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Since 2019, Matheon's application-oriented mathematical research activities are being continued in the framework of the Cluster of Excellence MATH+
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Running projects

Financed by ECMath

  • SE17

    Stochastic methods for the analysis of lithium-ion batteries

    Prof.Dr. Jean-Dominique Deuschel / Prof. Dr. Peter Karl Friz / Dr. Clemens Guhlke / Dr. Manuel Landstorfer

    Project heads: Prof.Dr. Jean-Dominique Deuschel / Prof. Dr. Peter Karl Friz / Dr. Clemens Guhlke / Dr. Manuel Landstorfer
    Project members: Dr. Michelle Coghi
    Duration: 01.06.2017 - 31.12.2019
    Status: running
    Located at: Technische Universität Berlin / Weierstraß-Institut


    Currently lithium-ion batteries are the most promising storage devices to store and convert chemical energy into electrical energy. An important class of modern lithium batteries contain electrodes that consist of many nano-particles. During the charging process of a battery, lithium is reversibly stored in the ensemble of the nano-particles and the particles undergo a phase transition from a Li-rich to a Li-poor phase. For this type of batteries a successful mathematical model was developed in the previous ECMath project SE8, based on a stochastic mean field interacting particle system. The new project focuses on modeling, analysis and simulations of extreme conditions in battery operation like fast charging, mostly full/empty discharge states, mechanical stresses within the electrode. The aim of the project is to achieve deeper understanding of the behavior of lithium-ion batteries in extreme conditions.
  • SE23

    Multilevel adaptive sparse grids for parametric stochastic simulation models of charge transport

    Dr. Sebastian Matera

    Project heads: Dr. Sebastian Matera
    Project members: Sandra Döpking
    Duration: 01.06.2017 - 31.12.2019
    Status: running
    Located at: Freie Universität Berlin


    Many computational models are stochastic and the model output needs require some sort of sampling. Besides this intrinsic stochasticity, the models usually depend on a number of uncertain parameters. We develop a multi-level adaptive sparse grid strategy to address this parametric uncertainty, where the sampling effort is adjusted to the level of the sparse grid. This methodology is applied to stochastic simulation models of charge transport, as they appear in photovoltaics and photocatalysis.

Financed by others

  • SE-AP2

    Pattern formation in systems with multiple scales

    Prof. Dr. Alexander Mielke

    Project heads: Prof. Dr. Alexander Mielke
    Project members: -
    Duration: 01.01.2011 - 31.12.2022
    Status: running
    Located at: Technische Universität Berlin


    Pattern formation in nonlinear partial differential equations depends on nontrivial interactions between different internal length scales and nonlinearities of the system as well as on the size and geometry of the underlying domain. The challenge is to understand how effects on the small scales generate effective pattern formation on the larger scales. Using well-chosen model problems reflecting the focus applications of the CRC, we will investigate the mathematical foundations of the derivation of effective models for pattern formation in multiscale problems. Controls for the effective models will be used to construct controls for the original system.
  • SE-AP8

    Entwicklung eines reduzierten Modells eines Pulsed Detonation Combustors

    Prof. Dr. Volker Mehrmann

    Project heads: Prof. Dr. Volker Mehrmann
    Project members: -
    Duration: 01.07.2012 - 30.06.2020
    Status: running
    Located at: Technische Universität Berlin


    In this project a model reduction of reactive flows is developed. Model reduction aims to replace complex, high-dimensional models by models of much smaller dimension. Goal of this project is to improve the existing techniques for systems where transport phenomena are dominant. To this end an appropriate error estimator is developed and combined with a model reduction. The small model can then be adaptively improved by adding physically motivated ansatz-functions. By this approach a low order model of a pulsed combustion is derived. This is used for control and design of a pulsed detonation combustor.

    The reduced order models shall not only describe the process of the combustion but also show the changes due to specific manipulation. The controllability in the context of mathematical fluid dynamics is determined via adjoint equations. For this the adjoint equations for reactive flows have to be differentiated and implemented.

    The reduced models are then used to design the combustor and to control the combustion process.
  • 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 - 30.11.2019
    Status: running
    Located at: Humboldt Universität Berlin


    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.
  • SE-AP20

    Analysis, numerical solution and control of delay differential-algebraic equations

    Prof. Dr. Volker Mehrmann

    Project heads: Prof. Dr. Volker Mehrmann
    Project members: -
    Duration: 01.01.2011 - 31.12.2022
    Status: running
    Located at: Technische Universität Berlin


    Delay differential-algebraic equations (DDAEs) arise in a variety of applications including flow control, biological systems and electronic networks. We will study existence and uniqueness as well as the development of numerical methods for general nonlinear DDAEs. For this, regularization techniques need to be performed that prepare the DDAE for numerical simulation and control. We will derive such techniques for DDAEs on the basis of a combination of time-differentiations and time-shifts, in particular for systems with multiple delays. We also plan to extend the spectral stability theory, i.e. the concepts of Lyapunov, Bohl and Sacker-Sell spectra, to DDAEs. We will also develop numerical methods for the computation of these spectra using semi-explicit integration methods. Another goal is to study the solution of algebraically constrained partial delay-differential equations arising in flow control and to derive discretization as well as optimal control methods in space and time.