# Open Master Thesis

# Supervisors

Dr. Carmen Gräßle MPI Magdeburg, Jun-Prof. Jan Heiland FMA

# Problem statement:

The method of *Dynamic Mode Decomposition* (DMD) is able to identify a surrogate model for a nonlinear system based on time series (*snapshots*).
Typically, surrogate models are less complex than the original model equations
so that they can be used to simulate the same phenomena but in less
computation time (*speedup*) and with lower memory requirements (*compression*).
The theory of DMD is more than 100 years old. In practice, DMD has experienced strong popularity within the last 10 years, mostly due to interesting and successful application examples in flow problems.

In the context of numerical investigation of PDEs in general and flow problems in particular, the *snapshots* can be considered as approximate solutions at given time instances. Each of these approximate solutions are discrete functions which are defined on a spatial mesh. If the mesh is constant over all time instances, DMD is readily applicable.

In this master’s thesis, we will pursue the case, in which the mesh changes over time, which is intended in applications. We will develop a formulation for DMD which is independent of the spatial meshes and propose numerical realizations which exceed simple interpolation approaches.

# Requirements

For this work, knowledge or particular interests in the following fields are of advantage:

- numerics of partial differential equations and
- numerical simulation

as well as programming expertise (most suitable in `Python`

or `C++`

).

# Contact

In case of interest or request for further details, please contact

- Dr. Carmen Gräßle – [graessle@mpi-magdeburg.mpg.de](mailto: graessle@mpi-magdeburg.mpg.de)

or

- Jun.-Prof. Jan Heiland – [jan.heiland@ovgu.de](mailto: jan.heiland@ovgu.de)