Adaptive computation of elliptic eigenvalue topology optimization with a phase-field approach
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Jing Li
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Shengfeng Zhu
Abstract
In this paper, we study adaptive approximations of an elliptic eigenvalue optimization problem in a phase-field setting by a conforming finite element method. An adaptive algorithm is proposed and implemented in several two-dimensional numerical examples for illustration of efficiency and accuracy. Theoretical findings consist in the vanishing limit of a subsequence of estimators and the convergence of the relevant subsequence of adaptively-generated solutions to a solution to the continuous optimality system.
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Research ethics: Not applicable.
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Informed consent: Not applicable.
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Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.
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Use of Large Language Models, AI and Machine Learning Tools: None declared.
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Conflict of interest: The authors state no conflict of interest.
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Research funding: We acknowledge the support by National Key Basic Research Program under grant 2022YFA1004402, National Natural Science Foundation of China under grants 12250013, 12261160361, 12271367, and 12471377, Science and Technology Commission of Shanghai Municipality through projects 20JC1413800, 22DZ2229014, 22ZR1421900, and 22ZR1445400, and General Research Fund (projects KF202318 and KF202468) from Shanghai Normal University.
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Data availability: Not applicable.
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