Projects

Projects#

The assessment is based on a project at the end of the semester. The project descriptions can be made available (please contact me).

Python
ABS Sensor

  • Maxwell’s equations in the 2d

  • Rotating subdomain (hybrid interfaces)

  • Sensor optimization

Python
Hot air balloon

  • Boussinesq approximation

  • rotationally symmetric Navier-Stokes equation

  • Coupling with heat conduction

  • Nonlinear coupled system

Python
Heated godet rollers

  • Harmonic Maxwell equations

  • axially symmetric field

  • Coupling with heat conduction

  • Temperature distribution on the surface of the rotor

Python
Mathematical image processing

  • Ginzburg-Landau functional

  • Time-dependent nonlinear boundary value problem

  • Phase separation

  • Influence of the diffusion constant

Python
Membrane

  • Eigenvalue problem

  • Eigenvalue solver for large systems

  • Bifurcation solutions of a nonlinear boundary value problem from the first eigenvalue

Python
Non-linear elasticity

  • Hyperelastic material model (Neo-Hook)

  • Comparison with linear elasticity theory

  • Geometry optimization with focus on

    • deformation

    • mass

    • stress

Python
Espresso sieve

  • Brinkman-Forchheimer equation

  • Navier-Stokes equation with extension in 2d

  • Study parameter dependence

    • porosity

    • mean particle diameter

Python
PI controller for given room temperature

  • Time-dependent heat conduction

  • Time-dependent boundary condition

  • PI controller with parabolic PDE model

  • Energy reduction

Python
Heat exchanger

  • Boussinesq approximation

  • Navier-Stokes equation

  • Coupling with heat conduction

  • Nonlinear coupled system

Python
Propagation of sound

  • Time-dependent wave equation

  • Influence of boundary conditions

  • Comparison with harmonic solution

PythonPython

Underfloor heating

  • Time-dependent heat convection, conduction

  • Coupling with Stokes equation

  • Nonlinear coupled system

  • Dimensional reduction from 3d to 2d

PythonPython

Pattern generation

  • Nonlinear time-dependent parabolic system

  • Coupled parametric equation

  • Periodic boundary condition

  • Large time-scale integration

PythonPython

Path optimization

  • Nonlinear partial differential equation

    • \(\Delta_p\)-Laplace Operator

  • Integration over gradient field

  • Adaptive mesh refinement

  • Approximation of distance function

PythonPython

Magnetic field

  • Maxwell equations for mageto static

  • H-curl discretization

  • Charged particles in magnetic field

  • Modeling of coils