Flexible Research Platform
If there is a current demand, due to certain problem areas and topics arising, additional temporary and short-term groups are set up in a flexible research platform. Currently, the following groups exist (besides the WIAS research groups):
Numerical methods for innovative semiconductor devices
- Head: Dr. Patricio Farrell
We solve nonlinear systems of partial differential equations, describing charge transport in semiconductors. Typical challenges include boundary layers, nonlinear diffusion and how to correctly preserve the physics. To efficiently solve the PDE system, we develop specialized finite volume methods on anisotropic Voronoi meshes as well as problem-dependent preconditioners. This allows us to simulate innovative semiconductor devices based on perovskites, nanowires and accurate lasers used in self-driving cars.
Modeling, Analysis, and Scaling Limits for Bulk-Interface Processes (Weierstrass group)
- Head: Dr. Marita Thomas
Research goal of the group is the development of mathematical methods for systems with bulk-interface processes for the thermodynamically consistent modeling of bulk-interface interaction with dissipative, Hamiltonian, and coupled dynamics. This includes the theory for the existence and qualitative properties of solutions, derivation and justification of interfacial processes and coupling conditions.
Quantitative analysis of stochastic and rough systems (Focus platform)
- Head: Prof. Dr. Peter K. Friz, Dr. Christian Bayer
Stochastics plays an increasingly central role in numerous scientific as well as engineering problems, both as a powerful computational tool and as a model of uncertainties inherent in complex phenomena. The aim of the work is to conduct research at the intersection and forefront of the afore-mentioned fields.
An overview of former groups of the flexible research platform may be found here » .