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Dr. Kersten Schmidt: Research

Research Interests

  • Numerics of partial differential equations
  • hp-finite elements with hanging nodes
  • asymptotic expansion techniques
  • modeling of electromagnetics
  • modeling of photonic crystals
  • boundary element method


Viscous acoustic equations in periodically perforated chamber

with P. Joly (POEMS, INRIA Rocquencourt)

The interest in this project is to predict the acoustics in a chamber perforated with small holes which prevent to use efficiently direct discretisation methods like the FEM. Instead we derive transmission conditions on the wall for the viscous acoustic equations (perturbation of the Navier-Stokes equation), which will approximate the behaviour of the perforations. To do so we investigate a two-scale approach by surface-homogenisation and matched asymptotic expansion.


Numerical computation of electromagnetic fields in thin conducting sheets

with S. Tordeux (Université de Toulouse)

The project is focused on the numerical simulation of the interaction of low-frequency time-harmonic electromagnetic fields with thin conducting sheets, which consists of linear, isotropic materials. The goal of the project is to develop and implement a sufficient accurate, efficient, and robust numerical method that allows the prediction of the spatial variation of electromagnetic fields inside the conductors. An asymptotic expansion of the conductor thickness is investigated, which give rise to impedance transmission conditions.


Band structure calculation in photonic crystal wave-guides

with R. Kappeler (ETH Zürich)

We propose a finite element formulation for the band structure calculation for a 2D super-cell inside a infinite loss-less photonic crystal wave-guide. The formulations leads to a quadratic eigenvalue problem in the wave vector k and is applicable for dispersive dielectric media.


hp-adaptive FE discretization for time-harmonic Maxwell equations in two and three dimensions

When solving Maxwell's equations in complex geometries with dielectric media the Finite Element Method with Edge Elements is a popular procedure. The basis functions of the Edge Elements lie in the space H(curl) and fulfill the interface boundary conditions. In this project an existing C++ class library Concepts is extended to incorporate a fully hp-adaptive edge discretisation in 2D, based on quadrilaterals. This includes adaptive refinement in polynomial degree in each direction (anisotropically) and in mesh size. The code allows for independent refinement of elements since conforming as well as non-conforming meshes can be dealt with. Boundary effects can be accurately resolved at low computational cost. Future work intends to extend the current implementation to include three-dimensional edge element classes.


Simulation of very fast transients in bushings

with R. Hiptmair (ETH Zürich), J. Ostrowski (ABB Corporate Research, Baden)

With the bushing one conducts the high voltage generated in a transformator outside its casing. The bushing consists in a compact copper wire in the middle and epoxy-paper-layers with aluminium foils around. The bushing should maintain a electromagnetic compatibility (EMC) test with very fast transients (VFT). The numerical modelling of bushings includes the difficulties of extreme aspect ratios and very fast transients. We use a simulation of the longitudinal section with hp-finite elements based on anisotropic quadrilaterals with hanging nodes and an implicit time scheme.

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