Running projects

Financed by ECMath

  • 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: running
    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/
  • OT2

    Turbulence and extreme events in non-linear optics

    PD Dr. Uwe Bandelow / Dr. M. Wolfrum

    Project heads: PD Dr. Uwe Bandelow / Dr. M. Wolfrum
    Project members: Dr Shalva Amiranashvili
    Duration: -
    Status: running
    Located at: Weierstraß-Institut

    Description

    Many modern photonic devices show complex dynamical features in space and time resulting from optical nonlinearities in active, often nanostructured materials. The project is focussed specifically on high-dimensional dynamical regimes in optoelectronic systems. Such a complex spatio-temporal behavior, in which nearly all modes are excited, is characterized by the fact that, in contrast to e.g. solitons or pulsations, it cannot be reduced to a low-dimensional description in terms of classical bifurcation theory. This so-called optical turbulence can be observed both in a Hamiltonian and in a dissipative context. A mathematical treatment of the resulting multi-scale and multi-physics problems presents major challenges for modelling, numerical, and analytical investigations. A simulation of the mostly 2+1 dimensional PDE-systems requires efficient parallelization strategies, instability mechanisms can be described only in terms of amplitude equations, and multi-scale effects in complex device structures can lead to singularly perturbed dynamical problems.

    http://www.wias-berlin.de/projects/ECMath-OT2/project_OT2.jsp
  • OT3

    Adaptive finite element methods for nonlinear parameter-dependent eigenvalue problems in photonic crystals

    Prof. Dr. Volker Mehrmann

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

    Description

    Photonic crystals are periodic materials that affect the propagation of electromagnetic waves. They occur in nature (e.g. on butterfly wings), but they can also be manufactured. They possess certain properties affecting the propagation of electromagnetic waves in the visible spectrum, hence the name photonic crystals. The most interesting (and useful) property of such periodic structures is that for certain geometric and material configurations they have the so-called bandgaps, i.e., intervals of wavelengths that cannot propagate in the periodic structure. Therefore, finding materials and geometries with wide bandgaps is an active research area. Mathematically, finding such bandgaps for different configurations of materials and geometries can be modelled as a PDE eigenvalue problem with the frequency (or wavelength) of the electromagnetic field as the eigenvalue. These eigenvalue problems depend on various parameters describing the material of the structure and typically involve nonlinear functions of the searched frequency. The configuration of the periodic geometry may also be modified and can be considered a parameter. Finally, through the mathematical treatment of the PDE eigenvalue problem another parameter, the quasimomentum, is introduced in order to reduce the problem from an infinite domain to a family of problems, parametrised by the quasimomentum, on a finite domain. These are more accurately solvable. In order to solve the problem of finding a material and geometric structure with an especially wide bandgap, one needs to solve many nonlinear eigenvalue problems during each step of the optimization process. Therefore, the main goal of this project is to find efficient nonlinear eigensolvers. It is well-known that an efficient way of discretizing PDE eigenvalue problems on geometrically complicated domains is an adaptive Finite Element method (AFEM). To investigate the performance of AFEM for the described problems reliable and efficient error estimators for nonlinear parameter dependent eigenvalue problems are needed. Solving the finite dimensional nonlinear problem resulting from the AFEM discretization in general cannot be done directly, as the systems are usually large, and thus produce another error to be considered in the error analysis. Another goal in this research project is therefore to equilibrate the errors and computational work between the discretization and approximation errors of the AFEM and the errors in the solution of the resulting finite dimensional nonlinear eigenvalue problems.

    http://www3.math.tu-berlin.de/numerik/NumMat/ECMath/OT3/
  • OT5

    Reduced basis computation of highly complex geometries

    Prof. Dr. Frank Schmidt

    Project heads: Prof. Dr. Frank Schmidt
    Project members: Sven Herrmann
    Duration: -
    Status: running
    Located at: Konrad-Zuse-Zentrum für Informationstechnik Berlin

    Description

    A typical trend in nanotechnology is to extend technology from basically 2D structures to 3D structures, from simple 2D layouts to complex 3D layouts. This has mainly two reasons: (i) There are fundamental physical effects bound to 3D structures, e.g., manifold properties in reciprocal space, and (ii) economic reasons as in semiconductor industry which enforce denser packaging and ever more complex functionalities.

    The automatic optimization of nano-photonic device geometries is becoming increasingly important and, due to enhanced complexity, increasingly difficult. Typical one-way simulations become unfeasible in many-query and real-time contexts. Model reduction techniques could be a way out. Potentially they offer online speed ups in the order of magnitudes. The reported success, however, is often linked to relatively simple structured objects. Slightly more complex examples fail immediately due to geometric and mesh constrains. To show the potential in real-world examples, however, complex 3D objects including comprehensive parametrizations have to be assembled.

    The project aims to establish a link from 3D solid models obtained by CAD techniques, including full parametrizations, to reduced basis models. Establishing this critical link would facilitate systematic device geometry optimizations to be carried out using rigorous 3D electromagnetic field simulations. The main question is, how we can realize a large scale parametrization maintaining topologically equivalent meshes.

    http://www.zib.de/projects/reduced-basis-computation-highly-complex-geometries




Financed by others

  • OT-AP1

    Multi-Dimensional Modeling and Simulation of Electrically Pumped Semiconductor-Based Emitters

    PD Dr. Uwe Bandelow / Dr. Thomas Koprucki / Prof. Dr. Alexander Mielke / Prof. Dr. Frank Schmidt

    Project heads: PD Dr. Uwe Bandelow / Dr. Thomas Koprucki / Prof. Dr. Alexander Mielke / Prof. Dr. Frank Schmidt
    Project members: -
    Duration: 01.01.2008 - 31.12.2019
    Status: running
    Located at: Weierstraß-Institut / Konrad-Zuse-Zentrum für Informationstechnik Berlin

    Description

    The aim of this joint project of WIAS and ZIB is the comprehensive and self-consistent optoelectronic modeling and simulation of electrically pumped semiconductor-based light emitters with spatially complex 3D device structure and quantum dot active regions. The required models and methods for an accurate representation of devices, such as VCSELs and single photon emitters, featuring open cavities, strong interactions between optical fields and carriers, quantum effects, as well as heating will be developed and implemented, resulting in a set of tools, that will be provided for our partners in the CRC 787.

    http://www.zib.de/projects/multi-dimensional-modeling-and-simulation-vertical-cavity-surface-emitting-lasers-vcsels / http://wias-berlin.de/projects/sfb787-b4/
  • OT-AP10

    Analysis of discretization methods for nonlinear evolution equations

    Prof. Dr. Etienne Emmrich

    Project heads: Prof. Dr. Etienne Emmrich
    Project members: -
    Duration: 01.09.2012 - 31.12.2018
    Status: running
    Located at: Technische Universität Berlin

    Description

    Nonlinear evolution equations are the mathematical models for time-dependent processes in science and engineering. Relying upon the theory of monotone operators and compactness arguments, we study existence of solutions, convergence of discretization methods, and feedback control for equations of dissipative type. We focus on nonlocality in time (distributed delay, memory effects) and interpret time-delayed feedback control as a nonlocal-in-time coupling. Applications arise in soft matter and dynamics of complex fluids such as liquid crystals.

    http://www.itp.tu-berlin.de/collaborative_research_center_910/sonderforschungsbereich_910/project_groups/a_theoretical_methods/tp_a8/