Sustainable Energies

The last years have brought a fundamental political change towards energy management in Germany: As soon as possible regenerative energies on all scales like wind and solar power are to replace nuclear as well as fossil fuel energies. Decentralized compact power stations with combined heat and power generation will have to be established and optimally linked. Electromobility is changing traffic profiles, in particular in urban areas. Apart from these individual aspects, the overall issue 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.

Energy performance of buildings. Buildings are responsible for 40% of energy consumption and 36% of CO2 emissions in the EU. Thus, in order to save energy, an important task is to reduce the building energy cost. One key issue for this purpose is the performance of building service systems, which can affect the climate and energy inside buildings. The control objective of buildings’ climate is to keep the room temperature in a predefined comfort zone. Matheon develops new strategies for the optimal placement of sensors, which sample the temperature and send back to the control center in the building, from where the control action (cool or heat) is made and then realized by a set of actuators.

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, it will have to be fed into the communal electrical network system. This gives rise to multiple problems of energy distribution and optimal network management, problems of utmost mathematical and computational complexity. Within Matheon, the stability of power networks is analyzed subject to adding extra power lines into the network grid or by removing some power lines. In addition, complex optimal control problems arising in energy production, storage, and trading on energy markets are studied, e.g., hydro-electricity production and storage coupled with a stochastic model of the electricity market.

One million electric vehicles on the road by 2020 and least six million in 2030: that is the objective of the German Government, announced in the "National Development Plan for Electromobility" in 2009 and in the energy concept of September 2010. Nevertheless, on Germany’s way to become the announced lead market for electromobility, major technological challenges still have to be mastered. The key words are fuel cells, novel batteries or plug-in hybrids.

Matheon helps to reach these ambitious goals by providing a novel modelling approach and a new simulation concept for the charging and discharging of lithium-ion batteries, which are currently the most promising devices to store and convert chemical energy into electrical energy and vice versa.



Topics

  • Reduced order modeling for data assimilation
  • Optimal Network Sensor Placement for Energy Efficiency
  • Stability analysis of power networks and power network models
  • Optimal design and control of optofluidic solar steerers and concentrators
  • Optimizing strategies in energy and storage markets
  • Stochastic methods for the analysis of lithium-ion batteries


Running projects

Financed by ECMath

  • SE1

    Reduced order modeling for data assimilation

    Prof. Dr. Volker Mehrmann / Dr. Christian Schröder

    Project heads: Prof. Dr. Volker Mehrmann / Dr. Christian Schröder
    Project members: Matthias Voigt
    Duration: 01.06.2014 - 31.05.2017
    Status: running
    Located at: Technische Universität Berlin

    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.

    http://www3.math.tu-berlin.de/numerik/NumMat/ECMath/SE1/
  • SE10

    Low rank tensor recovery

    Prof. Dr. Reinhold Schneider

    Project heads: Prof. Dr. Reinhold Schneider
    Project members: Sebastian Wolf
    Duration: 01.06.2014 - 31.05.2017
    Status: running
    Located at: Technische Universität Berlin

    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.

    http://d-se10.de
  • SE11

    Model order reduction for light-controlled nanocatalysis

    Prof. Dr. Carsten Hartmann

    Project heads: Prof. Dr. Carsten Hartmann
    Project members: PD Dr. Burkhard Schmidt
    Duration: 01.06.2014 - 31.05.2017
    Status: running
    Located at: Freie Universität Berlin

    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.

    https://sites.google.com/site/ecmathse11/

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Financed by others

  • SE-AP10

    Numerische Lösungsverfahren für gekoppelte Populationsbilanzsysteme zur dynamischen Simulation multivariater Feststoffprozesse am Beispiel der formselektiven Kristallisation

    Prof. Dr. Volker John

    Project heads: Prof. Dr. Volker John
    Project members: -
    Duration: 01.10.2013 - 30.09.2017
    Status: running
    Located at: Weierstraß-Institut

    Description

    Feststoffprozesse in der Verfahrenstechnik lassen sich durch Populationsbilanzsysteme beschreiben. Hierbei handelt es sich um ein gekoppeltes System von partiellen Differentialgleichungen zur Charakterisierung der kontinuierlichen Phase, sowie einer Populationsbilanzgleichung zur Beschreibung der Feststoffphase. Die Lösung dieser Populationsbilanzgleichung, die Partikelverteilungsdichte f(t,r,x), beschreibt die Partikelverteilung zum Zeitpunkt t in den Ortskoordinaten r und in einer bzw. mehreren Eigenschaftskoordinaten x.

    Ziel des Projektes ist der Vergleich und die Weiterentwicklung von numerischen Verfahren zur Lösung von Populationsbilanzsystemen. Dies soll am Beispiel der formselektiven Kristallisation von ausgewählten Modellsubstanzen, die sich über eine bzw. mehrere Eigenschaftskoordinaten beschreiben lassen, geschehen. Weiterhin sollen im Rahmen dieses Projektes optimale statistisch geplante wachstums- bzw. agglomerationsdominierte Benchmarkexperimente durchgeführt werden. Diese dienen sowohl zur Bestimmung von kinetischen Parametern wie Nukleations- und Wachstumsraten oder Agglomerationskernen, als auch zur Abschätzung der numerischen Fehler der zur Simulation verwendeten Lösungsverfahren. Abschließend sollen die entwickelten Methoden, sowie die ermittelten Prozesskinetiken zur Auslegung und Optimierung eines Gesamtprozesses zur kontinuierlichen und formselektiven Kristallisation verwendet werden.

    http://www.dynsim-fp.de/projekte/c-algorithmen/gekoppelte-populationsbilanzsysteme.html
  • SE-AP11

    Multiscale tensor decomposition methods for partial differential equations

    Prof. Dr. Rupert Klein / Prof. Dr. Reinhold Schneider / Prof. Dr. Harry Yserentant

    Project heads: Prof. Dr. Rupert Klein / Prof. Dr. Reinhold Schneider / Prof. Dr. Harry Yserentant
    Project members: -
    Duration: 01.10.2014 - 30.09.2018
    Status: running
    Located at: Freie Universität Berlin / Technische Universität Berlin

    Description

    Novel hierarchical tensor product methods currently emerge as an important tool in numerical analysis and scienti.c computing. One reason is that these methods often enable one to attack high-dimensional problems successfully, another that they allow very compact representations of large data sets. These representations are in some sense optimal and by construction at least as good as approximations by classical function systems like polynomials, trigonometric polynomials, or wavelets. Moreover, the new tensor-product methods are by construction able to detect and to take advantage of self-similarities in the data sets. They should therefore be ideally suited to represent solutions of partial differential equations that exhibit certain types of multiscale behavior.
    The aim of this project is both to develop methods and algorithms that utilize these properties and to check their applicability to concrete problems as they arise in the collobarative research centre. We plan to attack this task from two sides. On the one hand we will try to decompose solutions that are known from experiments, e.g., on Earthquake fault behavior, or large scale computations, such as turbulent flow fields. The question here is whether the new tensor product methods can support the devel­opment of improved understanding of the multiscale behavior and whether they are an improved starting point in the development of compact storage schemes for solutions of such problems relative to linear ansatz spaces.
    On the other hand, we plan to apply such tensor product approximations in the frame­work of Galerkin methods, aiming at the reinterpretation of existing schemes and at the development of new approaches to the ef.cient approximation of partial differential equations involving multiple spatial scales. The basis functions in this setting are not taken from a given library, but are themselves generated and adapted in the course of the solution process.
    One mid-to long-term goal of the project that combines the results from the two tracks of research described above is the construction of a self-consistent closure for Large Eddy Simulations (LES) of turbulent flows that explicitly exploits the tensorproduct approach’s capability of capturing self-similar structures. If this proves successful, we plan to transfer the developed concepts also to Earthquake modelling in joint work with partner project B01.

    http://sfb1114.imp.fu-berlin.de/research/index.php?option=com_projectlog&view=project&id=8
  • SE-AP14

    Foundation and application of generalized mixed FEM towards nonlinear problems in solid mechanics

    Prof. Dr. Carsten Carstensen

    Project heads: Prof. Dr. Carsten Carstensen
    Project members: Philipp Bringmann / Friederike Hellwig
    Duration: 01.09.2014 - 31.08.2017
    Status: running
    Located at: Humboldt Universität Berlin

    Description

    Despite the practical success in computational engineering and a few partial mathematical convergence proofs, many fundamental questions on the reliable and effective computer simulation in nonlinear mechanics are still open. The success of mixed FEMs in the linear elasticity with focus on the accuracy of the stress variable motivated the research of novel discretization schemes in the SPP1748. This and recent surprising advantages of related nonconforming finite element methods in nonlinear partial differential equations with guaranteed lower eigenvalue bounds or lower energy bounds in convex minimization problems suggests the investigation of mixed and simpler generalized mixed finite element methods such as discontinuous Petrov-Galerkin schemes for linear or linearized elasticity and nonlinear elasticity with polyconvex energy densities in this project. The practical applications in computational engineering will be the focus of the Workgroup LUH with all 3D simulations to provide numerical insight in the feasibility and robustness of the novel simulation tools, while the Workgroup HU will provide mathematical foundation of the novel schemes with rigorous a priori and a posteriori error estimates. The synergy effects of the two workgroups will be visible in that problems with a known rigorous mathematical analysis or the Lavrentiev gap phenomenon or cavitation will be investigated by engineers for the first time and, vice versa, more practical relevant models in nonlinear mechanics will be looked at from a mathematical viewpoint with arguments from the calculus of variations and the implicit function theorem combined with recent arguments for a posteriori error analysis and adaptive mesh-refining. A combination of ideas in least-squares finite element methods with those of hybridized methods recently led to discontinuous Petrov Galerkin (dPG) FEMs. They minimize a residual inherited from a piecewise ultra weak formulation in a nonstandard localized dual norm. This innovative ansatz will be generalized from Hilbert to Banach spaces to allow the numerical approximation of linearized problems in nonlinear mechanics which leads to some global inf-sup condition on the continuous and on the discrete level for stability of the novel ultra weak formulations. The joint interest is the design of adaptive algorithms for effective mesh-design and the understanding of the weak or penalized coupling of the nonlinear stress-strain relations. A key difficulty arises from the global or localized and then numerical inversion of the nonlinear stress-strain relation in some overall Hu-Washizu-type mixed formulation. While convex energy densities allow a formal inversion of the stress-strain relation via a duality in convex analysis, it contradicts the frame indifference in continuum mechanics. The extension for polyconvex energy densities is only possible for special cases in closed form but has, in general, to be localized and approximated.

    https://www.uni-due.de/spp1748/generalized_mixed_nonlinear_fem.php

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