| 2019Sergio Conti, Martin Lenz, Nora Lüthen, Martin Rumpf and Barbara Zwicknagl
Geometry of martensite needles in shape memory alloys
2019
https://arxiv.org/abs/1912.02274
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| Patrick W. Dondl, Patrina S. P. Poh, Martin Rumpf and Stefan Simon
Simultaneous elastic shape optimization for a domain splitting in bone tissue engineering
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 475(2227): 20180718 2019
10.1098/rspa.2018.0718
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| Alexander Effland, Sebastian Neumayer and Martin Rumpf
Convergence of the Time Discrete Metamorphosis Model on Hadamard Manifolds
2019
https://arxiv.org/abs/1902.10930
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| Alexander Effland, Erich Kobler, Thomas Pock, Marko Rajković and Martin Rumpf
Image Morphing in Deep Feature Spaces: Theory and Applications
2019
https://arxiv.org/abs/1910.12672
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| Alexander Effland, Erich Kobler, Thomas Pock and Martin Rumpf
Time Discrete Geodesics in Deep Feature Spaces for Image Morphing
In Lellmann, Jan and Burger, Martin and Modersitzki, Jan, editor, Scale Space and Variational Methods in Computer Vision
page 171--182.
Publisher: Springer International Publishing
2019
https://dx.doi.org/10.1007/978-3-030-22368-7_14
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| Alexander Effland, Erich Kobler, Anne Brandenburg, Teresa Klatzer, Leonie Neuhäuser, Michael Hölzel, Jennifer Landsberg, Thomas Pock and Martin Rumpf
Joint reconstruction and classification of tumor cells and cell interactions in melanoma tissue sections with synthesized training data
International Journal of Computer Assisted Radiology and Surgery, 14(4): 587--599 2019
https://dx.doi.org/10.1007/s11548-019-01919-z
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| 2018Sergio Conti, Martin Rumpf, Rüdiger Schultz and Sascha Tölkes
Stochastic Dominance Constraints in Elastic Shape Optimization
SIAM J. Control Optim., 56: 3021-3034 2018
10.1137/16M108313X
Abstract: 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 via comparison with benchmark random variables, from finite-dimensional stochastic programming to shape optimization. Rather than handling risk aversion in the objective, this enables risk aversion by including dominance constraints that single out subsets of nonanticipative shapes which compare favorably to a chosen stochastic benchmark. This new class of stochastic shape optimization problems arises by optimizing over such feasible sets. The analytical description is built on risk-averse cost measures. The underlying cost functional is of compliance type plus a perimeter term, in the implementation shapes are represented by a phase field which permits an easy estimate of a regularized perimeter. The analytical description and the numerical implementation of dominance constraints are built on risk-averse measures for the cost functional. A suitable numerical discretization is obtained using finite elements both for the displacement and the phase field function. Different numerical experiments demonstrate the potential of the proposed stochastic shape optimization model and in particular the impact of high variability of forces or probabilities in the different realizations. |
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| Sergio Conti, Martin Lenz, Matthäus Pawelczyk and Martin Rumpf
Homogenization in magnetic-shape-memory polymer composites
In Volker Schulz and Diaraf Seck, editor, Shape Optimization, Homogenization and Optimal Control, Volume 169 of International Series of Numerical Mathematics
page 1-17.
Publisher: Birkhäuser, Cham
2018
10.1007/978-3-319-90469-6_1
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| Sergio Conti, Benedict Geihe, Martin Lenz and Martin Rumpf
A posteriori modeling error estimates in the optimization of two-scale elastic composite materials
ESAIM: Mathematical Modelling and Numerical Analysis, 52: 1457-1476 2018
10.1051/m2an/2017004
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| Alexander Effland, Martin Rumpf and Florian Schäfer
Image extrapolation for the time discrete metamorphosis model -- existence and applications
SIAM J. Imaging Sci. 2018
https://arxiv.org/abs/1705.04490
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| 2017Benjamin Berkels, Michael Buchner, Alexander Effland, Martin Rumpf and Steffen Schmitz-Valckenberg
GPU Based Image Geodesics for Optical Coherence Tomography
In Bildverarbeitung für die Medizin, Informatik aktuell
page 68--73.
Publisher: Springer
2017
http://dx.doi.org/10.1007/978-3-662-54345-0_21
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| Alexander Effland, Martin Rumpf and Florian Schäfer
Time discrete extrapolation in a Riemannian space of images
In Proc. of International Conference on Scale Space and Variational Methods in Computer Vision, Volume 10302
page 473--485.
Publisher: Springer, Cham
2017
https://dx.doi.org/10.1007/978-3-319-58771-4_38
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| Matthias Erbar, Martin Rumpf, Bernhard Schmitzer and Stefan Simon
Computation of Optimal Transport on Discrete Metric Measure Spaces
Unknown
https://arxiv.org/abs/1707.06859
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| Behrend Heeren, Martin Rumpf and Benedikt Wirth
Variational time discretization of Riemannian splines
IMA J. Numer. Anal. 2017
https://arxiv.org/abs/1711.06069
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| Nora Lüthen, Martin Rumpf, Sascha Tölkes and Orestis Vantzos
Branching Structures in Elastic Shape Optimization
2017
https://arxiv.org/abs/1711.03850
Abstract: 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 Dirichlet boundary to ensure an effective load transfer. The paper discusses the optimization of such supporting structures in a specific class of domain patterns in 2D, which composes of periodic and branching period transitions on subdomain facets. These investigations can be considered as a case study to display examples of optimal branching domain patterns. In explicit, a rectangular domain is decomposed into rectangular subdomains, which share facets with neighbouring subdomains or with facets which split on one side into equally sized facets of two different subdomains. On each subdomain one considers an elastic material phase with stiff elasticity coefficients and an approximate void phase with orders of magnitude softer material. For given load on the outer domain boundary, which is distributed on a prescribed fine scale pattern representing the contact area of the shape, the interior elastic phase is optimized with respect to the compliance cost. The elastic stress is supposed to be continuous on the domain and a stress based finite volume discretization is used for the optimization. If in one direction equally sized subdomains with equal adjacent subdomain topology line up, these subdomains are consider as equal copies including the enforced boundary conditions for the stress and form a locally periodic substructure. An alternating descent algorithm is employed for a discrete characteristic function describing the stiff elastic subset on the subdomains and the solution of the elastic state equation. Numerical experiments are shown for compression and shear load on the boundary of a quadratic domain. |
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| Jan Maas, Martin Rumpf and Stefan Simon
Transport based image morphing with intensity modulation
In Proc. of International Conference on Scale Space and Variational Methods in Computer Vision
Publisher: Springer, Cham
2017
http://dx.doi.org/10.1007/978-3-319-58771-4_45
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| 2016Sergio Conti, Martin Lenz and Martin Rumpf
Hysteresis in Magnetic Shape Memory Composites: Modeling and Simulation
2016
10.1016/j.jmps.2015.12.010
Abstract: Magnetic shape memory alloys are characterized by the coupling between a structural phase transition and magnetic one. This permits to control the shape change via an external magnetic field, at least in single crystals. Composite materials with single-crystalline particles embedded in a softer matrix have been proposed as a way to overcome the blocking of the transformation at grain boundaries. We investigate hysteresis phenomena for small NiMnGa single crystals embedded in a polymer matrix for slowly varying magnetic fields. The evolution of the microstructure is studied within the rate-independent variational framework proposed by Mielke and Theil (1999). The underlying variational model incorporates linearized elasticity, micromagnetism, stray field and a dissipation term proportional to the volume swept by the phase boundary. The time discretization is based on an incremental minimization of the sum of energy and dissipation. A backtracking approach is employed to approximately ensure the global minimality condition. We illustrate and discuss the influence of the particle geometry (volume fraction, shape, arrangement) and the polymer elastic parameters on the observed hysteresis and compare with recent experimental results.
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| Patrick W. Dondl, Behrend Heeren and Martin Rumpf
Optimization of the branching pattern in coherent phase transitions
C. R. Math. Acad. Sci. Paris, 354(6): 639--644 2016
https://arxiv.org/abs/1512.06620
Abstract: Branching can be observed at the austenite-martensite interface of martensitic phase transformations. For a model problem, Kohn and Müller studied a branching pattern with optimal scaling of the energy with respect to its parameters. Here, we present finite element simulations that suggest a topologically different class of branching patterns and derive a novel, low dimensional family of patterns. After a geometric optimization within this family, the resulting pattern bears a striking resemblance to our simulation. The novel microstructure admits the same scaling exponents but results in a significantly lowered upper energy bound. |
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| Peter Hornung, Martin Rumpf and Stefan Simon
Material Optimization for Nonlinearly Elastic Planar Beams
2016
http://arxiv.org/abs/1604.02267
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| Jan Maas, Martin Rumpf and Stefan Simon
Generalized optimal transport with singular sources
2016
http://arxiv.org/abs/1607.01186
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