Successfully completed 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: Dr. Matthias Voigt
    Duration: -
    Status: completed
    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/
  • SE2

    Electrothermal modeling of large-area OLEDs

    PD Dr. Annegret Glitzky / Prof. Dr. Alexander Mielke

    Project heads: PD Dr. Annegret Glitzky / Prof. Dr. Alexander Mielke
    Project members: Dr. Matthias Liero
    Duration: -
    Status: completed
    Located at: Weierstraß-Institut

    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.
    Click here for more information

    http://www.wias-berlin.de/projects/ECMath-SE2/index.html
  • SE3

    Stability analysis of power networks and power network models

    Prof. Dr. Christian Mehl / Prof. Dr. Volker Mehrmann / Prof. Dr. Caren Tischendorf

    Project heads: Prof. Dr. Christian Mehl / Prof. Dr. Volker Mehrmann / Prof. Dr. Caren Tischendorf
    Project members: Dr. Andreas Steinbrecher
    Duration: -
    Status: completed
    Located at: Humboldt Universität Berlin / Technische Universität Berlin

    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.

    http://www.math.hu-berlin.de/~numteam1/projects/SE3.php
  • SE4

    Mathematical modeling, analysis and novel numerical concepts for anisotropic nanostructured materials

    Dr. Christiane Kraus / Prof. Dr. Gitta Kutyniok / Prof. Dr. Barbara Wagner

    Project heads: Dr. Christiane Kraus / Prof. Dr. Gitta Kutyniok / Prof. Dr. Barbara Wagner
    Project members: Esteban Meca Álvarez / Dr. Arne Roggensack
    Duration: -
    Status: completed
    Located at: Technische Universität Berlin / Weierstraß-Institut

    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...

    http://www.wias-berlin.de/people/roggensa/se4/
  • 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
  • SE6

    Plasmonic concepts for solar fuel generation

    Prof. Dr. Rupert Klein / Prof. Dr. Frank Schmidt

    Project heads: Prof. Dr. Rupert Klein / Prof. Dr. Frank Schmidt
    Project members: Dr. Sven Burger / Dr. Martin Hammerschmidt
    Duration: -
    Status: completed
    Located at: Konrad-Zuse-Zentrum für Informationstechnik Berlin

    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.

    http://www.zib.de/projects/plasmonic-concepts-solar-fuel-generation
  • SE7

    Optimizing strategies in energy and storage markets

    PD Dr. John Schoenmakers / Prof. Dr. Vladimir Spokoiny

    Project heads: PD Dr. John Schoenmakers / Prof. Dr. Vladimir Spokoiny
    Project members: Roland Hildebrand
    Duration: -
    Status: completed
    Located at: Weierstraß-Institut

    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.

    http://www.wias-berlin.de/projects/ECMath-SE7/
  • SE8

    Stochastic methods for the analysis of lithium-ion batteries

    Prof. Dr. Wolfgang Dreyer / Prof. Dr. Peter Karl Friz

    Project heads: Prof. Dr. Wolfgang Dreyer / Prof. Dr. Peter Karl Friz
    Project members: Paul Gajewski / Dr Mario Maurelli
    Duration: -
    Status: completed
    Located at: Weierstraß-Institut

    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...

    http://www.wias-berlin.de/projects/ECMath-SE8/
  • SE9

    Optimal control of evolution Maxwell equations and low rank approximation

    Prof. Dr. Reinhold Schneider / Prof. Dr. Fredi Tröltzsch

    Project heads: Prof. Dr. Reinhold Schneider / Prof. Dr. Fredi Tröltzsch
    Project members: Benjamin Huber
    Duration: -
    Status: completed
    Located at: Technische Universität Berlin

    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.

    http://www.d-se9.de
  • SE10

    Low rank tensor recovery

    Prof. Dr. Reinhold Schneider

    Project heads: Prof. Dr. Reinhold Schneider
    Project members: Sebastian Wolf
    Duration: -
    Status: completed
    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: -
    Status: completed
    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. Goals: Extending existing approaches to MOR from the linear to the bilinear case (required for LvN-based models) Developing, implementing and testing numerical methods for the solution of large-scale generalized Sylvester and Lyapunov equations Exploring structure preservation of MOR approaches Applying MOR approaches with optimal control of open quantum systems Identifying relevant photochemical benchmark systems to test various MOR / OC approaches

    https://sites.google.com/site/ecmathse11/
  • SE12

    Fast solvers for heterogeneous saddle point problems

    Prof. Dr. Carsten Gräser

    Project heads: Prof. Dr. Carsten Gräser
    Project members: Pawan Kumar
    Duration: -
    Status: completed
    Located at: Freie Universität Berlin

    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.

    Matheon-C-SE12.php">http://numerik.mi.fu-berlin.de/wiki/Projects/Matheon-C-SE12.php
  • SE13

    Topology optimization of wind turbines under uncertainties

    Dr. Martin Eigel / PD Dr. René Henrion / Prof. Dr. Dietmar Hömberg / Prof. Dr. Reinhold Schneider

    Project heads: Dr. Martin Eigel / PD Dr. René Henrion / Prof. Dr. Dietmar Hömberg / Prof. Dr. Reinhold Schneider
    Project members: Dr. Johannes Neumann / Dr. Thomas Petzold
    Duration: -
    Status: completed
    Located at: Technische Universität Berlin / Weierstraß-Institut

    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.

    http://www.wias-berlin.de/projects/ECMath-SE13/
  • SE14

    Error-aware analysis of multi-scale reactivity models for photochemical surface reactions

    Dr. Sebastian Matera

    Project heads: Dr. Sebastian Matera
    Project members: Sandra Doepking
    Duration: -
    Status: completed
    Located at: Freie Universität Berlin

    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. The purpose of this project is to address the aforementioned problems by development of tools for local and global sensitivity analyses. These are applied to models from classical catalysis, but also to models for photo-catalytic processes.

    http://www.mi.fu-berlin.de/math/groups/ag-photo/forschung/EC-Math-SE14/index.html
  • SE15

    Optimal Network Sensor Placement for Energy Efficiency

    Dr. Carlos Rautenberg

    Project heads: Dr. Carlos Rautenberg
    Project members: -
    Duration: -
    Status: completed
    Located at: Humboldt Universität Berlin

    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.

    http://www2.mathematik.hu-berlin.de/~rautenca/SE15.htm




Financed by others

  • 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: completed
    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
  • SE-AP15

    Structure Formation in Thin Liquid-Liquid Films

    Dr. Dirk Peschka / Prof. Dr. Barbara Wagner

    Project heads: Dr. Dirk Peschka / Prof. Dr. Barbara Wagner
    Project members: -
    Duration: 01.04.2011 - 30.09.2017
    Status: completed
    Located at: Weierstraß-Institut

    Description

    The main topic of this tandem proposal is the direct comparison of results from mathematical modeling, analysis and experimental investigations of rupture,dewetting dynamics and equilibrium patterns of a thin liquid-liquid system. The experimental system uses a PS (polystyrene)/ PMMA (polymethylmethacrylate) thin bilayer of a few hundred nanometer, whose liquid properties can be tuned from Newtonian to visoelastic rheological flow behavior by varying the length of the polymer chains. On these small scales, apart from capillary forces and viscous dissipation, intermolecular forces will play an important role in the dynamics and morphology of the interfaces. The mathematical analysis and numerical simulation of adequate thin film models that will be derived from the underlying fluid mechanical equations, will be used through direct comparisons with experiments. Thus, we aim at clarifying also fundamental properties, such as equilibrium contact angles, singularity formation or dewetting rates. This shall form the basis for more complex situations involving evaporation, surfactant monolayers, and slippage, to yield the understanding crucial for many important nanofluidic problems in nature and technology ranging from rupture of the human tear film to the interface dynamics of donor/acceptor polymer solutions used in organic solar cells.

    http://www.dfg-spp1506.de/project-seemann-wagner-peschka
  • SE-AP1

    Numerical algorithms for the simulation of finite plasticity with microstructures

    Prof. Dr. Carsten Carstensen

    Project heads: Prof. Dr. Carsten Carstensen
    Project members: -
    Duration: 01.10.2010 - 31.10.2015
    Status: completed
    Located at: Humboldt Universität Berlin

    Description

    The occurrence of microstructures in solid mechanics and, in particular, in finite plasticity can be attributed to a loss of the convexity of the underlying energy potentials. While the material deforms macroscopically, structures in the form of shear bands, cracks or lami- nates arise on microscopic scales. Common to these examples is that their macroscopic simulations have to be based on the quasiconvexification of the energy functional.The projects within the research group either concern the modelling or the simulation. In contrast, the object of this project is the justification of computer simulations with an analysis of discretisation and design of converging adaptive mesh-refining algorithms. The mathematical justification concerns numerical simulations on the microscopic scale (a), on the macroscopic scale (b), for time-evolving microstructure (c).In the first funding period, an efficient algorithm on the numerical relaxation in single- crystal finite plasticity has been established in (a). The degenerate nature of the (quasi-) convexified variational model in (b) required novel stabilisation techniques on adapted finite element grids. The influence of the perturbation of the computed macroscopic energy density W is examined in the combination of (a) and (b). The main result in the analysis of perturbed minimisation problems guarantees convergence of an adaptive mesh-refining algorithm for asymptotically exact computation of energies.The project continues to investigate the convergence of numerical simulations of rate- independent evolution problems for the full time-space discretisation (c). The second funding period shall investigate the improvements of nonstandard finite element methods in (a), (b), and (c).

    http://gepris.dfg.de/gepris/projekt/35736987
  • SE-AP21

    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: completed
    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-AP4

    Perspectives for rechargeable Mg/air batteries

    Dr. Jürgen Fuhrmann

    Project heads: Dr. Jürgen Fuhrmann
    Project members: Dr. Alexander Linke
    Duration: 01.06.2013 - 30.11.2016
    Status: completed
    Located at: Weierstraß-Institut

    Description

    The project aims at the development of macroscopic models for coupled flow and reaction processes in magnesium air batteries and in experimental electochemical cells to investigate its components. On this basis numerical simulation tools are developed to run calculations that support the experiments performed within the joint research project. The development of models and the simulations shall facilitate a deeper understanding of subprocesses and their interrelationship.

    http://www.wias-berlin.de/projects/mgair/index.jsp?lang=1
  • 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
  • SE-AP10

    Analysis of multiscale systems driven by functionals

    Prof. Dr. Alexander Mielke

    Project heads: Prof. Dr. Alexander Mielke
    Project members: -
    Duration: 01.03.2011 - 31.03.2016
    Status: completed
    Located at: Weierstraß-Institut

    Description

    Many complex phenomena in the sciences are described by nonlinear partial differential equations, the solutions of which exhibit oscillations and concentration effects on multiple temporal or spatial scales. To understand the interplay of effects on different scales, it is central to determine those quantities on the microscale that are needed for the correct description of the macroscopic evolution. Our aim is to develop a mathematical framework for modeling and analyzing systems with multiple scales. In particular, we want to derive new effective equations on the macroscale that fully take into account the effects on the microscale. This will include Hamiltonian dynamics as well as different types of dissipation like gradient flows or rate-independent dynamics. The choice of models will be guided by specific applications in
    • material modeling (e.g., thermoplasticity, pattern formation, porous media) and
    • optoelectronics (drift-diffusion equations, pulse interaction, Maxwell-Bloch systems).

    The research will address mathematically fundamental issues like existence and stability of solutions but will be mainly devoted to the modeling of multiscale phenomena in evolution systems. We will focus on systems with geometric structures, where the dynamics is driven by functionals. Thus, we can go much beyond the classical theory of homogenization and singular perturbations. The novel features of our approach to multiscale problems are
    • the combination of different dynamical effects in one framework,
    • the use of geometric and metric structures for partial differential equations,
    • the exploitation of Gamma-convergence for evolution systems driven by functionals.


    http://www.wias-berlin.de/projects/erc-adg/
  • SE-AP13

    Two-scale convergence in spaces with random measures applied to plasticity

    Sergiy Nesenenko

    Project heads: Sergiy Nesenenko
    Project members: -
    Duration: 01.11.2015 - 31.10.2016
    Status: completed
    Located at: Technische Universität Berlin

    Description

    Die Erforschung und Herstellung von neuen Werkstoffen basiert stark auf der Entwicklung von adäquaten Modellen zur Beschreibung des makroskopischen Verhalten von Materialien mit Mikrostruktur. In diesen Modellen müssen die Informationen aus einer Mikroskala über die hier vorhandenen Verbundstrukturen und Werkstoffmechanismen, die das Material- verhalten auf einer Makroskala bestimmen, inkorporiert werden. Experimentell ist es gut nachgewiesen, dass die Behinderung der Versetzungsbewegung durch verschiedene Mikro-Legierungselemente, andere Versetzungen oder durch Korngrenzen zu Aushärtungserscheinungen, die auf dem Makroniveau beobachtet werden können, führt. Die Keimbildung und die Vermehrung von Leerstellen führen zur Entwicklung von Mikrorissen entlang von Korngrenzen und weiter bis zum Versagen oder Bruch des Materials.Eine direkte Simulation von Modellen mit mehreren Skalen ist in der Regel aufgrund der Notwendigkeit, ein sehr feines Netz zu verwenden, um die Skaleneffekte zu erfassen, sogar auf modernen Rechnern numerisch sehr aufwendig. Für Werkstoffe, die eine periodische/stochastische Mikrostruktur besitzen, werden daher zur Entwicklung von effizienten numerischen Algorithmen verschiedene Homogenisierung-Methoden eingesetzt. Diese Methoden ermöglichen den mathematisch rigorosen Übergang von einer mikroskopischen zu einer makroskopischen Beschreibung des Werkstoffverhaltens. In dieser Arbeit muss die mathematisch rigorose Beschreibung der makroskopischen Evolution der elasto/visko-plastischen Materialien mit stochastisch verteilten oder geometrisch periodischen Verbundstrukturen unterschiedlicher Geometrie während der Deformation in den Sobolev-Räumen mit Maßen hergeleitet werden. Untersucht werden muss auch die Abhäangigkeit der makroskopischen Eigenschaften der mikro-strukturierten Materialien von der Form der konstituierenden Microinklusionen, von ihrer Konzentration, von ihrer geometrischen Anordnung und von den Materialparametern ihrer Bestandteile.

  • SE-AP17

    Modellierungskriterien für eine stabile Co-Simulation gekoppelter PDAE-Systeme

    Prof. Dr. Caren Tischendorf

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

    Description

    Eine zunehmend feinere Modellierung im Bereich der Elektronik und Mechanik berücksichtigt auch räumlich verteilte Effekte unter der Einbindung partieller Differentialgleichungen für bestimmte Teilkomponenten. Nach Ortsdiskretisierung erhält man für jede Teilkomponente DAEs von hoher Dimension. Zudem kommen je nach Modellkomponente verschiedene Ortsdiskretisierungen in Form von Simulationskomponenten zum Einsatz.

    Der neue FMI-Standard [4] ermöglicht eine Co-Simulation von beliebig gekoppelten DAE-Systemen. Je nach Formulierung der Kopplung kann dies zu erheblichen Instabilitäten bei der numerischen Integration führen [2,3]. In [1] wurden notwendige und hinreichende Kriterien für eine stabile Integration gekoppelter Index-1-Systeme entwickelt. Hierbei spielt die Formulierung der Kopplung eine entscheidende Rolle. In diesem Projekt sollen die in [1] erzielten Ergebnisse auf strukturierte Systeme vom Index 2 ausgedehnt werden, da diese trotz leichter Instabilität in der Praxis erfolgreich für Simulationen der Teilsysteme genutzt werden (siehe z. B. Netzwerkgleichungen für elektronische Schaltungen und GGL-Formulierungen mechanischer Mehrkörpersysteme). Hinsichtlich der Strukturen stehen insbesondere Hessenberg-Systeme und Systemgleichungen für elektronische Netzwerke im Fokus, um die Ergebnisse auf die Benchmark-Systeme der Industriepartner anwenden zu können. In Zusammenarbeit mit TP1 sollen die in AP1.1 modellreduzierten nichtlinearen DAE-Systeme dahingehend analysiert und gegebenenfalls die Modellreduktionstechniken so adaptiert werden, dass eine stabile Co-Simulation mittels dynamischer Iteration bei Realisierung der entwickelten Kopplungsbedingungen möglich wird.

    Darüber hinausgehend sollen formale mathematische Strukturen für allgemeine Teilsysteme und ihre Kopplung erarbeitet werden, die eine stabile gekoppelte Simulation ermöglichen. Basis hierfür sind einerseits die strukturellen Untersuchungen im Bereich elektronischer Schaltungen für gesteuerte Quellen (siehe [2]) und andererseits die Erfahrungen im Bereich der properen Formulierung von DAE-Systemen für eine stabilitätserhaltende numerische Integration [5,6].

    Das Arbeitsprogramm gliedert sich in folgende Schritte:

    Arbeitspaket 2.1: Stabilitätsanalyse für strukturierte (P)DAE-Systeme mit Teilkomponenten vom Index 1 und 2. Zu Beginn sollen die gekoppelten DAE-Systeme (auch ortsdiskretisierte PDAEs) in Hessenberg- oder Netzwerkform auf ihre Stabilitätseigenschaften untersucht werden. Diese Ergebnisse bilden die Grundlage für die weiteren Untersuchungen in AP 2.2 zur Erhaltung dieser Stabilitätseigenschaften bei einer Simulation mittels dynamischer Iteration der Teilsysteme. Zusätzlich sollen Stabilisierungstechniken für die modulare Zeitintegration gekoppelter Systeme entwickelt und getestet werden, die auf den mit FMI for Model Exchange and Co-Simulation v2.0 neu geschaffenen Möglichkeiten aufbauen (Jacobimatrizen der rechten Seiten und der Ausgangsgleichungen).

    Arbeitspaket 2.2: Untersuchung verschiedener Kopplungsformulierungen auf das Stabilitätsverhalten einer dynamischen Iteration. Die bereits bekannten Stabilitätsbedingungen für die dynamische Iteration gekoppelter DAE-Index-1-Systeme in semiexpliziter Form sollen zunächst auf quasilineare DAEs in Netzwerk-Form erweitert werden. Daran anschließend sollen hinreichende Bedingungen für eine stabile Kopplung mit Index-2-Teilsystemen in Hessenberg- und Netzwerk-Form entwickelt werden. In Zusammenarbeit mit TP3 soll untersucht werden, unter welchen Verfahrensbeschränkungen die entwickelten Kopplungsbdingungen auch Stabilität bei Nutzung der in AP3.1 untersuchten Multirate-Ansätze garantieren.

    Arbeitspaket 2.3: Entwicklung mathematischer Modellkriterien für eine stabile Co-Simulation von (P)DAE-Modellen. Schließlich sollen auf der Basis der Erkenntnisse von AP 2.2 für gekoppelte Systeme mit Komponenten in Hessenberg- oder Netzwerk-Form mathematische Modellkriterien für allgemeine (P)DAE-Systeme entwickelt werden, die eine stabile dynamische Iteration ermöglichen. Im Fokus stehen hierbei die in TP1 entwickelten modellreduzierten DAE-Systeme von ortsdiskretisierten PDAEs der gekoppelten elektromagnetischen Feld- und Schaltungssimulation.

    Literatur
    • [1] M. Arnold and M. Günther. Preconditioned dynamic iteration for coupled differential-algebraic systems. BIT, 41:1-25, 2001.
    • [2] D. Estévez Schwarz and C. Tischendorf. Structural analysis for electric circuits and consequences for MNA. Internat. J. Circuit Theory Appl., 28:131-162, 2000.
    • [3] D. Estévez Schwarz and C. Tischendorf. Mathematical problems in circuit simulation. Math. Comput. Model. Dyn. Syst., 7:215-223, 2001.
    • [4] FMI. The Functional Mockup Interface. https://www.fmi-standard.org/.
    • [5] I. Higueras, R. März, and C. Tischendorf. Stability preserving integration of index-1 DAEs. Appl. Numer. Math., 45:175-200, 2003.
    • [6] I. Higueras, R. März, and C. Tischendorf. Stability preserving integration of index-2 DAEs. Appl. Numer. Math., 45:201-229, 2003.


    http://scwww.math.uni-augsburg.de/projects/kosmos/TP2.htm
  • SE-AP18

    nanoCOPS - Nanoelectronic coupled problems solutions

    Prof. Dr. Caren Tischendorf

    Project heads: Prof. Dr. Caren Tischendorf
    Project members: -
    Duration: 01.11.2013 - 31.10.2016
    Status: completed
    Located at: Humboldt Universität Berlin

    Description

    The fp7-nanoCOPS project addresses the simulation of
    • Power-MOS devices, with applications in energy harvesting, that involve couplings between electromagnetics (EM), heat, and stress, and
    • RF-circuitries in wireless communication, which involves EM-circuit-heat coupling and multirate behaviour, together with analogue-digital signals.

    The research and development within fp7-nanoCOPS aims to
    • create efficient and robust simulation techniques for strongly coupled systems, that exploit the different dynamics of sub-systems and that allow designers to predict reliability and ageing
    • include a variability capability such that robust design and optimization, worst case analysis, and yield estimation with tiny failures are possible (including large deviations like 6-sigma)
    • reduce the complexity of the sub-systems while ensuring that the parameters can still be varied and that the reduced models offer higher abstraction models that are efficient to simulate


    http://fp7-nanocops.eu/
  • SE-AP19

    2D and 3D simulations of the particular thin-film solar-cell based on CuInS2-chalcopyrite

    Dr. Reiner Nürnberg

    Project heads: Dr. Reiner Nürnberg
    Project members: -
    Duration: 01.01.2010 - 31.12.2014
    Status: completed
    Located at: Weierstraß-Institut

  • SE-TU37

    Shape/Topology optimization methods for inverse problems

    Dr. Antoine Laurain

    Project heads: Dr. Antoine Laurain
    Project members: Houcine Meftahi
    Duration: 01.05.2012 - 30.04.2015
    Status: completed
    Located at: Technische Universität Berlin