Profile
Profile

Prof. Dr. Martin Rumpf

E-mail: martin.rumpf(at)ins.uni-bonn.de
Phone: +49 228 73 7866
Homepage: http://numod.ins.uni-bonn.de/people/rumpf/rumpf.php
Room: 2.035
Location: Mathematics Center
Institute: Institute for Numerical Simulation
Research Areas: Research Area B (Leader)
Research Area A
Date of birth: 28.May 1964
Mathscinet-Number: 604100

Academic Career

1992

Dr. rer. nat., University of Bonn

1993 - 1996

Postdoc, University of Freiburg

1996 - 2001

Professor (C3), University of Bonn

2001 - 2004

Professor (C4), University of Duisburg-Essen

Since 2004

Professor (C4/W3), University of Bonn

Research Profile

Variational problems and evolution problems arising in computer vision, in geometry processing, and in materials science are the major driving force of my research.

In computer vision I'm interested in the infinite dimensional geometry of shape spaces equipped with a Riemannian metric which is motivated by physical models of viscous dissipation. A central theme is a general variational time discrete Riemannian calculus on different shape spaces, including discrete geodesics, exponential map and parallel transport. Applications are warping of images or shell surfaces, shape extrapolation, and pattern or texture transfer. A comprehensive convergence theory based on \Gamma convergence, finite element and ODE estimates on Hilbert spaces could be developed. I'm also interested in the close links to the theory of optimal transport.

A major goal is to treat textured images and explore inherent multiple scales in image maps. To this end images are considered as pointwise maps into some patch manifold, describing local, high dimensional texture and structure. Furthermore, spline curves and other low dimensional, smooth submanifolds will be particular interest in time dependent data analysis and in geometry animation.

With respect to materials science, I'm particularly interested in two-scale elastic shape optimization and the formation of optimal branching and folding patterns in elastic materials. The minimization of compliance type cost functionals leads to microstructured shapes and branching patterns arising naturally at material interfaces or at boundary incompatibilities.

My focus is on robust a posteriori error control using functional error estimates for BV functionals, duality techniques and relaxation. The aim is an efficient simulation and optimization of the microscopic patterns, and a better understanding of branching-type patterns observed in natural elastic structures, as for example bones and thin sheets. The vision is to carry over the two-scale analysis of elastic bulk material to thin elastic plates and shells.

Research Projects and Activities

DFG Cluster of Excellence “Hausdorff Center for Mathematics”
Deputy coordinator, 2006 – 2012

Board of Directors of the Hausdorff Center for Mathematics
Member, since 2006

DFG-Project “Discrete Riemannian calculus on shape space”
jointly with Karl-Theodor Sturm, in the Collaborative Research Center SFB 1060 “The Mathematics of Emergent Effects”, 2012 - 2020

DFG-Project “Numerical optimization of shape microstructures”
jointly with Sergio Conti, in the Collaborative Research Center SFB 1060 “The Mathematics of Emergent Effects”, 2012 - 2020

DFG-Project “Geodesic Paths in Shape Space”
in the research network of the FWF S117 “Geometry + Simulation”, 2012 - 2020

DFG Collaborative Research Center SFB 1060 “The Mathematics of Emergent Effects”
Deputy coordinator, since 2014

GIF-Project “A Functional Map Approach to Shape Spaces”
by the German-Israeli Foundation for Scientific Research and Development, jointly with Miri Ben-Chen, 2017 - 2020

Oberwolfach Workshops on “Image and Surface Processing”
Organizer, 2005, 2007, 2011, 2016

Contribution to Research Areas

Research Area A
The proper discretization of geometric variational problems and geometric partial differential equations is a particular research focus in my group. In many applications in materials science, biology and geometric modeling evolution problems do not reside on a flat Euclidean domain but on curved surfaces. I am interested in geometrically consistent discretization concepts which lead to robust and efficient numerical algorithms [1].
Furthermore, we study higher order geometric functionals as they appear in shell models with bending energies. Instead of a discretization of the associated higher order differential operator, we propose a nested variational approach, where in an inner minimization problem curvature quantities in the integrand of the functional are themselves approximated by the solution of another associated geometric variational problem.
Research Area B
One of my major research interests is the simulation and optimisation of material microstructures.
Here, a particular focus is on the elastic behavior of trabecular bone microstructures with strong characteristic variations between different species and different health status. Elasticity also plays an important role in polycrystalline or composite shape memory material [2].
Numerically, we combine composite finite element [3] and boundary element methods with parametric, level set, or phase field models. Observing certain geometric microstructures, the question naturally arises if these structures are optimal under certain usually stochastic loading conditions [4,5].
Furthermore, a leading motive of my research is the application of concepts from rational mechanics in imaging and vision. We use models from nonlinear elasticity to define shape averages and a principle component analysis of shapes [6].
Furthermore, we link the geometry of shape space to concepts of viscous flow [7].

Selected Publications

[1] Martin Lenz, Simplice Firmin Nemadjieu, Martin Rumpf
A convergent finite volume scheme for diffusion on evolving surfaces
SIAM J. Numer. Anal. , 49: (1): 15--37
2011
DOI: 10.1137/090776767
[2] S. Conti, M. Lenz, M. Rumpf
Modeling and simulation of magnetic-shape-memory polymer composites
J. Mech. Phys. Solids , 55: (7): 1462--1486
2007
DOI: 10.1016/j.jmps.2006.12.008
[3] Tobias Preusser, Martin Rumpf, Stefan Sauter, Lars Ole Schwen
3D composite finite elements for elliptic boundary value problems with discontinuous coefficients
SIAM J. Sci. Comput. , 33: (5): 2115--2143
2011
DOI: 10.1137/100791750
[5] Patrick Penzler, Martin Rumpf, Benedikt Wirth
A phase-field model for compliance shape optimization in nonlinear elasticity
ESAIM Control Optim. Calc. Var. , 18: (1): 229--258
2012
DOI: 10.1051/cocv/2010045
[6] Martin Rumpf, Benedikt Wirth
An elasticity-based covariance analysis of shapes
Int. J. Comput. Vis. , 92: (3): 281--295
2011
DOI: 10.1007/s11263-010-0358-2
[7] Benedikt Wirth, Leah Bar, Martin Rumpf, Guillermo Sapiro
A continuum mechanical approach to geodesics in shape space
Int. J. Comput. Vis. , 93: (3): 293--318
2011
DOI: 10.1007/s11263-010-0416-9
[8] Patrick Dondl, Behrend Heeren, Martin Rumpf
Optimization of the branching pattern in coherent phase transitions
C. R. Math. Acad. Sci. Paris , 354: (6): 639--644
2016
DOI: 10.1016/j.crma.2016.03.013
[9] Martin Rumpf, Benedikt Wirth
Variational time discretization of geodesic calculus
IMA J. Numer. Anal. , 35: (3): 1011--1046
2015
DOI: 10.1093/imanum/dru027
[10] B. Berkels, A. Effland, M. Rumpf
Time discrete geodesic paths in the space of images
SIAM J. Imaging Sci. , 8: (3): 1457--1488
2015
DOI: 10.1137/140970719
[11] Sergio Conti, Harald Held, Martin Pach, Martin Rumpf, Rüdiger Schultz
Risk averse shape optimization
SIAM J. Control Optim. , 49: (3): 927--947
2011
DOI: 10.1137/090754315
[12] U. Clarenz, U. Diewald, G. Dziuk, M. Rumpf, R. Rusu
A finite element method for surface restoration with smooth boundary conditions
Comput. Aided Geom. Design , 21: (5): 427--445
2004
DOI: 10.1016/j.cagd.2004.02.004
[13] Günther Grün, Martin Rumpf
Nonnegativity preserving convergent schemes for the thin film equation
Numer. Math. , 87: (1): 113--152
2000
DOI: 10.1007/s002110000197
[14] M. Flucher, M. Rumpf
Bernoulli's free-boundary problem, qualitative theory and numerical approximation
J. Reine Angew. Math. , 486: : 165--204
1997
[15] Benjamin Berkels, Alexander Effland, Martin Rumpf
A Posteriori Error Control for the Binary Mumford-Shah Model
Mathematics of Computation
2015
DOI: doi.org/10.1090/mcom/3138
[16] Benjamin Berkels, Sebastian Bauer, Svenja Ettl, Oliver Arold, Joachim Hornegger, Martin Rumpf
Joint Surface Reconstruction and 4D Deformation Estimation from Sparse Data and Prior Knowledge for Marker-Less Respiratory Motion Tracking
Medical Physics
, 40: (9): 091703
2013
DOI: 10.1118/1.4816675

Publication List

Editorships

• Computing and Visualization in Science (since 1999)
• SIAM Journal on Imaging Science (since 2007)
• SIAM Journal on Numerical Analysis (since 2015)
• Journal of Mathematical Imaging and Vision (since 2015)

Selected Invited Lectures

2003

Plenary lecture, GAMM annual meeting, Padua / Abano Terme, Italy

2004

Plenary lecture, SIAM Conference on Image Science, Salt Lake City, UT, USA

2005

Plenary lecture, EQUADIFF, Bratislava, Slovakia

2006

Plenary lecture, Curves and Surface, Avignon, France

2008

Invited lecture course, CIME summer school, Cetraro, Italy

2010

Invited lecture course, CNA summer school, Pittsburgh, PA, USA

2013

Plenary lecture, SSVM, Graz, Austria

2015

Invited lecture course, CRC summer school, Barcelona, Spain

2016

Invited lecture, Geometry Summit, Berlin

Offers

2002

Chair in Mathematics, University of Zürich, Switzerland

2003

Chair, MATHEON, FU Berlin

2012

Director position of the Weierstrass Institute Berlin combined with a chair at the HU Berlin

Selected PhD students

Olga Wilderotter (2001): “Adaptive Finite-Elemente-Methode für singuläre parabolische Probleme”,
now Professor, HS Karlsruhe

Ulrich Weikard (2002): “Numerische Loesungen der Cahn-Hilliard-Gleichung und der Cahn-Larche-Gleichung”,
now Senior Economist, DekaBank Deutsche Girozentrale

Tobias Preußer (2003): “Anisotropic Geometric Diffusion in Image and Image-Sequence Processing”,
now Professor, Jacobs University Bremen, and Member of Management Board, and Head of Modelling & Simulation, Fraunhofer MEVIS, Bremen

Robert Strzodka (2004): “Hardware Efficient PDE Solvers in Quantized Image Processing”,
now Professor, University of Heidelberg

Benedikt Wirth (2010): “Variational Methods in Shape Space”,
now Associate Professor, University of Münster

Benjamin Berkels (2012): “Joint Methods in imaging based on diffuse image representations”,
now Professor, RWTH Aachen
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