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Certified Reduced Basis Method for Affinely Parametric Isogeometric Analysis NURBS Approximation

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Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 119))

Abstract

In this work we apply reduced basis methods for parametric PDEs to an isogeometric formulation based on NURBS. We propose an integrated and complete work pipeline from CAD to parametrization of domain geometry, then from full order to certified reduced basis solution. IsoGeometric Analysis (IGA), as well as reduced basis methods for parametric PDEs growing research themes in scientific computing and computational mechanics. Their combination enhances the solution of some class of problems, especially the ones characterized by parametrized geometries. This work shows that it is also possible for some class of problems to deal with affine geometrical parametrization combined with a NURBS IGA formulation. In this work we show a certification of accuracy and a complete integration between IGA formulation and parametric certified greedy RB formulation by introducing two numerical examples in heat transfer with different parametrization.

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Author information

Authors and Affiliations

  1. ETHZ SAM, Seminar for Applied Mathematics, CH-8092, Zurich, Switzerland

    Denis Devaud

  2. SISSA, International School for Advanced Studies, Mathematics Area, mathLab, Via Bonomea 265, 34136, Trieste, Italy

    Gianluigi Rozza

Authors
  1. Denis Devaud
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  2. Gianluigi Rozza
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Corresponding author

Correspondence to Denis Devaud .

Editor information

Editors and Affiliations

  1. School of Mechanical Engineering, University of Campinas, Campinas, Brazil

    Marco L. Bittencourt

  2. Department of Civil Engineering, Pontifical Catholic University of Rio de Janeiro, Rio de Janeiro, Brazil

    Ney A. Dumont

  3. EPFL-SB-MATHICSE-MCSS, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Jan S. Hesthaven

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Devaud, D., Rozza, G. (2017). Certified Reduced Basis Method for Affinely Parametric Isogeometric Analysis NURBS Approximation. In: Bittencourt, M., Dumont, N., Hesthaven, J. (eds) Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016. Lecture Notes in Computational Science and Engineering, vol 119. Springer, Cham. https://doi.org/10.1007/978-3-319-65870-4_3

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