Adaptive Computation of Elliptic Eigenvalue Topology Optimization with a Phase-Field Approach
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913723719876608 |
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| author | Li, Jing Xu, Yifeng Zhu, Shengfeng |
| author_facet | Li, Jing Xu, Yifeng Zhu, Shengfeng |
| contents | In this paper, we discuss 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_03970 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Adaptive Computation of Elliptic Eigenvalue Topology Optimization with a Phase-Field Approach Li, Jing Xu, Yifeng Zhu, Shengfeng Numerical Analysis 49M05, 49M41, 65N12, 65N20, 65N30, 65N50 In this paper, we discuss 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. |
| title | Adaptive Computation of Elliptic Eigenvalue Topology Optimization with a Phase-Field Approach |
| topic | Numerical Analysis 49M05, 49M41, 65N12, 65N20, 65N30, 65N50 |
| url | https://arxiv.org/abs/2310.03970 |