Mathematical Methods6 Videos

MM04–Completely Positive Trace Preserving Methods for the Lindblad Equation

Riesch M., Pikl A., Jirauschek C.

The Lindblad master equation is a valuable tool in quantum mechanics, which describes the dynamics of open systems. In the scope of our research, it is combined with the one-dimensional Maxwell’s equations to form the generalized Maxwell-Bloch equations. Since analytical solutions are not available in the general case, numerical methods have to be employed to […]

MM03–Comparison of Scharfetter-Gummel Schemes for (Non-)Degenerate Semiconductor Device Simulation

Abdel D., Fuhrmann J., Farrell P.

We consider Voronoi finite volume schemes for the discretization of the van Roosbroeck system and pay particular attention to the choice of flux approximations. The classical Scharfetter-Gummel scheme yields a thermodynamically consistent numerical flux, but cannot be used for general charge carrier statistics.We compare and analyze aspects of two state-of-the-art modified Scharfetter-Gummel schemes to simulate […]

MM02–Connecting numerical simulation and machine learning: How to bridge the gap between theory and reality?

Piprek J.

Machine learning and numerical simulation represent opposite approaches to computational analysis of the real world, inductive vs. deductive. However, both methods suffer from various uncertainties and even their combination often fails to link theory and reality. This paper presents a critical review of such connections and proposes improvement options for optoelectronic devices.

MM01–Green’s function integral equation methods for modeling of optical devices

Søndergaard T.

Green’s function integral equation methods are presented that can be applied for modeling of optical devices in cases where the problem can be formulated as a scattering problem. The methods are applied to study in three dimensions the effect of a cylindrical micro-lens on radiation emitted from a THz photoconductive antenna, and for studying the […]

MM06–Tight binding parameterization through particle swarm optimization algorithm

Di Vito A., Pecchia A., Auf der Maur M., Di Carlo A.

The tight binding (TB) approach represents a good trade-off between accuracy and computational burden. For this reason, it is widely used for device simulations. However, a proper description of a physical system by means of TB requires an accurate parameterization of the Hamiltonian matrix elements (HME), that is usually done by fitting over suitable properties […]

MM05–Project Skeletons for Scientific Software

Riesch M., Haider M., Jirauschek C.

Although research relies heavily on software packages such as mathematical libraries or data analysis tools, efforts to provide high-quality scientific software are hardly rewarded. As a possible way out of this dilemma, project skeletons can be employed to accelerate software development while ensuring code quality. In this work, we review existing project skeletons and present […]