97 citations · 223 across the 20 of their papers we have counts for
6 papers · 1 filter
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…