Recent progress in PDE constrained optimization on shape manifolds is based on the
Hadamard form of shape derivatives, ie, in the form of integrals at the boundary of the shape …

We compare surface metrics for shape optimization problems with constraints, consisting
mainly of partial differential equations (PDE), from a computational point of view. In …

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 …

In this article, we propose a shape optimization algorithm which is able to handle large
deformations while maintaining a high level of mesh quality. Based on the method of …

Often, the unknown diffusivity in diffusive processes is structured by piecewise constant
patches. This paper is devoted to efficient methods for the determination of such structured …

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 …

We review how diffeologies complete the settings classically used from infinite dimensional
geometry to partial differential equations, based on classical settings of functional analysis …

Shape optimization is of interest in many fields of application. In particular, shape
optimization problems arise frequently in technological processes which are modelled by …

The differential-geometric structure of the manifold of smooth shapes is applied to the theory
of shape optimization problems. In particular, a Riemannian shape gradient with respect to …

In this article we propose a scalable shape optimization algorithm which is tailored for large
scale problems and geometries represented by hierarchically refined meshes. Weak …