| 2018D. Dũng, M. Griebel, V. N. Huy and C. Rieger
$\varepsilon$-dimension in infinite dimensional hyperbolic cross approximation and application to parametric elliptic PDEs
Journal of Complexity, 46: 66--89 2018
10.1016/j.jco.2017.12.001
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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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| M. Griebel, C. Rieger and B. Zwicknagl
Regularized Kernel-Based Reconstruction in Generalized Besov Spaces
Foundations of Computational Mathematics, 18(2): 459--508 2018
10.1007/s10208-017-9346-z
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| Michael Griebel, Christian Rieger and Peter Zaspel
Kernel-based stochastic collocation for the random two-phase Navier-Stokes equations
2018
https://ins.uni-bonn.de/media/public/publication-media/INSPreprint1813.pdf
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| Celia Reina, Landry Fokoua Djodom, Michael Ortiz and Sergio Conti
Kinematics of elasto-plasticity: Validity and limits of applicability of $F=F_eF_p$ for general three-dimensional deformations
Journal of the Mechanics and Physics of Solids, 121: 99--113 2018
10.1016/j.jmps.2018.07.006
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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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| B. Bohn, M. Griebel and C. Rieger
A representer theorem for deep kernel learning
2017
http://wissrech.ins.uni-bonn.de/research/pub/bohn/INSPreprint_concatRegr.pdf
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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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| M. Griebel and C. Rieger
Reproducing kernel Hilbert spaces for parametric partial differential equations
SIAM/ASA J. Uncertainty Quantification, 5: 111-137 2017
10.1137/15M1026870
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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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| Celia Reina and Sergio Conti
Incompressible inelasticity as an essential ingredient for the validity of the kinematic decomposition $F=F^eF^i$
J. Mech. Phys. Solids, 107: 322--342 2017
10.1016/j.jmps.2017.07.004
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| C. Rieger and H. Wendland
Sampling Inequalities for Sparse Grids
Numerische Mathematik 2017
10.1007/s00211-016-0845-7
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| Angkana Rüland, Christian Zillinger and Barbara Zwicknagl
Higher Sobolev Regularity of Convex Integration Solutions in Elasticity: The Dirichlet Problem with Affine Data in int($K^lc$)
2017
https://arxiv.org/abs/1709.02880
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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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| Herbert Koch, Angkana Rüland and Wenhui Shi
The variable coefficient thin obstacle problem: Carleman inequalities
Adv. Math., 301: 820--866 2016
http://dx.doi.org/10.1016/j.aim.2016.06.023
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