Research Group "Numerical Mathematics and Scientific Computing"

The research group contributes to the following application oriented research topics of WIAS:

Electro-reaction-diffusion model for electrochemical systems

Numerical simulation of diffusive and reactive solute transport in thin layer flow cells is used as a tool to gain improved understanding of the heterogeneous catalytic reactions taking place in fuel cell catalyst layers. The determination of rate parameters for the catalytic reactions is crucial for the modeling and quantitative investigations. [>> more]

Modeling and simulation of photoresists

One option to for semiconductor device manufacturing is optical lithography. In this process a pattern defined in a photomask is transferred into a photosensitive film (photoresist) by light. [>> more]

Modeling and simulation of semiconductor structures

Modern semiconductor devices and optoelectronic devices such as semiconductor lasers are based on semiconductor structures, which e.g. can be given by doping profiles, heterostructures or nanostructures. For the qualitative and quantitative understanding of the properties of these devices, mathematical modeling and simulation of the most relevant and, respectively, of the limiting carrier transport processes is necessary. [>> more]

Numerical methods for the simulation of population balance systems

These applications are modeled by population balance systems. Accurate and efficient numerical methods will be developed, in collaboration with partners from academics and industry, which will be in the long term the basis of optimal control methods for the considered processes. [>> more]

Static and dynamic simulation in process engineering

Static and dynamic process simulation has become an indispensable tool for design, analysis, and operation of complex plants in the process engineering industry. Here initial value problems for large-scale systems of differential and algebraic equations (DAEs) have to be solved. The simulation concept developed at WIAS is based on divide-and-conquer techniques and exploits the modular structure of the process models. The DAE system is solved with block-structured Newton-type methods. The simulation concept has been implemented in the Block Oriented Process Simulator BOP and has been successfully used in different industrial applications. [>> more]