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arXiv · 2301.08690

PDE constrained shape optimisation with first-order and Newton-type methods in the $W^{1,\infty}$ topology

Klaus Deckelnick·Philip J. Herbert·Michael Hinze
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Abstract

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.

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Klaus Deckelnick, Philip J. Herbert, Michael Hinze. 2023-01-20. PDE constrained shape optimisation with first-order and Newton-type methods in the $W^{1,\infty}$ topology. https://doi.org/10.1080/10556788.2024.2424525

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