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Generalized B-Splines in Isogeometric Analysis

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Approximation Theory XV: San Antonio 2016 (AT 2016)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 201))

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Abstract

In this paper, we survey the use of generalized B-splines in isogeometric Galerkin and collocation methods. Generalized B-splines are a special class of Tchebycheffian B-splines and form an attractive alternative to standard polynomial B-splines and NURBS in both modeling and simulation. We summarize their definition and main properties, and we illustrate their use in a selection of numerical examples in the context of isogeometric analysis. For practical applications, we mainly focus on trigonometric and hyperbolic generalized B-splines.

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Acknowledgements

This work was partially supported by INdAM Gruppo Nazionale per il Calcolo Scientifico and by the MIUR “Futuro in Ricerca 2013” Program through the project “DREAMS” (RBFR13FBI3).

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Authors and Affiliations

  1. Department of Mathematics, University of Rome “Tor Vergata”, Via della Ricerca Scientifica, 00133, Rome, Italy

    Carla Manni & Hendrik Speleers

  2. Department of Mathematics, University of Turin, Via Carlo Alberto 10, 10123, Turin, Italy

    Fabio Roman

Authors
  1. Carla Manni
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  2. Fabio Roman
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  3. Hendrik Speleers
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Correspondence to Carla Manni .

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Editors and Affiliations

  1. Department of Applied Mathematics and Statistics, Colorado School of Mines, Golden, Colorado, USA

    Gregory E. Fasshauer

  2. Department of Mathematics, Vanderbilt University , Nashville, Tennessee, USA

    Larry L. Schumaker

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Manni, C., Roman, F., Speleers, H. (2017). Generalized B-Splines in Isogeometric Analysis . In: Fasshauer, G., Schumaker, L. (eds) Approximation Theory XV: San Antonio 2016. AT 2016. Springer Proceedings in Mathematics & Statistics, vol 201. Springer, Cham. https://doi.org/10.1007/978-3-319-59912-0_12

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