Research interests

My research lies in numerical analysis and scientific computing. More specifically, it can be grouped in the following four areas:

Finite volume and Scharfetter-Gummel schemes

flux-error

In order to simulate semiconductor devices, I study finite volume schemes. In particular, I solve the van Roosbroeck equations numerically via suitable generalisations of Scharfetter-Gummel schemes to non-Boltzmann (e.g. Fermi-Dirac or Gauss-Fermi) statistics. These schemes have the advantage that they fulfill properties discretely which are known to hold at a continuous level such as thermodynamic consistency, positivity and maximum principles.


Numerical methods for convection-dominated PDEs

convergence

How to obtain robust discretizations of singularly perturbed differential equations is also part of my research. In particular, I extended a version of the complete flux scheme to anisotropic grids. This scheme is provably guaranteed to converge with second order in the maximum norm.




Semiconductor device simulation

multilevel

For different 1D/2D/3D applications I simulate semiconductor devices, using the WIAS prototype ddfermi. This open source code is mostly written in C++ and can be called via a Python interface. It is designed to handle heterostructures as well as general semiconductor statistics (in particular non-Boltzmann statistics).


Radial basis functions

multilevel

During my DPhil (PhD) at the University of Oxford, I developed and analysed meshfree multilevel methods to solve PDEs. For these methods, I was able to prove convergence and stability results. My project was supervised by Prof. Holger Wendland and Dr. Kathryn Gillow. Previously, I completed a Diplom at the University of Hamburg, where I examined under the supervision of Prof. Armin Iske how radial basis functions could be used in computed tomography.