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M.Sc. Bianca Kretz

M.Sc. Bianca Kretz




EN-B 210


M.Sc. Bianca Kretz

Geomathematics Group


University of Siegen

Walter-Flex-Str. 3

57068 Siegen


from abroad:

+49 271 740 3509

from Germany:

0271 740 3509


from abroad:

+49 271 74013509

from Germany:

0271 74013509


kretz (a) mathematik.uni-siegen.de (please replace ' (a) ' by '@').

Betreute Lehrveranstaltungen

  • Analysis I +II +III
  • Höhere Mathematik I + II
  • Gewöhnliche Differentialgleichungen
  • Partielle Differentialgleichungen
  • Konstruktive Approximation
  • Geomathematik
  • Mathematische Modelle der Erdbebenforschung

Project description:

My PhD-thesis is concerned with multiscale modelling in poroelasticity.

Poroelasticity is part of the material research discipline and describes the interaction between a solid material and a fluid. This is done in our case by a set of partial differential equations, which were first established by Biot.

There are many applications one can think of for poroelasticity – our focus is geothermal research. Here the aim is to find an aquifer to use the hot water in it for electricity and heat generation. Mining this hot water has an effect on the surrounding material and this effect can be modelled by poroelasticity.

Multiscale modelling was used for other problems and equations before, namely the Laplace (with the aspect of decorrelation of potential and density data), the Helmholtz and the d’Alembert equation. Furthermore it was also used for the Cauchy-Navier equation as a tensor-valued ansatz.

Our aim is to apply this multiscale modelling in poroelasticity. For this purpose, we need the fundamental solution tensor of the partial differential equations and regularize their singularity (like it is done in the Laplace and the other cases mentioned above) to obtain scaling functions.

These scaling functions are convolved with given displacement and pore pressure data to decompose these data. This gives us the opportunity to see underlying structures for different scales that cannot be seen in the whole data. We get more detailed structures and information of our data.

We can show that the scaling functions fulfill the property of an approximate identity. Furthermore, numerical results will show the decomposition.



Talks and Conferences:

  • 05.2020: Virtual Conference "EGU2020: Sharing Geosciences Online", Poroelastic aspects in geothermics.
  • 04.2019: Conference "European Geosciences Union General Assembly 2019" in Vienna, Decorrelation of poroelastic data.
  • 03.2019: "SIAM Conference on Mathematical & Computational Issues in the Geosciences (GS19)" in Houston, Approximation and Wavelet-based Modelling in Poroelasticity.
  • 05.2018: Workshop "Inverse Problems and Approximation Techniques in Planetary Sciences" in Sophia Antipolis, Multicale Modelling in Poroelasticity.
  • 04.2018: Conference "European Geosciences Union General Assembly 2018" in Vienna, Study on parameter choice methods for the RFMP with respect to downward continuation.
  • 09.2017: Workshop "Geomathematics Meets Medical Imaging" in Speyer, Study on parameter choice methods for the RFMP with respect to downward continuation.