Control of bifurcation structures using shape optimization

N Boullé, PE Farrell, A Paganini - SIAM Journal on Scientific Computing, 2022 - SIAM
Many problems in engineering can be understood as controlling the bifurcation structure of a
given device. For example, one may wish to delay the onset of instability or bring forward a …

Higher-order moving mesh methods for PDE-constrained shape optimization

A Paganini, F Wechsung, PE Farrell - SIAM Journal on Scientific Computing, 2018 - SIAM
We present a new approach to discretizing shape optimization problems that generalizes
standard moving mesh methods to higher-order mesh deformations and that is naturally …

Reproducing kernel Hilbert spaces and variable metric algorithms in PDE-constrained shape optimization

M Eigel, K Sturm - Optimization Methods and Software, 2018 - Taylor & Francis
In this paper we investigate and compare different gradient algorithms designed for the
domain expression of the shape derivative. Our main focus is to examine the usefulness of …

Level-set based shape optimization for plane elastic structures using radial basis functions and Hilbertian descent direction

P Sobczak, T Sokół - Structural and Multidisciplinary Optimization, 2024 - Springer
Structural optimization problems are often associated with the so-called shape functionals
depending on a shape through its geometry and the state being a solution of given partial …

A priori error analysis of shape derivatives of linear functionals in structural topology optimization

A Klein, PB Nair, M Yano - Computer Methods in Applied Mechanics and …, 2022 - Elsevier
We provide theoretical analyses and numerical comparisons of boundary-based and
volumetric shape derivative expressions of linear objective functionals encountered in …

The strip method for shape derivatives

S Hardesty, H Antil, DP Kouri… - International Journal for …, 2022 - Wiley Online Library
A major challenge in shape optimization is the coupling of finite element method (FEM)
codes in a way that facilitates efficient computation of shape derivatives. This is particularly …