PDE constrained shape optimisation with first-order and Newton-type methods in the $W^{1,\infty}$ topology
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913866964795392 |
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| author | Deckelnick, Klaus Herbert, Philip J. Hinze, Michael |
| author_facet | Deckelnick, Klaus Herbert, Philip J. Hinze, Michael |
| contents | We present a general shape optimisation framework based on the method of mappings in the $W^{1,\infty}$ topology. We propose steepest descent and Newton-like minimisation algorithms for the numerical solution of the respective shape optimisation problems. Our work is built upon previous work of the authors in (Deckelnick, Herbert, and Hinze, ESAIM: COCV 28 (2022)), where a $W^{1,\infty}$ framework for star-shaped domains is proposed. To illustrate our approach we present a selection of PDE constrained shape optimisation problems and compare our findings to results from so far classical Hilbert space methods and recent $p$-approximations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_08690 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | PDE constrained shape optimisation with first-order and Newton-type methods in the $W^{1,\infty}$ topology Deckelnick, Klaus Herbert, Philip J. Hinze, Michael Optimization and Control We present a general shape optimisation framework based on the method of mappings in the $W^{1,\infty}$ topology. We propose steepest descent and Newton-like minimisation algorithms for the numerical solution of the respective shape optimisation problems. Our work is built upon previous work of the authors in (Deckelnick, Herbert, and Hinze, ESAIM: COCV 28 (2022)), where a $W^{1,\infty}$ framework for star-shaped domains is proposed. To illustrate our approach we present a selection of PDE constrained shape optimisation problems and compare our findings to results from so far classical Hilbert space methods and recent $p$-approximations. |
| title | PDE constrained shape optimisation with first-order and Newton-type methods in the $W^{1,\infty}$ topology |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2301.08690 |