Dr. Pia Domschke

Technische Universität Darmstadt
Fachbereich Mathematik
AG Numerik und Wissenschaftliches Rechnen
Dolivostr. 15
64293 Darmstadt

Raum: S4|10 114
E-Mail: domschkemathematik.tu-darmstadt.de
Tel: +49 (0)6151 16-23172
Fax: +49 (0)6151 16-23164

Current Projects

DFG SFB-Transregio 154, Teilprojekt B01: Adaptive Dynamische Multiskalenansätze

Adjoint-Based Control of Model and Discretization Errors for Gas Transport in Networked Pipelines

Recent demands for gas transmission companies are to satisfy the customers requirements at designated times. Therefore, one needs to react fast and flexibly to short-term changes in the requested quantity and quality of gas. To meet the demands, reliable mathematical models as a basis for decisions on changing the configuration of the network are needed. Realistic problems in practice necessitate the consideration of thousands of pipes which makes global optimization with high resolution impossible. We develop a strategy to automatically employ different models in different regions of the network according to actual measurements of the gas flow using adjoint techniques.

Non-Local Effects and Surface-Bound Reactions in Cancer Invasion

The ability to invade tissue and form metastases (secondary tumours) is what makes cancer so dangerous. Key biological processes occurring during invasion are the secretion of matrix degrading enzymes, cell proliferation, the loss of cell-cell adhesion on one hand and enhanced cell-matrix adhesion on the other hand as well as active migration. A better understanding of the effect that biochemical (intracellular) and cellular processes have on tissue scale rearrangement of cells and matrix may help to develop treatment strategies. Hence, the modelling and numerical simulation of cancer cell invasion is of great interest and is the subject of ongoing research. In this project, we focus on two key aspects in the modelling of cancer invasion: cell-cell and cell-matrix adhesion (tissue-level modelling) and surface-bound reactions involved in cancer invasion.

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