4 papers
PDE-constrained shape optimization: towards product shape spaces and stochastic models
Caroline Geiersbach, Estefania Loayza-Romero, Kathrin Welker
Shape optimization models with one or more shapes are considered in this chapter. Of particular interest for applications are problems in which where a so-called shape functional i…
Stochastic approximation for optimization in shape spaces
Caroline Geiersbach, Estefania Loayza-Romero, Kathrin Welker
In this work, we present a novel approach for solving stochastic shape optimization problems. Our method is the extension of the classical stochastic gradient method to infinite-di…
Efficient Techniques for Shape Optimization with Variational Inequalities using Adjoints
Daniel Luft, Volker H. Schulz, Kathrin Welker
In general, standard necessary optimality conditions cannot be formulated in a straightforward manner for semi-smooth shape optimization problems. In this paper, we consider shape…
Computational Aspects for Interface Identification Problems with Stochastic Modelling
Caroline Geiersbach, Estefania Loayza, Kathrin Welker
In this paper, a shape optimization problem constrained by a random elliptic partial differential equation with a pure Neumann boundary is presented. The model is motivated by appl…