Optimization of a regularized distortion measure to generate curved high-order unstructured tetrahedral meshes
Optimization of a regularized distortion measure to generate curved high-order unstructured tetrahedral meshes
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DOI：
10.1002/nme.4888
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发表时间：
2015-08-03
影响因子：
2.9
通讯作者：
Sarrate, J.
中科院分区：
文献类型：
--
作者：
Gargallo-Peiro, A.;Roca, X.;Sarrate, J.
本文提出了一种生成高次节点四面体曲面网格的方法。该方法包括修改初始线性网格，首先，引入高阶节点，第二，取代边界节点，以确保它们在计算机辅助设计表面上，第三，平滑和解开后得到的网格边界节点的位移，以产生一个有效的弯曲高阶网格。平滑算法是基于相对于原始线性网格的网格失真的正则化测量的优化。这意味着只要有可能，生成的网格就会保留初始线性网格的几何特征，例如形状、拉伸和大小。我们提出了几个例子来说明所提出的算法的性能。此外，实例表明，优化问题的实现是鲁棒的，能够处理的情况下，在优化前的网格包含大量的无效元素。我们考虑的情况下，多项式近似高达十度，大变形的弯曲边界，凹边界，高度拉伸边界层元素。所得网格适合于高阶有限元分析。版权所有（c）2015约翰威利父子有限公司
We present a robust method for generating high-order nodal tetrahedral curved meshes. The approach consists of modifying an initial linear mesh by first, introducing high-order nodes, second, displacing the boundary nodes to ensure that they are on the computer-aided design surface, and third, smoothing and untangling the mesh obtained after the displacement of the boundary nodes to produce a valid curved high-order mesh. The smoothing algorithm is based on the optimization of a regularized measure of the mesh distortion relative to the original linear mesh. This means that whenever possible, the resulting mesh preserves the geometrical features of the initial linear mesh such as shape, stretching, and size. We present several examples to illustrate the performance of the proposed algorithm. Furthermore, the examples show that the implementation of the optimization problem is robust and capable of handling situations in which the mesh before optimization contains a large number of invalid elements. We consider cases with polynomial approximations up to degree ten, large deformations of the curved boundaries, concave boundaries, and highly stretched boundary layer elements. The meshes obtained are suitable for high-order finite element analyses. Copyright (c) 2015 John Wiley & Sons, Ltd.