Juliane Entzian

Adaptive Kernel-Based Approaches for Fluid Flow Simulations

Kernel-based approximation methods are well-established tools in scattered data approximation. Radial kernels (i.e., “radial basis functions”) have proven a good performance in relevant applications, in particular in approximation quality and computational efficiency. Yet it remains to improve numerical stability and flexibility of radial kernels. Concerning their numerical stability, we will profit from the work of the RTG’s associated PhD student Kristof Albrecht, where problem-adapted precondtioners for kernel matrices are designed. As regards their flexibility, we will further improve adaptive approximation schemes, where we will work on the design of novel anisotropic kernels in particular. We expect that the new kernels will help to further improve the performance of kernel-based fluid flow simulation methods. Primarily, our target application is Magnetic Particle Imaging (MPI), where we will closely collaborate with the RTG’s project S3. MPI is a very recent concept of medical imaging, where a tracer is injected in a body and one asserts to reconstruct the time-dependent concentration of the tracer for clinical diagnosis.

Advisor: Prof. Dr. Armin Iske

Co-Advisor: Jun.-Prof. Dr. Christina Brandt

25.-26.09.2023

Two-day Workshop on Approximation Theory, Giessen (GER): "Product Kernels: An Efficient and Flexible Tool for High-Dimensional Interpolation"

06.-09.09.2021

Workshop on Modeling, Simulation & Optimisation of Fluid Dynamic Applications
2021, Groß Schwansee (GER): "Anisotropic Kernels for Fluid Flow Simulations"

22.-25.03.2021

Workshop on Modeling, Simulation & Optimization of Fluid Dynamic Applications 2021 (Online):  "On the Design of Anisotropic Kernels for Flow Simulation" https://www.c3s.uni-hamburg.de/rtg2583/teaching/workshops/workshop-maerz-2021

1. Albrecht, K., Entzian, J., Iske, I.: "Anisotropic Kernels for Particle Flow Simulation", to appear in
"Modeling, Simulation and Optimization of Fluid Dynamic Applications", Springer, preprint,  2023