PDE constrained shape optimisation with first-order and Newton-type methods in the $W^{1,\infty}$ topology
Optimization and Control
2025-06-02 v2
Abstract
We present a general shape optimisation framework based on the method of mappings in the 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 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 -approximations.
Cite
@article{arxiv.2301.08690,
title = {PDE constrained shape optimisation with first-order and Newton-type methods in the $W^{1,\infty}$ topology},
author = {Klaus Deckelnick and Philip J. Herbert and Michael Hinze},
journal= {arXiv preprint arXiv:2301.08690},
year = {2025}
}