Research Profile and Projects
The Research Training Group (RTG) aims at a holistic and research-based education in applied mathematics and simulation based fluid dynamics. The RTG can rely on well-developed interdisciplinary collaborations between internationally renowned and well-connected senior and junior members of a PI-team from mathematics, climate research & meteorology, engineering and medical imaging. The participants share a profound overlap in scientific interests. This is manifested in many joint activities within the Lothar Collatz Centre, which provides the platform of the integrated interdisciplinary research program of the RTG.
Nine innovative, coherent PhD projects are organized as research topics in the three core areas (M) Modeling, (S) Simulation, and (O) Optimization. Based on the team's core expertise, the RTG concentrates its research on MSO-mathematics, with application focus on computational fluid dynamics.
Area M (Coordination: Prof. Gasser). Research area M collects projects that have a clear focus on modeling in specific application areas and combines the design of mathematical models with numerical algorithms for their (approximate) solution. Adequate numerical algorithms typically exploit properties of the mathematical models for gaining efficiency. On the other hand numerical representations are required to conserve the physical properties of the modeled problem to ensure validity of computational solutions. Moreover, goal-oriented strategies directly adjust the discrete algorithm to the modeled question at hand. Topics and PhD-themes in this research area address challenging mathematical research questions referring to accurate modeling and analysis of thermo-fluid dynamics (M1), hierarchical modeling (M2), and numerical modeling with adaptive discretization concepts (M3). The team gathers researchers with comprehensive and complimentary skills in the analysis, modeling, and numerical simulation of complex problems. Scientific progress in this area will be facilitated through a strong collaboration between experts on the modeling and the algorithmic components.
- M1 (Thermal Convection) - Heat Transport in thermal convection
- M2 (Solar Plant Modeling) - Model-based design of solar thermal power plants
- M3 (Adaptive Modeling) - Optimized refinement criteria for adaptive modeling of transient flows
Area S (Coordination: Prof. Le Borne). Efficient and reliable implementations of simulation processes
require a thorough understanding of techniques combining adaptive discretization & approximation
efforts together with advanced solution procedures on the one hand, and on the other hand, of
current and future high-performance computing (HPC) aspects. The projects in this research area
develop novel adaption strategies for kernel-based approximations (S1), simulation strategies for
large-scale inverse problems (S3), and develop tailored preconditioning techniques for large-scale fluid dynamic applications (S2). An efficient use of these technologies usually requires not only a mere re-editing of software parts, but necessitates re-thinking of the employed mathematical approaches and algorithms.
- S1 (Adaptive Kernels) - Adaptive kernel-based approaches for fluid flow simulations
- S2 (Preconditioning) - Preconditioners for RBF-FD discretized fluid flow problems
- S3 (Blood Flow) - Blood Flow modeling and estimation by magnetic particle imaging
Area O (Coordination: Prof. Rung). Within the DFG Scientific Priority Programs 1253 Optimization
with PDE constraints and 1962 Non-smooth and Complementarity-based Distributed Parameter
Systems: Simulation and Hierarchical Optimization significant progress towards efficiently solving
optimization problems subject to constraints involving distributed parameter systems have been
achieved. It is now timely to mathematically improve the developed techniques in the direction of
the challenging applications this RTG is tailored for. The interaction of mathematical modeling,
optimization techniques and applied scientific computing is crucial in order to achieve this goal.
The projects in research area O cover the two essential ingredients of an optimization process. On
the one hand adjusting PDE models to measured data and on the other improving designs towards
optimality based on these calibrated models. In particular, the projects aim at developing novel
mathematical concepts related to PDE constrained optimization techniques for shape design and
data-assimilation. Shape optimization examples refer to two-phase flows around free- floating ships, modeled with diffusive phase-field approaches which will include fluid-structure interaction (O2), as well as aerodynamic shape design based on Euler and Navier-Stokes equations using efficient hardware architectures (O3). Data-assimilation is devoted to meteorological applications, in particular for global ocean modeling (O1). With the composition of the research team in area O, we
combine mathematical expertise in the field of PDE constrained optimization with engineering and
geophysical competence in challenging fluid dynamic applications.
- O1 (Data Assimilation) - Continous Data Assimilation for Ocean Modeling
- O2 (Ship Optimization) - CAD-free adjoint shape optimization of floating vessels
- O3 (Shape Design) - Scalable algorithms for shape design and interface identification