Prof. Dr. Michael Hintermüller

Executive Board Member

Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)/HU Berlin
Mohrenstraße 39
10117 Berlin
+49 (0) 30 +49 30 20372 586

Scientists in Charge of Application Fields Sustainable Energies



Research focus

Nonsmooth Variation Problems; Mathematical Optimization with Equilibrium Constraints in Function Space; Mathematical Image Processing; Nonlinear and Nonsmooth Optimization; Optimization with Partial Differential Equations; Numerical Algorithms for Inverse Problems

Projects as a project leader

  • CH12

    Advanced Magnetic Resonance Imaging: Fingerprinting and Geometric Quantification

    Prof. Dr. Michael Hintermüller

    Project heads: Prof. Dr. Michael Hintermüller
    Project members: -
    Duration: -
    Status: running
    Located at: Humboldt Universität Berlin

    Description

    Very recently, magnetic resonance fingerprinting (MRF) has been introduced as a highly promising MRI acquisition scheme which allows for the simultaneous quantification of the tissue parameters (e.g. T1, T2 and others) using a single acquisition process. In MRF, the tissue of interest is excited through a random sequence of pulses without needing to wait for the system to return to equilibrium between pulses. After each pulse, a subset of the signal's Fourier coefficients is collected, as in classical MRI, and a reconstruction of the net magnetization image is performed. These reconstructions suffer from the presence of artifacts since the Fourier coefficients are not fully sampled. The formed sequence of image elements is then compared to a family of predicted sequences (dictionary of fingerprints) each of which corresponds to a specific combination of values of the tissue parameters. This dictionary is computed beforehand by solving the Bloch equations. The idea is that, provided the dictionary is rich enough, every material element (voxel) can be then mapped to its parameter values. While first very promising results have been obtained in biomedical engineering, many aspects of MRF remain widely open and require a proper mathematization for optimizing and robustifying the procedure. The aim of this project is, thus, to provide a quantitative mathematical model for the MRF process, leading to a variational image reconstruction problem subject to dynamical constraints describing magnetization and an embedded reconstruction scheme. This model will be subject to a detailed mathematical analysis and its efficient numerical solution.

  • SE5

    Optimal design and control of optofluidic solar steerers and concentrators

    Prof. Dr. Michael Hintermüller

    Project heads: Prof. Dr. Michael Hintermüller
    Project members: Tobias Keil
    Duration: -
    Status: completed
    Located at: Humboldt Universität Berlin

    Description

    Solar energy is mostly harvested by means of photovoltaic (PV) or concentrating photovoltaic (CPV) solar cells. The efficiency of CPV is higher (at least twice) than the traditional PV but significantly more expensive. To reduce costs, optical condensers (e.g., a Fresnel lens) to concentrate solar light on each CPV cell are used. Moreover, since the energy production is maximized when the panels are perpendicular to the light beam, mechanical tracking systems that move the array of solar panels based on the position of the sun. But these tracking system increases costs, requires power and are error-prone. The goal of this project is the optimal design and control of steerers and concentrators for PV or CPV using electrowetting (EW) and electrowetting-on-dielectric (EWOD).

    https://www.math.hu-berlin.de/~hp_hint/SE5/index.html
  • SE-AP5

    Fully adaptive and integrated numerical methods for the simulation and control of variable density multiphase flows governed by diffuse interface models

    Prof. Dr. Michael Hintermüller

    Project heads: Prof. Dr. Michael Hintermüller
    Project members: -
    Duration: 01.07.2013 - 30.06.2016
    Status: completed
    Located at: Humboldt Universität Berlin

    Description

    Within this project we develop, analyze, and implement simulation and optimization procedures for variable density multiphase flows governed by di ffuse interface models. In the simulation part we in particular develop and analyse numerical methods for the simulation of multiphase flow problems with variable fluid densities which guarantee a locally re fined resolution of the local processes at the interface. In a next step we propose adaptive discretization concepts for the coupling of diff use interface models and surface partial di fferential equations (PDEs). In the optimization part we consider open - and closed - loop control approaches, where we formulate and analyze optimal control problems for multiphase flows governed by di ffuse interface models, develop robust and reliable solution strategies for their numerical solution, and develop, implement and analyze model-predictive feedback control strategies for multiphase flows governed by di ffuse interface models.

    http://www.dfg-spp1506.de/projecthintermuellerhinze
  • CH-AP24

    Free Boundary Problems and Level Set Methods

    Prof. Dr. Michael Hintermüller

    Project heads: Prof. Dr. Michael Hintermüller
    Project members: -
    Duration: 01.05.2011 - 31.03.2018
    Status: running
    Located at: Humboldt Universität Berlin

    Description

    Project part FREELEVEL will focus on two research streams: (i) shape and topological sensitivity-based solvers in tomography and (ii) the extension of spatially adapted regularization to more general image restoration problems, e.g., involving blind deconvolution, and non-convex regularization. Concerning tomography problems, a level-set-based algorithm relying on shape and extended topological sensitivities will be realized for FDOT and MIT, respectively. For MIT, first a reduced model leading to an elliptic PDE-system will be studied and, in a next step, the full Maxwell system will be taken into account. For numerical efficiency purposes, a shape-aware adaptive finite element method will be intertwined with the level-set solver (partly with FEMBEM). In the area of image restoration, we are motivated by optical diffusion tomography problems for detecting objects located behind turbid media and by convolution identification in dual-MR techniques (MRI). We formulate these problems in terms of blind deconvolution, preferably with non-convex regularization with respect to the image. The resulting problems will be studied and solved numerically. With respect to the latter - split Bregman - iteratively re-weighted total variation and semismooth Newton solvers will be investigated. Further, motivated by sparse magnetic resonance imaging, problems in compressed sensing with convex (OPTIM) and non-convex relaxation (MRI) of the 0-norm will be treated. The latter is interesting as there is evidence that non-convex regularization goes along with a possible reduction in acquired data. Further, FREELEVEL will focus on topics supporting other projects, such as piecewise polynomial Mumford-Shah based image segmentation using topological sensitivities (INVERSE).

    Within the SFB, FREELEVEL acts as a center of expertise for shape and topological sensitivity-based level-set solvers for tomography problems. Moreover, FREELEVEL contributes expertise and software in image restoration to the SFB through various cooperations with practitioners (MRI) as well as the applied mathematics group within the SFB (OPTIM, INVERSE).

    http://math.uni-graz.at/mobis/freelevel.html
  • MI-AP6

    Parameter identification, sensor localization and quantification of uncertainties

    Prof. Dr. Michael Hintermüller

    Project heads: Prof. Dr. Michael Hintermüller
    Project members: -
    Duration: 01.10.2014 - 30.06.2018
    Status: running
    Located at: Humboldt Universität Berlin

    Description

    The project work concentrates on modeling aspects as well as the conception and analysis of robust numerical methods for solving inverse problems for switching (or hybrid) systems of partial differential equations on graphs. In this context, the graph typically represents a transportation network for a specific substance or commodity. In accordance with the focus application of this collaborative research center (CRC), the main emphasis lies on networks transporting for (natural) gas. The project pursues several research goals:

    The identification of unknown parameters (e.g. the Darcy friction factor) and the detection of anomalies (leakage). the optimal arrangement of sensors in the network for a robustifying the identification tasks the quantification of uncertainties in the identified parameters or in other statistically relevant quantities.

    Within the CRC, this project will collaborate with other subprojects on (constrained) optimal control problems for hyperbolic or hybrid systems and their numerical realization, and on numerical methods for the identification of the friction coefficient. It will equip the hierarchy of models considered with the CRC with relevant physical parameters or statistical information resulting from solving various identification problems. The project participates in demonstrator D2.

    http://trr154.fau.de/index.php/en/subprojects/b02e
  • OT1

    Mathematical modeling, analysis, and optimization of strained Germanium-microbridges

    Prof. Dr. Michael Hintermüller / Prof. Dr. Alexander Mielke / Prof. Dr. Thomas Surowiec / Dr. Marita Thomas

    Project heads: Prof. Dr. Michael Hintermüller / Prof. Dr. Alexander Mielke / Prof. Dr. Thomas Surowiec / Dr. Marita Thomas
    Project members: Lukas Adam / Dr. Dirk Peschka
    Duration: -
    Status: completed
    Located at: Humboldt Universität Berlin / Weierstraß-Institut

    Description

    The goal of the project Mathematical Modeling, Analysis, and Optimization of Strained Germanium-Microbridges is to optimize the design of a strained Germanium microbridge with respect to the light emission. It is a joint project with the Humboldt-University Berlin (M. Hintermüller, T. Surowiec) and the Weierstrass Institute (A. Mielke, M. Thomas), that also involves the close collaboration with the Department for Materials Research at IHP (Leibniz-Institute for Innovative High Performance Microelectronics, Frankfurt Oder).

    http://www.wias-berlin.de/projects/ECMath-OT1/
  • OT6

    Optimization and Control of Electrowetting on Dielectric for Digital Microfluidics in Emerging Technologies

    Prof. Dr. Michael Hintermüller

    Project heads: Prof. Dr. Michael Hintermüller
    Project members: Soheil Hajian
    Duration: -
    Status: running
    Located at: Humboldt Universität Berlin

    Description

    A number of emerging key technologies in microbiology, medical diagnostic devices, personal genomics, as well as next-generation low-energy OLED displays and liquid lenses make use of a phenomenon known as electrowetting on dielectric (EWOD). Electrowetting involves the manipulation of small (microscopic) droplets on a dielectric surface by the actuation of the underlying current. In fact, droplets in a typical EWOD device are situated between two separated hydrophobic surfaces, one of which contains an array of controllable electrodes. The air-liquid-solid contact angle can then by changed by varying the voltages on separate electrodes, which causes the droplets to move. Thus, the voltages are a natural choice for influencing (controlling) the motion of a droplet. The project pursues both sharp interface and phase field models, respectively, for the movement of droplets in an EWOD device. Both models make use of a macroscopic description for contact line pinning, which is due to contact angle hysteresis as well as molecular adhesion at the solid-liquid-air interface, for a faithful representation of the droplets velocity and cover different aspects properly. Due to the non-trivial dependencies on the moving interface in the sharp interface context, the proof of existence of an optimal control remains impossible without further restrictive assumptions or constraints, e.g., on the geometry, and the complexity of the phase field model poses severe challenges for a fast (real-time) numerical solution as needed for EWOD devices. For these reasons, instead of computing time-discrete or optimal controls the project work pursues an idea from model predictive control (MPC).