Pia Domschke

Dr. Pia Domschke

Numerics of partial differential equations
Athene Young Investigator

Dolivostraße 15
64293 Darmstadt

Office: S4|10 114

+49 6151 16-23172
+49 6151 16-23164

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Working areas

  • Mathematical modelling and simulation of biological processes, escpecially in the field of cancer invasion
  • Adaptive simulation and optimal control of transport processes on networks
  • Plätzchen backen mit Gauß (a lecture for high school students within the series Math on Demand)

Current Projects

Athene Young Investigator (2019-2022)
Mathematical Modelling and Simulation of Cancer Invasion: Investigating the Role of Molecular-Binding Processes and Adhesion

DFG CRC-Transregio 154, Subproject B01: Adaptive Dynamical Multiscale Methods

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.