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Mathematics for Sustainable Energies

The last years has brought a fundamental political change towards energy management in Germany: As soon as possible regenerative energies on all scales are to replace nuclear as well as fossil fuel energies. Electromobility is changing traffic profiles, in particular urban traffic. Decentralized compact power stations that save one portion of the inevitable thermodynamic degree of efficiency by consuming the heat at the generation site will have to be established and optimally linked. Apart from these individual topics, the overall topic of energy efficiency has gained a dominant importance. All of these topics induce numerous new quantitative problems of high complexity, which are the source of new mathematical challenges.

Photovoltaics is one of the fastest growing regenerative energy sectors. In the focus of present interest are demands of higher efficiency with lower material usage and production costs.

In the Action Plan for Electromobility 2020, Berlin sets the goal of becoming Europe's leading location for electromobility. As for the technological basis, the key words are fuel cells, novel batteries or plug-in hybrids. Of course, urban traffic will be the topic of main interest for Berlin.

Decentralized power station networks. In the years to come, an increasing number of buildings will produce energy in a regenerative way, e.g., via solar cell roofs and walls. Whenever the produced electrical energy is not needed at the homes, the locally available electrical power will have to be fed into the communal electrical network systems. This gives rise to multiple problems of energy distribution and optimal network management, problems of utmost mathematical and computational complexity.

Projects

Project heads
Staff
SE1
Project heads Prof. Dr. Volker Mehrmann
Dr. Christian Schröder
Staff Matthias Voigt
Duration: 01.06.2014 - 31.05.2017 Status: running Located at: Technische Universität Berlin (TU)

Description

One of the bottlenecks of current procedures for the generation and distribution of green (wind or solar) energy is the accurate and timely simulation of processes in the ocean and atmosphere that can be used in short term planning and real time control of energy systems. A particular difficulty is the real time construction of physically plausible model initializations and 'controls/inputs' to bring simulations into coherence with available observations when observation locations and observations are coming in at variable times and locations.

The currently best approach for fixed observation times and locations are variational data assimilation techniques. These methods use a four dimensional model that is adapted to the incoming observations using a combination of different filtering techniques and numerical integration of the dynamical system. In order to make these methods efficient in real time data assimilation they have to be combined with appropriate model order reduction methods. A major difficulty in these techniques is the combination of approximate transfer functions and approximate initial and boundary conditions as well as the construction of guaranteed error estimates and the capturing of essential features of the original model. The so-called representer approach formulates the data assimilation problem as the numerical solution of a large-scale nonlinear optimal control problem and incorporates the assimilation of the model to the observations, via an extended ensemble Kalman filter, and the adaptation of the initial data in one approach. Adding further assumptions and linearization this optimization problem usually reduces to a linear quadratic optimal control problem which is solved via the solution of a boundary value problem with Hamiltonian structure.

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SE2
Project heads PD Dr. Annegret Glitzky
Prof. Dr. Alexander Mielke
Staff Dr. Matthias Liero
Duration: 01.06.2014 - 31.05.2017 Status: running Located at: Weierstraß-Institut (WIAS)

Description

The aim of the project D-SE2 is to find adequate spatially resolved PDE models for the electrothermal description of organic semiconductor devices describing self-heating and thermal switching phenomena. Moreover, the project intends to investigate their analytical properties, derive suitable numerical approximation schemes, and provide simulation results which can help to optimize large-area organic light emitting diodes.
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SE3
Project heads Prof. Dr. Christian Mehl
Prof. Dr. Volker Mehrmann
Prof. Dr. Caren Tischendorf
Staff Dr. Jan Philipp Pade
Dr. Andreas Steinbrecher
Duration: 01.06.2014 - 31.05.2017 Status: running Located at: Humboldt Universität Berlin (HU) , Technische Universität Berlin (TU)

Description

In the project the stability of power networks and power network models is analyzed. The classical way of modeling a power network is via a large differential-algebraic system of network equations (DAE). Modifications of the power network by adding extra power lines into the network grid or by removing some power lines can be interpreted as low rank perturbations of matrices and matrix pencils that linearize the DAE system mentioned above. In the project, the influence of these perturbation on the stability of the network is analyzed.

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SE4
Project heads Dr. Christiane Kraus
Prof. Dr. Gitta Kutyniok
Prof. Dr. Barbara Wagner
Staff Esteban Meca Álvarez
Dr. Arne Roggensack
Duration: 01.06.2014 - 31.05.2017 Status: running Located at: Technische Universität Berlin (TU) , Weierstraß-Institut (WIAS)

Description

The project SE4 aims to develop and study mathematical models in order to understand, functionalize and optimize modern nanostructured materials. Such materials are fundamental for the design of next generation thin-film solar cells as well as batteries for the production and storage of sustainable energy, respectively. Besides the mathematical modeling, the main goals of this research project are the analysis of the developed phase field systems and the construction of numerical algorithms that efficiently capture the material properties and, in particular, their anisotropic nature. More information...

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SE5
Project heads Prof. Dr. Michael Hintermüller
Staff Soheil Hajian
Tobias Keil
Duration: 01.06.2014 - 31.05.2017 Status: running Located at: Humboldt Universität Berlin (HU)

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).

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SE6
Project heads Prof. Dr. Rupert Klein
Prof. Dr. Frank Schmidt
Staff Dr. Sven Burger
Martin Hammerschmidt
Duration: 01.06.2014 - 31.05.2017 Status: running Located at: Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB)

Description

Artificial photosynthesis and water splitting, i.e. the sustainable production of chemical fuels like hydrogen and carbohydrates from water and carbon dioxide, has the potential to store the abundance of solar energy that reaches the earth in chemical bonds. Fundamental in this process is the conversion of electromagnetic energy. In photoelectrochemical water splitting semiconductor materials are employed to generate electron hole pairs with sufficient energy to drive the electrochemical reactions. In this project we investigate the use of metallic nanoparticles to excite plasmonic resonances by means of numerical simulations. These resonances localize electromagnetic nearfields which is beneficial for the electrochemical reactions. We develop electromagnetic models and numerical methods to facilite in depth analysis of these processes in close contact with our collaboration partners within the ECMath and the joint lab ``Berlin Joint Lab for Optical Simulation for renewable Energy research'' (BerOSE) between the ZIB, FU and HZB.

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SE7
Project heads PD Dr. John Schoenmakers
Prof. Dr. Vladimir Spokoiny
Staff Roland Hildebrand
Duration: 01.06.2014 - 31.05.2017 Status: running Located at: Weierstraß-Institut (WIAS)

Description

The project aims at developing numerical methods for the solution of complex optimal control problems arising in energy production, storage, and trading on energy markets. As a first step, we implement a Monte-Carlo approach to a hydro-electricity production and storage problem coupled with a stochastic model of the electricity market. Further we develop algorithms for pricing of complex energy derivatives based on the dual martingale approach.

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SE8
Project heads Prof. Dr. Wolfgang Dreyer
Prof. Dr. Peter Karl Friz
Staff Paul Gajewski
Mario Maurelli
Duration: 01.06.2014 - 31.05.2017 Status: running Located at: Weierstraß-Institut (WIAS)

Description

The aim of the project is to better understand and to give simulations for a successful model for the charging and discharging of lithium-ion batteries, which are currently the most promising storage devices to store and convert chemical energy into electrical energy and vice versa. The model exhibits phase transition under different small parameter regimes and gives rise to hysteresis. We study these phenomena using the interpretation of the model as a stochastic particle system, with the goal of providing stability bounds, fast simulations, improvement of the model itself and optimization of the device. More information...

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SE9
Project heads Prof. Dr. Reinhold Schneider
Prof. Dr. Fredi Tröltzsch
Staff Benjamin Huber
Duration: 01.06.2014 - 31.05.2017 Status: running Located at: Technische Universität Berlin (TU)

Description

The project D-SE9 focuses on the analysis and efficient numerical solution of optimal control problems for nonlinear evolution equations with Maxwell's evolution equations as a challenging benchmark example. In particular, we aim at developing low rank approximation techniques for the solution of forward-backward optimality systems that arise whenever optimal control problems for evolution equations are considered. In this project, we thus merge existing expertise in optimal control and low rank matrix and tensor approximation.

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SE10
Project heads Prof. Dr. Reinhold Schneider
Staff Sebastian Wolf
Duration: 01.06.2014 - 31.05.2017 Status: running Located at: Technische Universität Berlin (TU)

Description

In the project D-SE10 we aspire to recover higher order tensors from a relatively small number of measurements using low rank assumptions. As straight forward generalizations of the matrix recovery techniques to the problem of tensor recovery are often either infeasible or impossible, the focus of this project is twofold. First, to investigate those generalizations that might still be feasible in a tensor setting in particular Riemannian methods on low rank tensor manifolds, and second, to apply and specialize existing techniques from tensor product approximation like the ALS to the tensor recovery and completion settings.

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SE11
Project heads Prof. Dr. Carsten Hartmann
Staff PD Dr. Burkhard Schmidt
Duration: 01.06.2014 - 31.05.2017 Status: running Located at: Freie Universität Berlin (FU)

Description

Photocatalysis is a key application in the field of femtochemistry where chemical reaction dynamics is controlled by temporally shaped femtosecond laser pulses, with the target to promote specific product channels while suppressing competing undesired channels, e.g. pollutants. The optimal shaping of the laser pulse requires a detailed insight into the underlying reaction mechanisms at the atomic or molec- ular level that can often only be obtained by theoretical modelling and computer simulations of the quantum mechanical equations of motion. For catalytic system, this boils down to the iterated integration of the dissipative Liouville–von–Neumann (LvN) equation for reduced quantum mechanical density matrices, which represents the computational bottleneck for theoretical modelling, as the size of the matrices grows quadratically with the number of quantum states involved. The aim of this project is to study model order reduction (MOR) of LvN-based models to beat the curse of dimensionality in the simulation and (optimal) control of photocatalytic processes. In the setting of first-order perturbation theory, the laser field in these models is linearly coupled to the density matrix, which leads to a time- inhomogeneous bilinear system of equations of motion. MOR of bilinear systems has recently been a field of intense research. The downside of many available methods is their lack of structure preservation, most importantly, asymptotic stability of fixed points. An alternative that is in the focus of this project is MOR based on balancing the controllable and observable subspace of the system. Even though the identification of the essential subspace requires the solution of large-scale Lyapunov equations, which limits the applicability of the method to systems of moderate size (up to 100,000 DOFs), it has proven powerful for linear control systems in terms of computable error bounds and structure preservation. Whether these results carry over to the bilinear case is still open.

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SE12
Project heads Prof. Dr. Carsten Gräser
Staff Pawan Kumar
Duration: 01.06.2014 - 31.05.2017 Status: running Located at: Freie Universität Berlin (FU)

Description

The aim of this project is to develop fast linear solvers for heterogeneous saddle point problems as appearing during the iterative solution of non-smooth optimization problems, e.g., in the context of phase field models. While the development of nonlinear solvers for phase field models has reached a certain maturity, the existing solvers for the linear subproblems are still unsatisfactory. As a first step, we focus on two-phase models. Later, we plan to extend these solvers for multiphase systems.

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SE13
Project heads Dr. Martin Eigel
PD Dr. René Henrion
Prof. Dr. Dietmar Hömberg
Prof. Dr. Reinhold Schneider
Staff Johannes Neumann
Dr. Thomas Petzold
Duration: 01.06.2014 - 31.05.2017 Status: running Located at: Technische Universität Berlin (TU) , Weierstraß-Institut (WIAS)

Description

The application focus of this project is the topology optimization of the main frame of wind turbines. This is the central assembly platform at the tower head accommodating the drive train, the generator carrier, the azimuth bearing and drives and a lot of small components. Topology optimization should not be mistaken for legally mandated structural analysis computations. For the latter, it is standard to solicit a number of single load scenarios based on available time series data. While this approach is questionable already for stress analysis, it is prohibitive for topology optimization. Disregarding the multivariate distribution of the random loads would not provide any probabilistic certificate for bounding stresses. Moreover, the natural way to choose weights is to derive a stochastic load from available time series data. The main frame is made of cast iron which is prone to a number of material impurities like shrink holes, dross, and chunky graphite. This motivates the additional consideration of randomness for the material stiffness. Structures resulting from topology optimization often exhibit unacceptably high stresses necessitating costly subsequent shape design works. To avoid this already during the optimization, state constraints have to be included in the optimization problem. The main novelty of this project is that it combines a phase field relaxed topology optimisation problem not only with uncertain loading and material data but also with chance state constraints. Even in the finite-dimensional case, the derivation of optimality conditions including gradient formulas is completely open. In the long run, including an appropriate damage model as additional state equation will be a further task of great practical importance.

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SE14
Project heads Dr. Sebastian Matera
Staff Sandra Doepking
Duration: 01.06.2014 - 31.05.2017 Status: running Located at: Freie Universität Berlin (FU)

Description

On the route to a more efficient exploitation of energy and materials, the design of new heterogenous catalysts is a central aspect, be it for the production of fine chemicals or the conversion of solar energy to fuels. Ideally, such a design is based on an atomistic understanding of the origin of catalytic activity. In order to enable this detailed undestanding, first-principles kinetic Monte Carlo approaches have been established during the last decade. Despite their success, these still have some some limitations. On the one hand, the electronic structure methods, employed to determine required rate parameters, introduce a non-negligible error into the later. On the other hand, the need for stochastic simulation and the typically large dimension of the parameter space hampers the determination of the rate determining steps by sensitivity analysis, i.e. the most interesting input for a rational catalyst design.

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SE15
Project heads Dr. Carlos Rautenberg
Staff Masoumeh Mohammadi
Duration: 01.06.2014 - 31.05.2017 Status: running Located at: Humboldt Universität Berlin (HU)

Description

The optimal sensor placement problem for the estimation of the temperature distribution in buildings is a highly nonlinear and multi-scale problem where stochastic perturbations are usually present. The main goal here is to properly locate sensors in order to reliably estimate the temperature distribution in certain areas. Since feedback controllers are usually in use, a proper estimation of the state is of utmost importance in order to reduce energy consumption of such controllers.

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