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Computational Reduction for Parametrized PDEs: Strategies and Applications

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Abstract

In this paper we present a compact review on the mostly used techniques for computational reduction in numerical approximation of partial differential equations. We highlight the common features of these techniques and provide a detailed presentation of the reduced basis method, focusing on greedy algorithms for the construction of the reduced spaces. An alternative family of reduction techniques based on surrogate response surface models is briefly recalled too. Then, a simple example dealing with inviscid flows is presented, showing the reliability of the reduced basis method and a comparison between this technique and some surrogate models.

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Authors and Affiliations

  1. CMCS – Modelling and Scientific Computing, MATHICSE – Mathematics Institute of Computational Science and Engineering, EPFL – Ecole Polytechnique Fédérale de Lausanne, Station 8, CH-1015, Lausanne, Switzerland

    Andrea Manzoni, Alfio Quarteroni & Gianluigi Rozza

  2. MOX – Modellistica e Calcolo Scientifico, Dipartimento di Matematica “F. Brioschi” – Politecnico di Milano, P.za Leonardo da Vinci 32, I-20133, Milano, Italy

    Alfio Quarteroni

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  1. Andrea Manzoni
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  2. Alfio Quarteroni
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Manzoni, A., Quarteroni, A. & Rozza, G. Computational Reduction for Parametrized PDEs: Strategies and Applications. Milan J. Math. 80, 283–309 (2012). https://doi.org/10.1007/s00032-012-0182-y

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