Christoph Gersbacher

Abteilung für Angewandte Mathematik
Universität Freiburg
Hermann-Herder-Str. 10
D-79104 Freiburg im Breisgau

gersbacher.jpg

 

Scientific Interests

  • Grid Development: Dune-PrismGrid is a Dune meta grid implementation. Generic prismatic elements are constructed from the host grid's elements yielding a higher-dimensional prismatic grid. 

 

hostgrid_prismgrid.png  
 
 
 		 column_iterator.png
Element iterator over a single column.
layer_iterator.png

Two-dimensional host grids (top) and resulting prismatic grids (bottom).

 Element iterator over a single layer.

 

  • Explicit higher order methods for systems of nonlinear hyperbolic conservation laws (higher order finite volume methods, Runge-Kutta discontinuous Galerkin methods) and development of slope limiters for arbitrary grids

shock_diffraction.gif        

Numerical solution to the Euler equations of gas dynamics (the animation shows the density component) computed using an adaptive second order Runge-Kutta discontinuous Galerkin method.

 

  • hp-adaptive discontinuous finite element spaces and their implementation in Dune and Dune-Fem
hpIP.gif
Numerical solution to the Poisson equation computed using an hp-adaptive Interior Penalty method.

 

 

Publications

Recent and Submitted Publications

  • Ch. G. and M. Nolte. “Constrained reconstruction in MUSCL-type finite volume schemes”. arXiv: 1608.02578
  • Ch. G. “Implementation of hp-adaptive discontinuous finite element methods in Dune-Fem”. arXiv: 1604.07242
  • M. Blatt et al. “The distributed and unified numerics environment, version 2.4”. In: Arch. Numer. Softw. 4.100 (2016), pp. 13–29

Book Chapters and Proceedings

  • Ch. G. “Explicit higher order schemes for the coupling of dimensionally heterogeneous free-surface flow models”. In: Hyperbolic problems: Theory, numerics, applications. Ed. by F. Ancona et al. Vol. 8. AIMS Series on Applied Mathematics. 2014, pp. 591–598
  • Ch. G. “The Dune-PrismGrid module”. In: Advances in Dune. Ed. by A. Dedner et al. Springer Berlin Heidelberg, 2012, pp. 33–44
  • A. Dedner and Ch. G. “A local discontinuous Galerkin discretization for hydrostatic free surface flows using σ-transformed coordinates”. In: Hyperbolic problems: Theory, numerics and applications. Ed. by T. Li and S. Jian. Vol. 2. Ser. Contemp. Appl. Math. CAM 17–18. Higher Ed. Press, Beijing, 2012, pp. 382–389

Theses

  • Ch. G. Local Discontinuous Galerkin Verfahren zur Simulation flacher dreidimensionaler Strömungen mit freier Oberfläche. Diploma thesis, University of Freiburg, 2008

Miscellaneous

  • Ch. G., Th. Müller, A. Pfeiffer, and N. Shokina. Large-scale simulation of geophysical flows. At International Conference on Simulation Technology (SimTech) 2011, Stuttgart, 2011 (Finalist for the Best Poster Award)

 

Talks

  • 16th International Conference on Hyperbolic Problems: Theory, Numerics, Applications (HYP2016), Aachen, 2016
  • Oberseminar Angewandte Mathematik, Department of Applied Mathematics, University of Freiburg, 2016
  • PDESoft, Heidelberg, 2014
  • Numerical approximations of hyperbolic systems with source terms and applications (NumHyp2013), Aachen, 2013
  • 14th International Conference on Hyperbolic Problems: Theory, Numerics, Applications (HYP2012), Padova, 2012
  • PDE Software Frameworks, Münster, 2012
  • 1st DUNE User Meeting, Stuttgart, 2010
  • 13th International Conference on Hyperbolic Problems: Theory, Numerics, Applications (HYP2010), Beijing, 2010
  • SIAM Conference on Mathematical and Computational Issues in the Geosciences, Leipzig, 2009
  • Oberseminar Angewandte Mathematik, Institute for Computational and Applied Mathematics, University of Münster, 2009
  • Oberseminar Angewandte Mathematik, Department of Applied Mathematics, University of Freiburg, 2009