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首页> 外文期刊>International Journal for Numerical Methods in Engineering >A distortion measure to validate and generate curved high-order meshes on CAD surfaces with independence of parameterization
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A distortion measure to validate and generate curved high-order meshes on CAD surfaces with independence of parameterization

机译：变形量度，用于验证和生成CAD曲面上的弯曲高阶网格，而不受参数设置的影响

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摘要

A framework to validate and generate curved nodal high-order meshes on Computer-Aided Design (CAD) surfaces is presented. The proposed framework is of major interest to generate meshes suitable for thin-shell and 3D finite element analysis with unstructured high-order methods. First, we define a distortion (quality) measure for high-order meshes on parameterized surfaces that we prove to be independent of the surface parameterization. Second, we derive a smoothing and untangling procedure based on the minimization of a regularization of the proposed distortion measure. The minimization is performed in terms of the parametric coordinates of the nodes to enforce that the nodes slide on the surfaces. Moreover, the proposed algorithm repairs invalid curved meshes (untangling), deals with arbitrary polynomial degrees (high-order), and handles with low-quality CAD parameterizations (independence of parameterization). Third, we use the optimization procedure to generate curved nodal high-order surface meshes by means of an a posteriori approach. Given a linear mesh, we increase the polynomial degree of the elements, curve them to match the geometry, and optimize the location of the nodes to ensure mesh validity. Finally, we present several examples to demonstrate the features of the optimization procedure, and to illustrate the surface mesh generation process. Copyright (C) 2015 John Wiley & Sons, Ltd.
机译：提出了一个框架来验证和生成计算机辅助设计（CAD）曲面上的弯曲节点高阶网格。所提出的框架对于使用非结构化高阶方法生成适用于薄壳和3D有限元分析的网格具有重大意义。首先，我们为参数化曲面上的高阶网格定义了一种变形（质量）度量，我们证明该度量与表面参数化无关。其次，我们基于所提出的失真测度的正则化的最小化，推导出平滑和解理过程。根据节点的参数坐标执行最小化，以强制节点在表面上滑动。此外，该算法修复了无效的弯曲网格（解缠结），处理了任意多项式度（高阶），并处理了低质量的CAD参数化（参数化的独立性）。第三，我们使用优化程序通过后验方法生成弯曲的节点高阶曲面网格。给定线性网格，我们增加元素的多项式度，将它们弯曲以匹配几何形状，并优化节点的位置以确保网格有效性。最后，我们提供一些示例来说明优化程序的功能，并说明曲面网格的生成过程。版权所有（C）2015 John Wiley＆Sons，Ltd.

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