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Quadrature Rules in the Isogeometric Galerkin Method: State of the Art and an Introduction to Weighted Quadrature

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Advanced Methods for Geometric Modeling and Numerical Simulation

Part of the book series: Springer INdAM Series ((SINDAMS,volume 35))

Abstract

In this paper we introduce the quadrature needed in the isogeometric Galerkin method. Quadrature rules affect the cost of the assembly of the discrete counterpart of the IGA method, so that the search for efficient quadrature is an active research topic. The focus of the first part is on a brief survey on the contributions available for the reduction of computational costs for such issue. We review the generalized Gaussian strategies and the reduced quadrature. Then we present the novelty of weighted quadrature, recently proposed by Calabrò, Sangalli and Tani for the efficient assembly. We detail the construction of such rules and give some examples. Finally, we end with some remarks on current work and further developments.

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Notes

  1. 1.

    Throughout the paper the constant C is in general different at each occurrence.

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”, Università degli Studi di Napoli “Federico II”, Naples, Italy

    Francesco Calabrò

  2. Dipartimento di Matematica, Università degli Studi di Pavia, Pavia, Italy

    Gabriele Loli, Giancarlo Sangalli & Mattia Tani

Authors
  1. Francesco Calabrò
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  2. Gabriele Loli
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  3. Giancarlo Sangalli
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  4. Mattia Tani
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Corresponding author

Correspondence to Francesco Calabrò .

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Editors and Affiliations

  1. Department of Mathematics and Computer Science "U. Dini", University of Florence, Florence, Italy

    Carlotta Giannelli

  2. Department of Mathematics, University of Rome Tor Vergata, Rome, Italy

    Hendrik Speleers

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Calabrò, F., Loli, G., Sangalli, G., Tani, M. (2019). Quadrature Rules in the Isogeometric Galerkin Method: State of the Art and an Introduction to Weighted Quadrature. In: Giannelli, C., Speleers, H. (eds) Advanced Methods for Geometric Modeling and Numerical Simulation. Springer INdAM Series, vol 35. Springer, Cham. https://doi.org/10.1007/978-3-030-27331-6_3

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