Research

Research in the Numerics Group

Biannual Reports

The full reports of the Department of Mathematics are available here.

Currently Funded Projects

 
Logo SFB-TRR154

CRC-TRR 154: Mathematical Modelling, Simulation and Optimization using the Example of Gas Networks

Subprojects:
• B01: Adaptive Dynamical Multiscale Methods
• C04: Galerkin methods for the simulation, calibration, and control of partial differential equations on networks
Project partners: Friedrich-Alexander-Universität Erlangen-Nürnberg, TU Berlin, TU Darmstadt, WIAS Berlin, Universität Duisburg-Essen, DFG, 2014 – 2022

Logo SFB-TRR 146

CRC-TRR 146: Multiscale Simulation Methods for Soft Matter Systems

Subproject C3: Spinodal decomposition of polymer-solvent systems
Project partners: Johannes Gutenberg Universität Mainz, Max-Planck-Institut für Polymerforschung, DFG, 2014 – 2022

In-Vivo Wall Shear Stress Measurements using Magnetic Resonance Imaging

Wall shear stress is believed to play a key role in the development of vascular diseases, but in context of clinical imaging techniques wall shear stress is an unobservable quantity. The mathematical part of this joint project deals with the inverse problem of reconstructing the wall shear stress from velocity data given by magnetic resonance imaging.

Project partners:
Institute for Fluid Mechanics and Aerodynamics (SLA), Department of Mechanical Engineering, TU Darmstadt
Department of Radiology – Medical Physics, University Medical Center Freiburg
DFG-EG 331/1-1, 2016 – 2019

Logo DFG-SPP 1748

Structure Preserving Adaptive Enriched Galerkin Methods for Pressure-Driven 3D Fracture Phase-Field Models

The project is concerned with the development of innovative enriched Galerkin methods for the reliable simulation of pressure-driven fracture problems. Within this project, convergent adaptive mesh-refinement schemes based on new efficient error estimators for the variational inequality associated with the fracture irreversibility will be developed.

Project within DFG-SPP 1748, 2018 – 2021

Dynamical spatially heterogeneous model adaptation in compressible flows

Chemically reacting fluid mixtures can be described by a variety of models which differ regarding their complexity. For efficient numerical discretizations it is desirable to solve complex models only where necessary and simple models everywhere else. The goal of this project is to make this domain decompositions transparent and automatizable by providing a posteriori error estimates for modeling errors.

DFG-GI 1131/1-1, 2017 – 2020

 

Workshops

 

Past Projects