PDE constrained shape optimisation with first-order and Newton-type methods in the W^1,∞ topology

2023/01/20 by Klaus Deckelnick, Philip J. Herbert, Deckelnick, Klaus +3 · 1 citation
Engineering · #Advanced Numerical Analysis Techniques #FOS: Mathematics #Optimization and Control (math.OC) #Piezoelectric Actuators and Control #Topology Optimization in Engineering

paper · pdf · doi:10.48550/arxiv.2301.08690

openalex publication_date 2023/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a general shape optimisation framework based on the method of mappings in the W^1,∞ 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,∞ 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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