97 citations · 223 across the 20 of their papers we have counts for
23 papers
Retraction based regression methods on Riemannian manifolds
Estefanía Loayza-Romero, Benedikt Sibum, Kathrin Welker
Geodesic regression generalizes classical regression models to manifold-valued data by replacing affine models in Euclidean spaces with geodesic models on Riemannian manifolds. In…
On an optimization framework for damage localization in structures
Owais Saleem, Tim Suchan, Natalie Rauter +1
Efficient structural damage localization remains a challenge in structural health monitoring (SHM), particularly when the problem is coupled with uncertainty of conditions and comp…
Fracture propagation by using shape optimization techniques based on outer Riemannian metrics
Tim Suchan, Winnifried Wollner, Kathrin Welker
In this work, we investigate a novel approach for the simulation of two-dimensional, brittle, quasi-static fracture problems based on a shape optimization approach. In contrast to…
Numerical techniques for geodesic approximation in Riemannian shape optimization
Estefania Loayza-Romero, Kathrin Welker
Shape optimization is commonly applied in engineering to optimize shapes with respect to an objective functional relying on PDE solutions. In this paper, we view shape optimization…
A Riemannian approach for PDE-constrained shape optimization over the diffeomorphism group using outer metrics
Estefania Loayza-Romero, Lidiya Pryymak, Kathrin Welker
In this paper, we study the use of outer metrics, in particular Sobolev-type metrics on the diffeomorphism group in the context of PDE-constrained shape optimization. Leveraging th…
Crack propagation in anisotropic brittle materials: from a phase-field model to a shape optimization approach
Tim Suchan, Chaitanya Kandekar, Wolfgang E. Weber +1
The phase-field method is based on the energy minimization principle which is a geometric method for modeling diffusive cracks that are popularly implemented with irreversibility b…
Optimization of piecewise smooth shapes under uncertainty using the example of Navier-Stokes flow
Caroline Geiersbach, Tim Suchan, Kathrin Welker
We investigate a complex system involving multiple shapes to be optimized in a domain, taking into account geometric constraints on the shapes and uncertainty appearing in the phys…
A product shape manifold approach for optimizing piecewise-smooth shapes
Lidiya Pryymak, Tim Suchan, Kathrin Welker
Spaces where each element describes a shape, so-called shape spaces, are of particular interest in shape optimization and its applications. Theory and algorithms in shape optimizat…
Stochastic Augmented Lagrangian Method in Riemannian Shape Manifolds
Caroline Geiersbach, Tim Suchan, Kathrin Welker
In this paper, we present a stochastic augmented Lagrangian approach on (possibly infinite-dimensional) Riemannian manifolds to solve stochastic optimization problems with a finite…
Parameter-free shape optimization: various shape updates for engineering applications
Lars Radtke, Georgios Bletsos, Niklas Kühl +4
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. Howev…
On diffeologies from infinite dimensional geometry to PDE constrained optimization
Nico Goldammer, Jean-PIerre Magnot, Kathrin Welker
We review how diffeologies complete the settings classically used from infinite dimensional geometry to partial differential equations, based on classical settings of functional an…
A new shape optimization approach for fracture propagation
Tim Suchan, Kathrin Welker, Winnifried Wollner
Within this work, we present a novel approach to fracture simulations based on shape optimization techniques. Contrary to widely-used phase-field approaches in literature the propo…
Gâteaux semiderivative approach applied to shape optimization for contact problems
Nico Goldammer, Volker H. Schulz, Kathrin Welker
Shape optimization problems constrained by variational inequalities (VI) are non-smooth and non-convex optimization problems. The non-smoothness arises due to the variational inequ…
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…
Towards optimization techniques on diffeological spaces by generalizing Riemannian concepts
Nico Goldammer, Kathrin Welker
Diffeological spaces firstly introduced by J.M. Souriau in the 1980s are a natural generalization of smooth manifolds. However, optimization techniques are only known on manifolds…
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…
Suitable Spaces for Shape Optimization
Kathrin Welker
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 respe…
Algorithmic aspects of multigrid methods for optimization in shape spaces
Martin Siebenborn, Kathrin Welker
We examine the interaction of multigrid methods and shape optimization in appropriate shape spaces. Our aim is a scalable algorithm for application on supercomputers, which can onl…
Efficient PDE constrained shape optimization based on Steklov-Poincaré type metrics
Volker Schulz, Martin Siebenborn, Kathrin Welker
Recent progress in PDE constrained optimization on shape manifolds is based on the Hadamard form of shape derivatives, i.e., in the form of integrals at the boundary of the shape u…
Structured inverse modeling in parabolic diffusion processess
Volker Schulz, Martin Siebenborn, Kathrin Welker
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 structur…
Towards a Lagrange-Newton approach for PDE constrained shape optimization
Volker H. Schulz, Martin Siebenborn, Kathrin Welker
The novel Riemannian view on shape optimization developed in [Schulz, FoCM, 2014] is extended to a Lagrange-Newton approach for PDE constrained shape optimization problems. The ext…