Successfully completed projects

Financed by others

  • OT-AP2

    Direct and inverse interaction problems with unbounded interfaces between acoustic, electromagnetic and elastic waves

    Dr. Guanghui Hu

    Project heads: Dr. Guanghui Hu
    Project members: -
    Duration: 01.08.2012 - 31.07.2015
    Status: completed
    Located at: Weierstraß-Institut

    Description

    Direct and inverse interaction problems between acoustic, electromagnetic and elastic waves occur in many applications in natural sciences and engineering. The project is devoted to the investigation of scattering of time harmonic acoustic and electromagnetic waves by an unbounded elastic body in the case of periodic structures (diffraction gratings) as well as in the non-periodic case (rough surfaces). This leads to direct and inverse transmission problems between the Helmholtz (or Maxwell) equations and the Navier equation in unbounded domains, the analytical and numerical treatment of which is challenging. One objective of the project is to develop a new solvability theory (existence and uniqueness of solutions, Fredholm property) for the direct scattering problems using variational methods. In the more general and difficult case of rough interfaces, this requires the derivation of novel a priori estimates in weighted Sobolev spaces. The second goal of the project is the development and theoretical justification of efficient numerical methods for the solution of the direct and inverse interaction problems. The approximate solution of the direct problems will be based on finite element and boundary element methods, whereas for the solution of the inverse problem of reconstructing the interface from near and far field measurements of the scattered acoustic or electromagnetic field, optimization and factorization methods will be used. For both tasks, inspiration should be taken from recent results on electromagnetic and elastic diffraction gratings and rough surfaces and on interaction problems with bounded elastic obstacles.

    http://www.wias-berlin.de/projects/interaction/
  • OT-TU26

    Asymptotic analysis of the wave-propagation in realistic photonic crystal wave-guides

    Dr. Kersten Schmidt

    Project heads: Dr. Kersten Schmidt
    Project members: Dirk Klindworth / Adrien Semin
    Duration: 01.06.2014 - 31.12.2016
    Status: completed
    Located at: Technische Universität Berlin

    Description

    Photonic crystal wave-guides are devices that allow for exceptional tailoring of the properties of light propagation. Currently, the prediction of the properties relies mainly on models for infinite, perfect photonic crystal wave-guides. For photonic crystal circuits scattering matrix approaches have been proposed. In this project we study imperfect photonic crystal wave-guides and circuits of finite lengths with techniques of asymptotic expansion.

    http://www.math.tu-berlin.de/?matheon-d26
  • OT-AP5

    MODSIMCONMP - Modeling, simulation and control of multiphysics systems

    Prof. Dr. Volker Mehrmann

    Project heads: Prof. Dr. Volker Mehrmann
    Project members: -
    Duration: 01.04.2011 - 31.03.2016
    Status: completed
    Located at: Technische Universität Berlin

    Description

    The project aims at developing and analyzing a fundamentally new interdisciplinary approach for the modeling, simulation, control and optimization of multi-physics and multi-scale dynamical systems.

    The innovative feature is to generate models via a network of modularized uni-physics components, where each component incorporates a mathematical model for the dynamical behavior as well as a model for the uncertainties, arising, e.g., by modeling, discretization or finite precision computation errors.

    Based on this new modeling concept also new numerical simulation,control, and optimization techniques will be developed and incorporated, that allow a systematic adaptive error control - including the appropriate treatment of different scales, and the uncertainties - for the components as well as for the whole multi-physics model.

    The new remodeled systems will be designed such that they allow an efficient and accurate dynamical simulation with high order numerical integration techniques as well as the application of efficient methods for model reduction and open and closed loop control.

    In order to cope with the differential-algebraic and multi-scale character of the systems we plan to develop and analyze remodeling techniques for the components as well as for the whole network including the uncertainties as well as special structures of the system.

    In an interdisciplinary corporation with colleagues from engineering and computer science we plan to extend the modeling language Modelica to incorporate the new features - in particular the uncertainties and modeling errors - and to implement the complete approach as a new software platform.

    http://www3.math.tu-berlin.de/multiphysics/Description/

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