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Reduced Basis Methods: Success, Limitations and Future Challenges

Proceedings of ALGORITMY 2016, 20th Conference on Scientific Computing, Vysoke Tatry, Podbanske, Slovakia, March 13-18, 2016, page 1--12 - 2016
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Parametric model order reduction using reduced basis methods can be an effective tool for obtaining quickly solvable reduced order model of parametrized partial differential equation problems. With speedups that can reach several orders of magnitude, reduced basis methods enable high fidelity real-time simulations of complex systems and dramatically reduce the computational costs in many-query applications. In this contribution we analyze the methodology, mainly focussing on the theoretical aspects of the approach. In particular we discuss what is known about the convergence properties of these methods: when they succeed and when they are bound to fail. Moreover, we highlight some recent approaches employing nonlinear approximation techniques which aim to overcome the current limitations of reduced basis methods.

Références BibTex

@InProceedings{OR16,
  author       = {Ohlberger, M. and Rave, S.},
  title        = {Reduced Basis Methods: Success, Limitations and Future Challenges},
  booktitle    = {Proceedings of ALGORITMY 2016, 20th Conference on Scientific Computing, Vysoke Tatry, Podbanske, Slovakia, March 13-18, 2016},
  pages        = {1--12},
  year         = {2016},
  editor       = {A. Handlovi\čova and D. Sev\čovi\č,},
  publisher    = {Publishing House of Slovak University of Technology in Bratislava},
  note         = {http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/389},
  issn         = {978-80-227-4454-4},
  url          = \{/2016/OR16},
}

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