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TU Berlin

Inhalt des Dokuments

Forschung

Forschungsinteressen

  • Numerik partieller Differentialgleichungen
  • hp-Finite Elemente mit hängenden Knoten
  • Asymptotische Entwicklungen
  • Modellierung von Elektromagnetismus
  • Modellierung von Photonischen Kristallen und Halbleitern
  • Randelementemethode

Projekte

MATHEON-Projekt D26 Asymptotic Analysis of the Wave-Propagation in Realistic Photonic Crystal Wave-Guides

Photonic crystal wave-guides are devices that allow for tailoring exceptional 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.

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MATHEON-Projekt B-MI2 Optimized noise reduction in transportation and interior spaces

The reduction of the excited noise of transportation, especially in gas turbines of airplanes and ships or mufflers of cars, is currently of major public and industrial interest. We aim to describe the effective absorption properties of sound absorbing resonator structures and perforated walls. As the governing equations and structures possess several scales, we study the problems asymptotically. In this project we derive and study approximative boundary and transmission conditions, that take into account the physical phenomena on the small scales inside the holes of the perforated absorber and the boundary layers in their neighbourhood.

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Einstein-Projekt Asymptotic analysis of finite periodic thin layers ending with corner singularities

It is known in the engineering that materials with small multiple co-axial wires, or multi-perforated materials helps to reduce the sound propagating inside the media containing. The difficulty lies in a high density of small holes which makes a direct numerical simulation impossible because the equations to be solved would be too large. However the small holes have a significant influence on the outgoing noise. In this project we study a thin periodic multi-perforated layer ending with two corners singularities with techniques of asymptotic expansion.

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

The design and manufacturing of new engineering materials relies heavily on the development of adequate models for the description of the macroscopic behavior of materials with microstructure. These models have to incorporate the information from a microscale on the presence of voids or particle/fiber-reinforced structures in materials and on the mechanisms that determine the behavior under consideration. Experimentally it is well demonstrated that the hindering of the dislocation motion by other dislocations, reinforced micro-particles/fibers or by grain boundaries in alloys cause the hardening effects, which are observed at the structural scale. The nucleation and the growth of grain boundary cavities lead to microcracks developing along a gain boundary and further to failure or rupture of the material.

The primal goal of this project is to derive the mathematically rigorous description of the macroscopic evolution of elasto/visco-plastic materials, which are periodically/randomly voided or reinforced by micro-inclusions of different geometry, during the deformation in Sobolev spaces with measures. Dependence of the macroscopic properties of porous or micro-structured materials on the shape of voids or constituent micro-inclusions, on their concentration, on their geometric arrangement and on the material parameters of their constituents must be investigated as well.

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TU Berlin
Institut für Mathematik
Sekr. MA 6-4
Straße des 17. Juni 136
D-10623 Berlin

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Mathematikgebäude (MA)
3. Obergeschoss
Räume 363, 365 u. 379