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Global optimization of optimal Delaunay triangulation with modified whale optimization algorithm

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Abstract

In this paper, we introduce an innovative approach to generate a high-quality mesh with a density function in a given domain. Our method involves solving a variational problem that optimizes the energy function of the optimal Delaunay triangulation (ODT). To achieve this, we have developed a modified whale optimization algorithm (MWOA) based population that is combined with the quasi-Newton method (L-BFGS) to optimize ODT energy on a global level. Our experiments have demonstrated the impressive efficiency of this optimization algorithm in searching for better minima and producing high-quality meshes. Remarkably, the algorithm’s powerful global optimization capability makes it insensitive to initialization, which eliminates the need for any special initialization procedures. Furthermore, our proposed algorithm can easily handle complex domains and non-uniform density functions, making it a versatile tool for mesh generation. Overall, our method offers a promising solution for generating practicable meshes with a density function.

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The data that support the findings of this study are available upon reasonable request.

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Acknowledgements

This work was supported by the National Key R&D Program of China (No. 2022YFB3303400), National Natural Science Foundation of China (Nos. 61972327, 62272402, and 62372389), Natural Science Foundation of Fujian Province (No. 2022J01001), and Fundamental Research Funds for the Central Universities (No. 20720220037).

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Authors and Affiliations

  1. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, Fujian, China

    Yongjia Weng & Juan Cao

  2. Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computation, Xiamen University, Xiamen, 361005, Fujian, China

    Yongjia Weng & Juan Cao

  3. School of Informatics, Xiamen University, Xiamen, 361005, Fujian, China

    Zhonggui Chen

Authors
  1. Yongjia Weng
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  2. Juan Cao
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Contributions

YW: Methodology, Investigation, Software, Visualization, Writing-Original draft preparation, Writing-Reviewing and Editing. JC, ZC: Methodology, Validation, Supervision, Formal analysis, Writing-Reviewing and Editing.

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Correspondence to Zhonggui Chen.

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Weng, Y., Cao, J. & Chen, Z. Global optimization of optimal Delaunay triangulation with modified whale optimization algorithm. Engineering with Computers (2024). https://doi.org/10.1007/s00366-023-01928-2

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