分割为规则的子体域，从而将调和向量场引导下的六面体划分方法应用于各个子体域上，实现对复杂实体的高质量的六面体网格生成。本项目的研究结果表明，基于离散微分技术的体网格生成方法能够生成高质量的六面体网格，同时具有比传统六面体网格方法更加广泛的适用范围，但对复杂形体的整体求解效率较低,有必要进一步研究子体域分解技术,以实现高质量高效率的体网格划分。

中文关键词： 六面体网格；离散微分方法；参数化映射；调和向量场

英文摘要： The ability to generate ideal hexahedral mesh automatically for arbitrary objects, which has huge potential applications, is a bottleneck problem in the 3D simulation field. This project researched the high quality hexahedral meshing methods based on discrete differential methods. Firstly, we constructed volumetric harmonic fields and their gradient vector fields based on Laplacian equations with boundary constrain conditions. Then, the research generated hexahedral meshes in two different methods. On one hand, we adopted three mutually conjugate harmonic vector fields to construct quasi-conformal parameterization mappings, which are then used to transfer hexahedral meshes. On the other hand, we studied sweeping and advancing front methods under the guidance of harmonic vector fields, which generate high quality hexahedral meshes with orthogonal anisotropic properties. Finally, to construct hexahedral meshes for the complex solids, we segmented these volumes into regular sub-volumes, where the hexahedral meshing methods guided by vector fields can be employed. The research results show that hexahedral meshing methods based on the discrete differential techniques can generate high quality hexahedral meshes, and have more widely applicable ranges than the traditional hexahedral meshing methods. However, the hexahedral meshing efficiency for complex solids is still low, further research on the volume decomposition method is necessary to achieve efficient hexahedral meshing.

英文关键词： Hexahedral mesh; Discrete differential method; Parameterization mapping; Harmonic vector field