This article introduces a novel method for the implementation of shape optimisation with
Lipschitz domains. We propose to use the shape derivative to determine deformation fields …

In this article we consider shape optimization problems as optimal control problems via the
method of mappings. Instead of optimizing over a set of admissible shapes, a reference …

We study distributed and boundary integral expressions of Eulerian and Fréchet shape
derivatives for several classes of nonsmooth domains such as open sets, Lipschitz domains …

The purpose of this article is to introduce a gradient-flow algorithm for solving equality and
inequality constrained optimization problems, which is particularly suited for shape …

We propose in this paper two kinds of continuity preserving discrete shape gradients of
boundary type for PDE-constrained shape optimizations. First, a modified boundary shape …

We consider the energy dissipation minimization constrained by steady Navier–Stokes
flows. The nonlinearity of the Navier–Stokes equation causes its numerical solver …

Mesh degeneration is a bottleneck for fluid–structure interaction (FSI) simulations and for
shape optimization via the method of mappings. In both cases, an appropriate mesh motion …

We consider shape optimization problems subject to elliptic partial differential equations. In
the context of the finite element method, the geometry to be optimized is represented by the …

The phase-field method is based on the energy minimization principle which is a geometric
method for modelling diffusive cracks that are popularly implemented with irreversibility …

In the last decade, parameter-free approaches to shape optimization problems have
matured to a state where they provide a versatile tool for complex engineering applications …