Evaluating Hex-mesh Quality Metrics via Correlation Analysis
Evaluating Hex-mesh Quality Metrics via Correlation Analysis
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DOI：
10.1111/cgf.13249
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发表时间：
2017-08-01
影响因子：
2.5
通讯作者：
Chen, Guoning
中科院分区：
文献类型：
--
作者：
Gao, Xifeng;Huang, Jin;Chen, Guoning
在科学计算和机械工程应用中，六面体网格是求解偏微分方程组的重要方法。已经提出了许多方法来生成具有高比例雅可比的六面体网格。虽然众所周知，六面体网格应该是无逆的(即在其六面体的每个角落都有一个正的雅可比测量)，但考虑到现有的几十种六角网格的质量度量，缩放的雅可比是否是在无逆六角网格上执行的模拟质量的最有效指标还没有得到很好的研究。由于精确定义指标之间的关系是一个挑战，研究不同质量指标之间的相关性以及它们与模拟的稳定性和准确性的相关性是解决上述问题的第一个也是有效的方法。在这项工作中，我们提出了一个相关性分析框架来系统地研究这些相关性。具体地说，在给定一个大型六角网格数据集的情况下，我们根据它们的相关性将现有的质量度量分类为组，这表征了它们在度量六角元素质量方面的相似性。此外，我们还根据各个度量与精度和稳定性度量之间的相关性对各个度量进行排序，以用于解决一些椭圆型偏微分方程问题的仿真。我们的初步实验表明，评估元素条件的度量与求解椭圆型偏微分方程组的质量比其他度量更相关。此外，具有较高平均质量(以任何质量指标衡量)的无逆六角网格通常会导致椭圆型偏微分方程组的计算更加准确和稳定。为了支持我们的相关性研究，并解决缺乏公开可用的具有足够不同质量度量值的大型六角网格数据集的问题，我们还提出了一种两级扰动策略，从少量网格生成所需的数据集，以排除单元数量、顶点连通性和体积大小对我们研究的影响。
Hexahedral (hex-) meshes are important for solving partial differential equations (PDEs) in applications of scientific computing and mechanical engineering. Many methods have been proposed aiming to generate hex-meshes with high scaled Jacobians. While it is well established that a hex-mesh should be inversion-free (i.e. have a positive Jacobian measured at every corner of its hexahedron), it is not well-studied that whether the scaled Jacobian is the most effective indicator of the quality of simulations performed on inversion-free hex-meshes given the existing dozens of quality metrics for hex-meshes. Due to the challenge of precisely defining the relations among metrics, studying the correlations among different quality metrics and their correlations with the stability and accuracy of the simulations is a first and effective approach to address the above question. In this work, we propose a correlation analysis framework to systematically study these correlations. Specifically, given a large hex-mesh dataset, we classify the existing quality metrics into groups based on their correlations, which characterizes their similarity in measuring the quality of hex-elements. In addition, we rank the individual metrics based on their correlations with the accuracy and stability metrics for simulations that solve a number of elliptic PDE problems. Our preliminary experiments suggest that metrics that assess the conditioning of the elements are more correlated to the quality of solving elliptic PDEs than the others. Furthermore, an inversion-free hex-mesh with higher average quality (measured by any quality metrics) usually leads to a more accurate and stable computation of elliptic PDEs. To support our correlation study and address the lack of a publicly available large hex-mesh dataset with sufficiently varying quality metric values, we also propose a two-level perturbation strategy to generate the desired dataset from a small number of meshes to exclude the influences of element numbers, vertex connectivity, and volume sizes to our study.