Scientific Computing Lab

Simulation of a frontal crash — Visualisation of a simulated frontal crash

Modelling of a biological process: comparison of measurement data, classical (memory-free) and fractional (with memory) mathematic model — For the example of a biological process, a comparison of measurement data on the one hand and classical memory-free model or fractional model with memory, respectively, on the other hand demonstrates the significantly better coincidence of the latter.

Representation of the creep behaviour of viscoelastic materials like polymers with fractional models replicates the real behaviour determined by experiment considerably more precisely than descriptions — Representation of the creep module over time for a creep experiment with a polymer material: Comparison between experiment, classical model and fractional model (image source: M. Hinze, University of Stuttgart)

The Scientific Computing Lab bridges the boundaries between mathematics, computer science and the natural and engineering sciences. Its tasks include
•   the description of processes in science and engineering with the help of mathematical methods,
•   the mathematical analysis of the model equations arising in this process,
•   the development of numerical methods for the approximate solution of these equations,
•   the efficient implementation of these algorithms on computer systems of different performance classes, from embedded systems and “simple” desktop computers up to current high performance computers,
•   the effective simulation of the processes mentioned above using these software systems, and
•   the evaluation and interpretation of the simulation results.

Currently, the research activities focus on the analysis of the mechanical properties of viscoelastic materials, a main characteristic of which is the presence of memory effects that require the use of mathematical models involving differential operators of fractional (i.e., non-integer) order. Further projects deal with the efficient discretization of geometric objects for finite element simulations, mainly for applications related to technical computations in the vehicle development process of the automotive industry (crash simulations, life cycle analysis, passenger comfort, etc.).