• Postal Address
  • Ulm University
  • Institute for Numerical Mathematics
  • Helmholtzstraße 20 (Room 1.04)
  • D-89081 Ulm



A large number of technical applications include chemically reactive flows comprising an interplay between convective and diffusive species transport and chemical reaction processes. In many realistic kinetic models the occurrence of a large number of chemical species and reactions as well as a high degree of stiffness due to multiple time scales give rise to significant challenges for numerical simulations and call for multiscale approaches and model reduction techniques. 
The goal of this project is the development of a practical numerical reduction technique that can be applied to high-dimensional realistic chemical reaction mechanisms and automatically computes slow invariant manifolds (SIM) as low-dimensional approximations of long-term system dynamics in chemical kinetics with multiple time scales and spectral gaps.



  • Lebiedz, D., Unger, J.
    On Unifying Concepts for Trajectory-Based Slow Invariant Attracting Manifold Computation in Kinetic Multiscale Models.
    Math. Comp. Model. Dyn. (accepted)


  • Lebiedz, D., Unger, J.
    A Boundary Value View on the Reverse Trajectory-Based Optimization
    Approach for Kinetic Model Reduction.
    Proceedings of the 4th International Workshop on Model Reduction in Reacting Flows, San Francisco.


  • Lebiedz, D., Unger, J.
    Model Reduction in Chemical Kinetics via Slow Manifold Computation.
    Proceedings of the Second International Workshop on Model Reduction for Parametrized Systems, Günzburg.


  • Dedner, A., Fein, M., Klöfkorn, R., Kröner, D., Lebiedz, D., Siehr, J., Unger, J.
    On the Computation of Slow Manifolds in Chemical Kinetics via Optimization and their Use as Reduced Models in Reactive Flow Systems.
    Proceedings of the 13th International Conference on Numerical Combustion, Corfu.
  • Lebiedz, D., Siehr, J. Unger, J. 
    A Variational Principle for Computing Slow Invariant Manifolds in Dissipative Dynamical Systems.
    SIAM J. Sci. Comput. 33, 703.


  • Lebiedz, D. Reinhardt, V., Siehr, J. Unger, J.
    Geometric Criteria for Model Reduction in Chemical Kinetics via Optimization of Trajectories.
    In "Coping with complexity: Model reduction and data analysis''.     
    Springer Series "Lecture Notes in Computational Science and Engineering''.


WS 2015/2016

SS 2015

WS 2014/2015

SS 2014

WS 2013/2014

SS 2013

WS 2012/2013

SS 2012

WS 2011/2012

  • Mathematik für Bioinformatik und Systembiologie

SS 2011

  • Profilmodul Mathematik (für Systembiologie)

SS 2010

  • Einführung in Theorie und Numerik von Optimierungsproblemen

WS 2008/2009

  • Mathematik I für Studierende des Ingenieurwesens und der Informatik (Tutor)

SS 2008

  • Mathematik für Studierende des Ingenieurwesens II (Tutor)

WS 2007/2008

  • Mathematik für Informatiker und Ingenieure I (Tutor)

Short Curriculum Vitae

04/2012 - 01/2016

03/2011 - 03/2012


  • Diploma in Mathematics, University of Freiburg

10/2005 - 02/2011

  • Studies of Mathematics, University of Freiburg

10/2007 - 07/2010

  • Student research assistant, University of Freiburg


  • Abitur, Gymnasium Bildungszentrum Weissacher Tal


  • Born in Backnang, Baden-Württemberg, Germany

Dr. Jonas Unger