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Evaluating mesh quality with graph neural networks

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Abstract

The quality of the finite element mesh has a considerable effect on the efficiency and accuracy of computational fluid dynamics (CFD) simulations. To ensure the generated mesh is of good quality, many quality metrics have been proposed to assess the generated mesh, such as aspect ratio, skewness, Jacobian ratio, etc. Such metrics, however, are primarily employed to detect locally distorted mesh elements. There are still no justifiable thresholds for determining whether the generated mesh is of sufficient quality for simulation. Consequently, it is necessary for the professionals to assess the generated mesh afterward which is time-consuming and labor-intensive work. With the ability to learn features on the graph, the graph neural networks have been successfully applied in many application areas to reduce human-computer interaction. In this paper, we define mesh quality evaluation as a graph classification problem. We first propose a novel and sparse-implemented algorithm to transform the mesh data into graph data. We then introduce a deep graph neural network, GMeshNet, to evaluate the mesh quality. Experimental results on the NACA-Market and NACA6510 mesh datasets demonstrate the effectiveness of our proposed network.

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Funding

This research work was supported in part by the National Numerical Windtunnel project (NNW2019ZT5-A10) and National Key Research and Development Program of China.

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Author notes

  1. Zhichao Wang and Xinhai Chen contributed equally to this work.

Authors and Affiliations

  1. Science and Technology on Parallel and Distributed Processing Laboratory, National University of Defense Technology, Changsha, 410073, China

    Zhichao Wang, Xinhai Chen, Chunye Gong & Jie Liu

  2. Laboratory of Software Engineering for Complex System, National University of Defense Technology, Changsha, 410073, China

    Zhichao Wang, Xinhai Chen, Tieju Li, Chunye Gong & Jie Liu

  3. China Aerodynamics Research and Development Center, Mianyang, 621000, China

    Yufei Pang

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  1. Zhichao Wang
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Contributions

All authors contributed to the study conception and design. Data collection and analysis, network design, experiment and result analysis were performed by ZW and XC. The first draft of the manuscript was written by ZW and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Jie Liu.

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Wang, Z., Chen, X., Li, T. et al. Evaluating mesh quality with graph neural networks. Engineering with Computers 38, 4663–4673 (2022). https://doi.org/10.1007/s00366-022-01720-8

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