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

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

Abstract

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.

Keywords

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.

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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

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