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A Two-Grid Binary Level Set Method for Eigenvalue Optimization

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Abstract

Two-grid methods are popular and efficient discretization techniques for solving nonlinear problems. In this paper, we propose a new two-grid binary level set method for eigenvalue optimization. An efficient yet effective two-grid finite element method is used to solve the nonlinear eigenvalue problem in two topology optimization models. By the binary level set method, the algorithm can perform topological and shape changes. Numerical examples are presented to illustrate the effectiveness and efficiency of the algorithm.

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Authors and Affiliations

  1. School of Mathematical Sciences, East China Normal University, Shanghai, 200241, China

    Jing Zhang & Shengfeng Zhu

  2. School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai, 201209, China

    Chunxiao Liu

  3. School of Sciences, Xi’an University of Technology, Xi’an, 710054, China

    Xiaoqin Shen

Authors
  1. Jing Zhang
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  2. Shengfeng Zhu
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  3. Chunxiao Liu
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  4. Xiaoqin Shen
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Correspondence to Shengfeng Zhu.

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The work was supported in part by the National Key Research and Development Program of China (Grant No. 2018AAA0101001), the National Natural Science Foundation of China (Grant Nos. 12071149 and  11971379), Natural Science Foundation of Shanghai (Grant No. 19ZR1414100), and Science and Technology Commission of Shanghai Municipality (No. 18dz2271000).

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Zhang, J., Zhu, S., Liu, C. et al. A Two-Grid Binary Level Set Method for Eigenvalue Optimization. J Sci Comput 89, 57 (2021). https://doi.org/10.1007/s10915-021-01662-1

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  • DOI: https://doi.org/10.1007/s10915-021-01662-1

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