Optimizing triangular high-order surface meshes by energy-minimization
Optimizing triangular high-order surface meshes by energy-minimization
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DOI：
10.1007/s00366-017-0565-3
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发表时间：
2018-10
影响因子：
8.7
通讯作者：
Karsten Bock;J. Stiller
中科院分区：
文献类型：
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作者：
Karsten Bock;J. Stiller
高阶方法在计算流体力学中越来越受欢迎，但构造合适的曲线网格仍然是一个挑战。本文提出了一种严格的局部优化方法来构造高质量、高精度的高阶三角曲面片。它结合了拟合和能量最小化，其中近似弯曲和拉伸泛函通过增量过程最小化。该方法适用于分析定义的光滑表面以及来自扫描数据的散乱表面数据。在这两种情况下，优化产生了相当大的改善补丁的质量，同时保持纯最小二乘拟合的准确性。正如预期的那样，该方法在粗网格和高多项式阶数的情况下实现了最大的益处。
High-order methods are increasingly popular in computational fluid dynamics, but the construction of suitable curvilinear meshes still remains a challenge. This paper presents a strictly local optimization method to construct high-order triangular surface patches of high quality and accuracy. It combines fitting and energy-minimization, in which approximate bending and stretching functionals are minimized by means of an incremental procedure. The method was applied to analytically defined smooth surfaces as well as scattered surface data derived from scanning data. In both cases the optimization yielded considerable improvements in patch quality, while preserving the accuracy of pure least-squares fitting. As intended, the method achieves the greatest benefit with coarse meshes and high polynomial order.