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 propose a new embedded finite element method to simulate partial differential equations
over domains with internal interfaces. Our approach belongs to the family of …

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

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 …

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 …

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

Abstract Die vorliegende Arbeit untersucht Formoptimierungsprobleme mit nichtlinearen
Nebenbedingungen in Form von partiellen Differentialgleichungen. Wir geben eine kurze …

This article presents a finite element method on a fixed mesh for solving a group of inverse
geometric problems for recovering the material interface of a linear elasticity system. A …

Shape optimization models with one or more shapes are considered in this chapter. Of
particular interest for applications are problems in which a so-called shape functional is …

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 …