Since the end of 2020, Dr. Benjamin Unger is a junior research group leader in SimTech and conducts research in the field of dynamical systems. Together with Dr. Robert Altmann from the University of Augsburg, he has successfully acquired a first DFG project.
“This is the first time I have submitted a proposal to the DFG and I’m very happy that the DFG decided to fund our project. The positive feedback enables us to bring our research idea to the next level, and at the same time, helps me to strengthen my new research group at SimTech”, underlines Benjamin Unger.
Entitled "Decoupling integration schemes of higher order for poroelastic networks", the project will focus on the development of an efficient time integration of poroelastic networks. Poroelastic equations play a central role in numerous fields of application such as geomechanics or biomedicine. For example, when modeling the deformation of brain tissue, several pressure variables are needed,l which leads to a multiple-network poroelastic model. The corresponding model is described by a coupled system of elliptic-parabolic differential equations, which is very computationally intensive, especially in the three-dimensional case. The direct application of standard methods therefore constitutes a major challenge even for modern computers.
The stated goal is therefore to develop highly efficient higher-order semi-explicit time integration methods that combine the simplicity of monolithic approaches with the speed of iterative methods that decouple the problem into the elliptic and parabolic parts. The basis for the project is the joint publication with Dr. Roland Maier (Chalmers University) Semi-explicit discretization schemes for weakly coupled elliptic-parabolic problems (Mathematics of Computations, 90:1089-1118 (2021)), in which both developed a first-order semi-explicit method and proved its convergence. For the convergence proof, a new proof technique was developed that relates the convergence of the time discretization to the asymptotic stability of a time-delayed equation. Besides the development and analysis of the new time integration methods, an additional focus is on the further development of this proof technique and the resulting results.
The project has a duration of 36 months. In a next step, a research associate (m/f/d) is now to be found.