zum Inhalt springen

Mathematisch-Naturwissenschaftliche FakultätProf. Dr. Axel Klawonn

Dr. A. Heinlein - Fields of Research

Numerical methods for multiscale problems

Multiscale vertex basis function.
Multiscale edge basis function.

  • Multiscale finite element discretizations
  • Multiscale and adaptive coarse spaces for domain decomposition methods 

Development of scalable and robust overlapping Schwarz methods

FROSch logo.
Overlapping domain decomposition in two dimensions.

  • Development of the Trilinosdomain decomposition solver FROSch (Fast and Robust Overlapping Schwarz) 
  • Monolithic overlapping Schwarz preconditioners for multiphysics/coupled problems
  • Robust multilevel overlapping Schwarz methods
  • Nonlinear two-level Schwarz methods 

Numerical simulations with biomedical applications

Fluid-Structure Interaction (FSI) in curved pipe benchmark geometry.
Wall shear stresses of a flow field in an aneurysm benchmark test.

  • Fluid-Structure Interaction (FSI) of blood flow and arterial walls
  • Computational Fluid Dynamics (CFD) simulations in the circulatory system

Machine learning in finite element simulations

Neural network architecture.

  • Constructing robust preconditioners using smart data and machine learning techniques 
  • Flow predictions using convolutional neural networks

Tuning domain decomposition solvers for simulations involving Uncertainty Quantification (UQ)

Flow in a backward facing step geometry with uncertainty in the viscosity: mean flow.
Flow in a backward facing step geometry with uncertainty in the viscosity: standard deviation.