Research in the Numerics Group

Biannual Reports

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

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

• B01: Adaptive Dynamical Multiscale Methods
• C04: Galerkin methods for the simulation, calibration, and control of partial differential equations on networks
• C05: Observer-based data assimilation for time-dependent flows in gas networks
Project partners: Friedrich-Alexander-Universität Erlangen-Nürnberg, TU Berlin, TU Darmstadt, WIAS Berlin, Universität Duisburg-Essen, DFG, 2014 – 2022

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

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

Variational quantitative phase-field modeling and simulation of powder bed fusion additive manufacturing

Powder bed fusion additive manufacturing (PBF-AM) is a promising alternative to conventional process technology of metal materials and enables a new route for the design of materials with controlled microstructure. This project aims at a new mathematical approach and numerical analysis to derive quantitative variational non-isothermal phase-field models which, beyond the state-of-art, are able to describe the interactive processes of heat-melt-microstructure-stress evolution during PBF-AM.

Project within DFG-SPP 2256

M3TB2015 International Workshop Multiscale Models in Mechano and Tumor Biology:
Modeling, Homogenization, and Applications
Project Funding period
EWAVE-ERWAS, Energiemanagement Wasserversorgung (BMBF) 2014 – 2017
Multiscale structure-functional modeling of musculoskeletal mineralized tissues (in DFG-SPP 1420) 2009 – 2016
Biomimetic Materials Research (DFG) 2009 – 2015
Direkte und Inverse Probleme nichtlinearer Drift-Diffusionsgleichungen 2012 – 2014
Skalenübergreifende Modellierung in der Strömungsmechanik und Meteorologie (DFG) 2007 – 2013
Vollständig Raum-Zeit-adaptive Verfahren für die numerische Berechnung von transienten Magnetfeldern (DFG) 2006 – 2009
Strömung und Verbrennung in zukünftigen Gasturbinenbrennkammern (DFG) 2004 – 2008