A Software Framework for Reduced Basis Methods Using Dune-RB and RBmatlab

  • Martin Drohmann
  • Bernard Haasdonk
  • Sven Kaulmann
  • Mario Ohlberger


Many applications from science and engineering are based on parametrized evolution equations and depend on time–consuming parameter studies or need to ensure critical constraints on the simulation time. For both settings, model order reduction by the reduced basis approach is a suitable means to reduce computational time. The method is based on a projection of an underlying high–dimensional numerical scheme onto a low–dimensional function space. In this contribution, a new software framework is introduced that allows fast development of reduced schemes for a large class of discretizations of evolution equations implemented in Dune. The approach provides a strict separation of low–dimensional and high–dimensional computations, each implemented by its own software package RBmatlab, respectively Dune-RB. The functionality of the framework is exemplified for a finite–volume approximation of an instationary linear convection–diffusion problem.


Software Framework Discrete Operator Dimensional Computation Solution Trajectory Linear Evolution Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Barrault, M., Maday, Y., Nguyen, N., Patera, A.: An ’empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations. C. R. Math. Acad. Sci. Paris Series I 339, 667–672 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Dedner, A., Klöfkorn, R., Nolte, M., Ohlberger, M.: A generic interface for parallel and adaptive discretization schemes: abstraction principles and the DUNE-FEM module. Computing 90, 165–196 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Drohmann, M., Haasdonk, B., Ohlberger, M.: Reduced Basis Approximation for Nonlinear Parametrized Evolution Equations based on Empirical Operator Interpolation. SIAM J. Sci. Comput. 34(2), 937–969 (2012)CrossRefGoogle Scholar
  4. 4.
    Haasdonk, B., Dihlmann, M., Ohlberger, M.: A training set and multiple bases generation approach for parametrized model reduction based on adaptive grids in parameter space. Math. Comput. Model. Dyn. Syst. 17(4), 423–442 (2011)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Haasdonk, B., Ohlberger, M.: Adaptive basis enrichment for the reduced basis method applied to finite volume schemes. In: Proc. 5th International Symposium on Finite Volumes for Complex Applications, pp. 471–478 (2008)Google Scholar
  6. 6.
    Haasdonk, B., Ohlberger, M.: Reduced basis method for finite volume approximations of parametrized linear evolution equations. M2AN, Math. Model. Numer. Anal. 42(2), 277–302 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Knezevic, D., Petterson, J.: A high-performance parallel implementation of the certified reduced basis method. Comput. Meth. Appl. Mech. Eng. 200, 1455–1466 (2011)zbMATHCrossRefGoogle Scholar
  8. 8.
    Kröner, D.: Numerical Schemes for Conservation Laws. John Wiley & Sons and Teubner (1997)Google Scholar
  9. 9.
    Patera, A., Rozza, G.: Reduced Basis Approximation and a Posteriori Error Estimation for Parametrized Partial Differential Equations. MIT (2007),; Version 1.0, Copyright MIT 2006-2007, to appear in (tentative rubric) MIT Pappalardo Graduate Monographs in Mechanical Engineering

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Martin Drohmann
    • 1
  • Bernard Haasdonk
    • 2
  • Sven Kaulmann
    • 1
  • Mario Ohlberger
    • 1
  1. 1.Institute of Computational and Applied MathematicsUniversity of MünsterMünsterGermany
  2. 2.Institute of Applied Analysis and Numerical SimulationUniversity of StuttgartStuttgartGermany

Personalised recommendations