Quadrilateral and Hexahedral Mesh Generation Based on Surface Foliation Theory II

Na Lei Dalian University of Technology Xiaopeng Zheng Jiliin University Jian Jiang Stony Brook University Yu-Yao Lin Stony Brook University David Xianfeng Gu Stony Brook University

Computational Geometry mathscidoc:1705.09001

Computer Methods in Applied Mechanics and Engineering (CMAME), 2017
Automatic hexahedral mesh generation plays a fundamental role in CAD/CAE fields, especially for IGA (isogeometric analysis). Recently, an automatic hex-mesh generation method has been proposed, which is based on the equivalence among three key concepts: colorable quadrilateral meshes, finite measured foliations and Strebel differentials. This work focuses on the computational aspect of Strebel differentials on high genus surfaces, which is based on graph-valued harmonic mapping. The algorithmic pipeline is as follows: first, the user inputs an admissible curve system, which induces a cylindric-decomposition graph; then the user specifies the lengths of the edges of the graph; third, the algorithm finds the unique harmonic map from the surface to the metric graph by a non-linear heat flow; finally, the harmonic map induces a Strebel differential, which can be further utilized to generate the hex-mesh. The method has solid theoretic foundation, which guarantees the existence and the uniqueness of the graph-valued harmonic map. The algorithm is capable of handling surfaces with complicated topologies, and producing all possible Strebel differentials on the surface. The user has full control of the combinatorial type and the geometry of the Strebel differential. The computational pipeline is automatic. The experimental results show the efficiency and efficacy of the algorithm, and demonstrate the great potential for automating the structured hexahedral mesh generation.
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@inproceedings{na2017quadrilateral,
  title={Quadrilateral and Hexahedral Mesh Generation Based on Surface Foliation Theory II },
  author={Na Lei, Xiaopeng Zheng, Jian Jiang, Yu-Yao Lin, and David Xianfeng Gu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170530163632009091775},
  booktitle={Computer Methods in Applied Mechanics and Engineering (CMAME)},
  year={2017},
}
Na Lei, Xiaopeng Zheng, Jian Jiang, Yu-Yao Lin, and David Xianfeng Gu. Quadrilateral and Hexahedral Mesh Generation Based on Surface Foliation Theory II . 2017. In Computer Methods in Applied Mechanics and Engineering (CMAME). http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170530163632009091775.
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