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Effective Integration of Sophisticated Operators in Isogeometric Analysis with igatools

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Isogeometric Analysis and Applications 2014

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 107))

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Abstract

igatools is a newly released library for operators assembly in isogeometric analysis. The library, which is object oriented designed and written in C++11, is general purpose, therefore it is not devoted to any specific application. In this paper we show that such a design makes igatools an effective tool in assembling isogeometric discretizations of sophisticated differential operators. This effectiveness will be demonstrated showing code snippets relating one-to-one with the operators written on paper. To embrace a wide audience, applications from nonlinear incompressible solid and fluid mechanics will be addressed. In both cases we are going to deal with mixed isogeometric formulations. The applicative nature of this paper will be stressed solving industrially relevant tests cases.

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Acknowledgements

The authors are grateful to C. Lovadina for the useful discussion. N. Cavallini and O. Weeger have been supported by the TERRIFIC project, European Community’s Seventh Framework Programme, Grant Agreement 284981 Call FP7-2011-NMP-ICT-FoF. In all the experiments in this paper we used linear algebra packages from deal.II [2, 3].

Author information

Authors and Affiliations

  1. Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, Trieste, Italy

    Nicola Cavallini

  2. Faculty of Mathematics, TU Kaiserslautern, 3049, 67653, Kaiserslautern, Germany

    Oliver Weeger

  3. Instituto de Matemática Aplicada del Litoral (IMAL), Consejo Nacional de Investigaciones científicas y técnicas (CONICET), Santa Fe, Argentina

    M. Sebastian Pauletti

  4. Istituto di Matematica Applicata e Tecnologie Informatiche (IMATI), Consiglio Nazionale delle Ricerche (CNR), Pavia, Italy

    Massimiliano Martinelli

  5. Dipartimento di Ingegneria Civile ed Architettura, Università degli Studi di Pavia, Via Ferrata 3, 27100, Pavia, Italy

    Pablo Antolín

Authors
  1. Nicola Cavallini
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  2. Oliver Weeger
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  3. M. Sebastian Pauletti
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  4. Massimiliano Martinelli
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  5. Pablo Antolín
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Corresponding author

Correspondence to Nicola Cavallini .

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Editors and Affiliations

  1. Johannes Kepler Universität Linz Institut für Angewandte Geometrie, Linz, Austria

    Bert Jüttler

  2. Technische Universität Kaiserslautern Fachbereich Mathematik, Kaiserslautern, Germany

    Bernd Simeon

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Cavallini, N., Weeger, O., Pauletti, M.S., Martinelli, M., Antolín, P. (2015). Effective Integration of Sophisticated Operators in Isogeometric Analysis with igatools . In: Jüttler, B., Simeon, B. (eds) Isogeometric Analysis and Applications 2014. Lecture Notes in Computational Science and Engineering, vol 107. Springer, Cham. https://doi.org/10.1007/978-3-319-23315-4_9

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