12 citations · 69 across the 29 of their papers we have counts for
41 papers
Two-Scale Finite Element Approximation of a Homogenized Plate Model
Martin Rumpf, Stefan Simon, Christoph Smoch
This paper studies the discretization of a homogenization and dimension reduction model for the elastic deformation of microstructured thin plates proposed by Hornung, Neukamm, and…
Parametrizing Product Shape Manifolds by Composite Networks
Josua Sassen, Klaus Hildebrandt, Martin Rumpf +1
Parametrizations of data manifolds in shape spaces can be computed using the rich toolbox of Riemannian geometry. This, however, often comes with high computational costs, which ra…
Approximation of Splines in Wasserstein Spaces
Jorge Justiniano, Martin Rumpf, Matthias Erbar
This paper investigates a time discrete variational model for splines in Wasserstein spaces to interpolate probability measures. Cubic splines in Euclidean space are known to minim…
Convergent autoencoder approximation of low bending and low distortion manifold embeddings
Juliane Braunsmann, Marko Rajković, Martin Rumpf +1
Autoencoders, which consist of an encoder and a decoder, are widely used in machine learning for dimension reduction of high-dimensional data. The encoder embeds the input data man…
Two-scale elastic shape optimization for additive manufacturing
Sergio Conti, Martin Rumpf, Stefan Simon
In this paper, a two-scale approach for elastic shape optimization of fine-scale structures in additive manufacturing is investigated. To this end, a free material optimization is…
Finite Element Approximation of Large-Scale Isometric Deformations of Parametrized Surfaces
Martin Rumpf, Stefan Simon, Christoph Smoch
In this paper, the numerical approximation of isometric deformations of thin elastic shells is discussed. To this end, for a thin shell represented by a parametrized surface, it is…
Consistent Approximation of Interpolating Splines in Image Metamorphosis
Jorge Justiniano, Marko Rajković, Martin Rumpf
This paper investigates a variational model for splines in the image metamorphosis model for the smooth interpolation of key frames in the space of images. The Riemannian manifold…
A Pessimistic Bilevel Stochastic Problem for Elastic Shape Optimization
Johanna Burtscheidt, Matthias Claus, Sergio Conti +3
We consider pessimistic bilevel stochastic programs in which the follower maximizes over a fixed compact convex set a strictly convex quadratic function, whose Hessian depends on t…
Mean curvature motion of point cloud varifolds
Blanche Buet, Martin Rumpf
This paper investigates a discretization scheme for mean curvature motion on point cloud varifolds with particular emphasis on singular evolutions. To define the varifold a local c…
On Material Optimisation for Nonlinearly Elastic Plates and Shells
Peter Hornung, Martin Rumpf, Stefan Simon
This paper investigates the optimal distribution of hard and soft material on elastic plates. In the class of isometric deformations stationary points of a Kirchhoff plate function…
Consistent Curvature Approximation on Riemannian Shape Spaces
Alexander Effland, Behrend Heeren, Martin Rumpf +1
We describe how to approximate the Riemann curvature tensor as well as sectional curvatures on possibly infinite-dimensional shape spaces that can be thought of as Riemannian manif…
Geometry of martensite needles in shape memory alloys
Sergio Conti, Martin Lenz, Nora Lüthen +2
We study the geometry of needle-shaped domains in shape-memory alloys. Needle-shaped domains are ubiquitously found in martensites around macroscopic interfaces between regions whi…
Image Morphing in Deep Feature Spaces: Theory and Applications
Alexander Effland, Erich Kobler, Thomas Pock +2
This paper combines image metamorphosis with deep features. To this end, images are considered as maps into a high-dimensional feature space and a structure-sensitive, anisotropic…
Geometric optimization using nonlinear rotation-invariant coordinates
Josua Sassen, Behrend Heeren, Klaus Hildebrandt +1
Geometric optimization problems are at the core of many applications in geometry processing. The choice of a representation fitting an optimization problem can considerably simplif…
Convergence of the Time Discrete Metamorphosis Model on Hadamard Manifolds
Alexander Effland, Sebastian Neumayer, Martin Rumpf
Continuous image morphing is a classical task in image processing. The metamorphosis model proposed by Trouvé, Younes and coworkers casts this problem in the frame of Riemannian ge…
Simultaneous elastic shape optimization for a domain splitting in bone tissue engineering
Patrick Dondl, Patrina S. P. Poh, Martin Rumpf +1
This paper deals with the simulateneous optimization of a subset of some domain and its complement both co…
Homogenization in magnetic-shape-memory polymer composites
Sergio Conti, Martin Lenz, Matthäus Pawelczyk +1
Magnetic-shape-memory materials (e.g. specific NiMnGa alloys) react with a large change of shape to the presence of an external magnetic field. As an alternative for the difficult…
Variational time discretization of Riemannian splines
Behrend Heeren, Martin Rumpf, Benedikt Wirth
We investigate a generalization of cubic splines to Riemannian manifolds. Spline curves are defined as minimizers of the spline energy - a combination of the Riemannian path energy…
Branching Structures in Elastic Shape Optimization
Nora Lüthen, Martin Rumpf, Sascha Tölkes +1
Fine scale elastic structures are widespread in nature, for instances in plants or bones, whenever stiffness and low weight are required. These patterns frequently refine towards a…
Computation of Optimal Transport on Discrete Metric Measure Spaces
Matthias Erbar, Martin Rumpf, Bernhard Schmitzer +1
In this paper we investigate the numerical approximation of an analogue of the Wasserstein distance for optimal transport on graphs that is defined via a discrete modification of t…
Image Extrapolation for the Time Discrete Metamorphosis Model - Existence and Applications
Alexander Effland, Martin Rumpf, Florian Schäfer
The space of images can be equipped with a Riemannian metric measuring both the cost of transport of image intensities and the variation of image intensities along motion lines. Th…
Smooth Interpolation of Key Frames in a Riemannian Shell Space
Pascal Huber, Ricardo Perl, Martin Rumpf
Splines and subdivision curves are flexible tools in the design and manipulation of curves in Euclidean space. In this paper we study generalizations of interpolating splines and s…
Generalized optimal transport with singular sources
Jan Maas, Martin Rumpf, Stefan Simon
We present a generalized optimal transport model in which the mass-preserving constraint for the -Wasserstein distance is relaxed by introducing a source term in the continuit…
Stochastic Dominance Constraints in Elastic Shape Optimization
Sergio Conti, Martin Rumpf, Rüdiger Schultz +1
This paper deals with shape optimization for elastic materials under stochastic loads. It transfers the paradigm of stochastic dominance, which allows for flexible risk aversion vi…