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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…