Christoph Lehrenfeld

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Dr. rer. nat. Christoph Lehrenfeld

 

Contact

Institute for Analysis and Scientific Computing
Wiedner Hauptstrasse 8-10
1040 Wien, Austria

Room: DA 03 K22
Tel: +43 1 58801 10108
Email: christoph.lehrenfeld@gmail.com
Homepage: | http://num.math.uni-goettingen.de/~lehrenfeld/

I am now at the University of Goettingen, see | my homepage there

Research Interests (see Media)

  • Numerical methods for PDEs (Finite Elements),
  • Higher order numerical integration on implicit domains
  • Advanced Finite Element methods:
    • (Hybrid) Discontinuous Galerkin methods
    • H(div)-conforming FEM
    • Extended FEM (XFEM/CutFEM)
    • Space-Time Finite Elements
  • Applications:
    • Interface problems
    • problems with moving interfaces/boundaries (e.g. two-phase flows)
    • Fluid dynamics
  • Finite element software development


Publications

Recent work

  1. C. Lehrenfeld: "High order unfitted finite element methods on level set domains using isoparametric mappings", submitted to Comp. Appl. Mech. Eng., 2015, arxiv:1509.02762
  2. C. Lehrenfeld, J. Schöberl, "High order exactly divergence-free Hybrid Discontinuous Galerkin Methods for unsteady incompressible flows", ASC Report No. 27/2015, ASC, TU Wien, 2015, pdf
  3. C. Lehrenfeld, "On a Space-Time Extended Finite Element Method for the Solution of a Class of Two-Phase Mass Transport Problems", Ph.D. thesis, IGPM, RWTH Aachen, 2015, pdf(A4), pdf(A5)
  4. C. Lehrenfeld, A. Reusken: "Finite Element Techniques for the Numerical Simulation of Two-Phase Flows with Mass Transport", to appear in Computational Methods for Complex Liquid-Fluid Interfaces - Vol. 7 of "Progress in Colloid and Interface Science" (Taylor&Francis), preprint
  5. C. Lehrenfeld, A. Reusken: "Optimal preconditioners for Nitsche-XFEM discretizations of interface problems", submitted to Numerische Mathematik, 2014, arxiv:1408.2940, preprint

Journal Publications

  1. C. Lehrenfeld: "The Nitsche XFEM-DG space-time method and its implementation in three space dimensions", SIAM Journal on Scientific Computing, 2015, Volume 37, No. 1, pp. A245-A270, DOI: 10.1137/130943534, ps.gz, pdf
  2. H. Marschall, S. Boden, C. Lehrenfeld, , C. Falconi Delgado, U.Hampel, A. Reusken, M. Wörner, D. Bothe: "Validation of Interface Capturing and Tracking Techniques with different Surface Tension Treatments against a Taylor Bubble Benchmark problem", Computers & Fluids, 2014, DOI: 10.1137/120875260, pdf
  3. C. Lehrenfeld, A. Reusken: "Analysis of a DG-XFEM Discretization for a class of two-phase mass transport problems", SIAM Journal on Numerical Analysis, 2013, Volume 51, No. 2, pp. 958-983, DOI: 10.1137/120875260, ps.gz, pdf
  4. C. Lehrenfeld, A. Reusken: "Nitsche-XFEM with Streamline Diffusion Stabilization for a Two-Phase Mass Transport Problem", SIAM Journal on Scientific Computing, 2012, Volume 34, No. 5, pp. A2740-A2759, DOI: 10.1137/110855235, ps.gz, pdf

Book Chapters

  1. J. Schöberl, C. Lehrenfeld: "Domain Decomposition Preconditioning for High Order Hybrid Discontinuous Galerkin Methods on Tetrahedral Meshes", Lecture Notes in Applied and Computational Mechanics, 2013, Volume 66, Advanced Finite Element Methods and Applications, pp. 27-56, DOI: 10.1007/978-3-642-30316-6_2, ps.gz, pdf
  2. C. Koutschan, C. Lehrenfeld, J. Schöberl, "Computer Algebra meets Finite Elements: an Efficient Implementation for Maxwell's Equations", Numerical and Symbolic Scientific Computing: Progress and Prospects, Ulrich Langer, Peter Paule (ed.), pp. 105-122, 2011, Springer, Wien, DOI: 10.1007/978-3-7091-0794-2_6, arxiv:1104.4208, preprint, bib

Proceedings

  1. S. Aland, C. Lehrenfeld, H. Marschall, C. Meyer, S. Weller, "Accuracy of two-phase flow simulations", Proceedings in Applied Mathematics and Mechanics (PAMM) 2013, Volume 13, pp. 595-598, DOI: 10.1002/pamm.201110296, pdf
  2. C. Lehrenfeld, "Nitsche-XFEM for a transport problem in two-phase incompressible flows", Proceedings in Applied Mathematics and Mechanics (PAMM) 2011, Volume 11, pp. 613-614, DOI: 10.1002/pamm.201310278, pdf

Theses

  1. C. Lehrenfeld, "On a Space-Time Extended Finite Element Method for the Solution of a Class of Two-Phase Mass Transport Problems", Ph.D. thesis, IGPM, RWTH Aachen, 2015, pdf(A4), pdf(A5)
  2. C. Lehrenfeld, "Hybrid Discontinuous Galerkin methods for incompressible flow problems", Diploma thesis, MathCCES, RWTH Aachen, 2010, pdf

Talks (Selection)

  1. "Space-Time XFEM for Mass Transport", European Finite Element Fair 2015, Prague, Czech republic, June 5, 2015, pdf
  2. "Two-Phase Flow Benchmark Computations using Level-Set based FEM", presented at GAMM 2013, Novi Sad, Serbia, March 19, 2013
  3. "Domain Decomposition Preconditioners for High Order Hybrid Discontinuous Galerkin Methods", presented at DD21, Rennes, France, June 27, 2012, pdf
  4. "Streamline Diffusion Stabilisation for mass transport in two phase incompressible flows", presented at International Workshop: Transport Processes at Fluidic Interfaces - from Experimental to Mathematical Analysis, Aachen, Germany, December 7, 2011, pdf, (video 1: avi, video 2: avi)
  5. "Nitsche-XFEM for a transport problem in two-phase incompressible flows", presented at GAMM 2011, Graz, Austria, April 20, 2011
  6. "Efficient High Order DG Method for Time-domain Maxwells Equations", presented at MAFELAP 2009, London, Great Britain, June 11, 2009, pdf

Teaching


Media


  • XFEM/CutFEM:
    (here: pressure of a two-phase flow problem)
  • Incompressible flow:
    (here: Flow around cylinder, Re=100)
  • Hybrid Discontinuous Galerkin:
    (here: Sketch of tets and facets)





































Old stuff

other stuff