TU Chemnitz: Fak. f. Mathematik: Professur Mathematik in Industrie und Technik: Rene Schneider: CV

Work in progress

• The discrete adjoint method (DAM) has been developed to efficiently evaluate derivatives of quantities derived form the solution of discretised PDEs with respect to large numbers of parameters.
• This is very advantageous in shape optimisation where the goal is to optimise the parameterised shape of objects with respect to performance criteria derived from the solution of a PDE.
• We investigate application of the DAM for different shape optimisation problems (Navier-Stokes, structural mechanics, Darcy-flows) and efficient solution techniques for the resulting adjoint equations (preconditioned iterative solvers, multi-grid).
• Our second main research interest is in different approaches to automatic anisotropic mesh refinement.

Ongoing collaboration projects

• Karsten Eppler (Dresden, Germany): Comparison of different approaches to the evaluation of shape sensitivities in linear elasticity.
• Hermann Mena (Quito, Ecuador): Simulation of the Glyphosate Aerial Spray Drift at the Ecuador-Colombia border.
• Andrea Walther (Paderborn, Germany): Structure exploiting Algorithmic Differentiation of a FEM solver.
• Petr Knobloch (Prague, Czech Republic): Anisotropic mesh refinement for convection dominated convection diffusion problems.

Publications

• Schneider R, With a new refinemet paradigm towards anisotropic mesh refinement, in preparation.
• Mena H, Schneider R, Simulation of the Glyphosate Aerial Spray Drift at the Ecuador-Colombia border, in preparation
• Walther A, Schneider R, Shape optimization using structure-exploiting algorithmic differentiation of a FEM Navier-Stokes solver, in preparation.
• Knobloch P, Schneider R, Anisotropic adaptivity by optimisation of node positions in convection-diffusion problems, in preparation.
• Jimack P, Schneider R, Implementing the Zero-Mean-Pressure Condition for the incompressible Navier-Stokes Equations by projections, in preparation.
• Schneider R, A review of anisotropic refinement methods for triangular meshes in FEM, submitted July 2011, to appear
• Krell S, Schneider R, Röber M, Kahl S, Schufft W, Free Virtual Impulse Generator (VIG) to determine the Impulse Generator Settings online, proceedings ISH - International Symposium on High Voltage Engineering, August 2011
• Schneider R, FEINS: Finite element solver for shape optimization with adjoint equations, accepted for proceedings of ECMI 2010, to appear in Springer series Mathematics in Industry, 2010.
• Schneider R, Systems Modeling, from Simulation to Optimization, proceedings of the Fourth Conference of Ingeniería de Sistemas Informáticos y de Computación ISIC (Information Systems and Computational Engineering), pp. 101–108, Quito, Ecuador, November 2008
• Schneider R, Jimack P, On the evaluation of finite element sensitivities to nodal coordinates, Electronic Transactions on Numerical Analysis, 32:134–144, , Special Volume: Selected Papers from the 20th Chemnitz Finite Element Symposium, 2008.
  http://etna.mcs.kent.edu/
• Schneider R, Rothaug T, Benner P, Flow stabilisation by Dirichlet boundary control, PAMM : Vol. 8, pp. 10961-10962; 2008.
• Schneider R, Jimack P, Anisotropic mesh adaption based on a posteriori estimates and optimisation of node positions, in G. Lube, G. Rapin : BAIL 2006, Proceedings of Int. Conference on Boundary and Interior Layers, University of Göttingen, 2006.
• Schneider R, Applications of the Discrete Adjoint Method in Computational Fluid Dynamics, PhD Thesis, University of Leeds, 2006.
  http://www.comp.leeds.ac.uk/cgi-bin/sis/ext/rs_pub.cgi?cmd=listtheses#2006
• Schneider R, Jimack P, Toward anisotropic mesh adaption based upon sensitivity of a posteriori error estimates, School of Computing Research Report Series 2005.03, University of Leeds, 2005.
  http://www.comp.leeds.ac.uk/research/pubs/reports/2005/2005_03.pdf
• Schneider R, Jimack P, Efficient preconditioning of the discrete adjoint equations for the incompressible Navier-Stokes equations, International Journal for Numerical Methods in Fluids, 47:1277–1283, 2005.
• Schneider R, Riedel A, Verdult V, Verhaegen M, Sima V, SLICOT system identification toolbox for nonlinear Wiener systems, SLICOT Working Note 2002-6: June 2002.
  http://www.win.tue.nl/niconet/NIC2/reports.html

Published Software

• FEINS (Finite Element solver for stationary Incompressible Navier Stokes),
  • A finite element solver suite for the Poisson equation, linear elasticity, incompressible Navier-Stokes and convection-diffusion equations in two dimensions, using unstructured triangular elements and iterative solvers with multi-grid preconditioning.
  • Geared to allow shape optimisation.
  • Latest performance tops:
    • Solving stationary Navier-Stokes with 37,769,219 degrees of freedom (Taylor-Hood Elements) on single processor in 8.9 hours, computing shape gradient in 10.55 hours (February 2009).
    • Solving stationary linear elasticity with 35,419,650 degrees of freedom (P₂ Elements) on single processor in 12.2 minutes, computing shape gradient in the same time (November 2009).
  • First parts have been parallelised with OpenMP
  • http://www.feins.org
  • Started in April 2003 as platform for PhD research. First publication under GPL license, July 2008.
  • Approximately 46,200 lines of C code.

Invited Conference Talks and Minisymposia

• Plenary lecture,
  Systems Modeling, from Simulation to Optimization,
  Fourth Conference of Ingeniería de Sistemas Informáticos y de Computación ISIC (Information Systems and Computational Engineering), Quito, Ecuador, November 2008
• Introductory talk,
  From Simulation to Optimization: discrete adjoint equations, Welcome colloquium for Prof. Peter Benner at MPI Magdeburg, Magdeburg, November 2010
• Talk in Minisymposium on Adaptive Methods,
  With optimisation towards anisotropic adaptive FEM, Algorithmy 2009, Podbanske, Slovakia, March 2009
• Talk in Minisymposium on Adaptive Methods,
  Anisotropic mesh adaption based on a posteriori estimates and optimisation of node positions,
  BAIL 2006, Göttingen, July 2006
• Talk in Minisymposium on Anisotropic Finite Elements,
  Anisotropic mesh adaption based on a posteriori estimates and optimisation of node positions,
  MAFELAP 2006, Uxbridge, June 2006

Conference Talks

• With edge based refinement towards anisotropic adaptive refinement in FEM,
  Workshop Numerical Analysis for Singularly Perturbed Problems (dedicated to the 60th birthday of Martin Stynes), TU Dresden, November 2011
• Adaptive anisotropic mesh refinement based on a new adaptivity paradigm,
  ENUMATH, Leicester, UK, September 2011
• Ein neuer Ansatz zur anisotropen adaptiven Netz Verfeinerung in FEM,
  Südostdeutsches Kolloquium zur Numerischen Mathematik, Ilmenau, May 2011
• Adaptive anisotropic mesh refinement based on a new adaptivity paradigm,
  Chemnitz FEM Symposium, Lichtenwalde, September 2010
• FEINS: Finite element solver for shape optimization with adjoint equations,
  ECMI 2010, Wuppertal, July 2010
• Shape optimisation for elliptic PDEs with the Discrete Adjoint Technique,
  SPP1253 Workshop, Lambrecht, July 2010
• Anisotropic mesh adaption based on a posteriori estimates,
  BAIL 2010, Zaragoza, Spanien, July 2010
• Shape optimisation for elliptic PDEs with the Discrete Adjoint Technique,
  CMAM, Bedlewo, Polen, June 2010
• Shape optimisation for stationary Navier-Stokes with the Discrete Adjoint Technique,
  BIT50, Lund, Schweden, June 2010
• Differentiation of a finite element solver for stationary Navier-Stokes,
  AD Workshop, Paderborn, June 2010
• Shape optimisation for stationary Navier-Stokes with the Discrete Adjoint Technique,
  GAMM 2010, Karlsruhe, March 2010
• On the evaluation of finite element sensitivities to nodal coordinates,
  Chemnitz FEM Symposium, Oberwiesenthal, September 2009
• With optimisation towards anisotropic adaptive FEM,
  Adaptive Finite Elements: Analysis and Applications, Workshop, Kirchzarten,
  September 2009
• Shape optimisation for stationary Navier-Stokes with the Discrete Adjoint Technique,
  Conference on Optimization with interfaces and free boundaries, Regensburg, March 2009
• Anisotropic mesh adaption based on a posteriori estimates and optimisation of node positions,
  BAIL 2008, Limerick, Ireland, July 2008
• Flow stabilisation by Dirichlet boundary control,
  GAMM 2008, Bremen, April 2008
• Anisotropic mesh adaption based on a posteriori estimates and optimisation of node positions,
  Chemnitz FEM Symposium, Chemnitz, September 2007
• With discrete adjoint based optimisation towards anisotropic adaptive FEM,
  ENUMATH 2007, Graz, Austria, September 2007
• With discrete adjoint based optimisation towards anisotropic adaptive FEM,
  IFIP 2007, Cracow, Poland, July 2007
• Anisotropic mesh adaptation based on a posteriori estimates and optimisation of node positions,
  NAConf 2007, Dundee, UK, June 2007
• Anisotropic mesh adaption based on a posteriori estimates and optimisation of node positions,
  Chemnitz FEM Symposium, Chemnitz, September 2006
• Automatic anisotropic mesh adaption,
  Südostdeutsches Kolloquium zur Numerischen Mathematik, Halle, May 2006
• Anisotropic mesh adaption based upon sensitivity of a posteriori estimates,
  GAMM 2006, Berlin, March 2006
• Anisotropic mesh adaption based on a posteriori estimates and optimisation of node positions,
  Chemnitz FEM Symposium, Chemnitz, September 2004

Languages

Personal interests

• target shooting
• refurbishment of our family home
• Member of the city council of the town Oederan (Freie Wähler). Member of Freien Wählergemeinschaft Oederan mit Ortsteilen e.V. since March 2009, voted council member since August 2009.
• Vice president of Breitenauer Carnevals Club e.V.. Member since 1998, vice president since 2008.
• Board member of Schützengesellschaft Schönerstadt 1862 e.V. (crossbow and gun club). Member since 1995, vice president 2006–2010, board member/organiser since 2010.

Dr. Rene Schneider
13. Januar 2012

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Technische Universität Chemnitz, 09107 Chemnitz

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