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Reduced Order Isogeometric Analysis Approach for PDEs in Parametrized Domains

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Quantification of Uncertainty: Improving Efficiency and Technology

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 137 ))

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Abstract

In this contribution, we coupled the isogeometric analysis to a reduced order modelling technique in order to provide a computationally efficient solution in parametric domains. In details, we adopt the free-form deformation method to obtain the parametric formulation of the domain and proper orthogonal decomposition with interpolation for the computational reduction of the model. This technique provides a real-time solution for any parameter by combining several solutions, in this case computed using isogeometric analysis on different geometrical configurations of the domain, properly mapped into a reference configuration. We underline that this reduced order model requires only the full-order solutions, making this approach non-intrusive. We present in this work the results of the application of this methodology to a heat conduction problem inside a deformable collector pipe.

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Acknowledgements

This work was partially funded by the project SOPHYA, “Seakee** Of Planing Hull YAchts”, supported by Regione FVG, POR-FESR 2014–2020, Piano Operativo Regionale Fondo Europeo per lo Sviluppo Regionale, and partially supported by European Union Funding for Research and Innovation—Horizon 2020 Program—in the framework of European Research Council Executive Agency: H2020 ERC CoG 2015 AROMA-CFD project 681447 “Advanced Reduced Order Methods with Applications in Computational Fluid Dynamics” P.I. Gianluigi Rozza.

This work was also partially supported by Fondazione Cariplo–Regione Lombardia through the project “Verso nuovi strumenti di simulazione super veloci ed accurati basati sull’analisi isogeometrica”, within the program RST—rafforzamento.

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Authors and Affiliations

  1. Department of Civil Engineering and Architecture, Università degli Studi di Pavia, Pavia, Italy

    Fabrizio Garotta, Massimo Carraturo & Alessandro Reali

  2. mathLab, Mathematics Area, SISSA, Trieste, Italy

    Nicola Demo & Marco Tezzele

  3. mathLab, Mathematics Area, SISSA, Trieste, Italy

    Gianluigi Rozza

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  1. Fabrizio Garotta
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  2. Nicola Demo
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  3. Marco Tezzele
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  4. Massimo Carraturo
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  5. Alessandro Reali
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  6. Gianluigi Rozza
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Correspondence to Gianluigi Rozza .

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Editors and Affiliations

  1. Computational Multiscale, Sandia National Laboratories, Albuquerque, NM, USA

    Marta D'Elia

  2. Dept of Scientific Computing, Florida State Univ, Tallahassee, FL, USA

    Max Gunzburger

  3. SISSA mathLab, Mathematics Area, International School for Advanced Studie, Trieste, Italy

    Gianluigi Rozza

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Garotta, F., Demo, N., Tezzele, M., Carraturo, M., Reali, A., Rozza, G. (2020). Reduced Order Isogeometric Analysis Approach for PDEs in Parametrized Domains. In: D'Elia, M., Gunzburger, M., Rozza, G. (eds) Quantification of Uncertainty: Improving Efficiency and Technology. Lecture Notes in Computational Science and Engineering, vol 137 . Springer, Cham. https://doi.org/10.1007/978-3-030-48721-8_7

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