Dispersion-optimized quadrature rules for isogeometric analysis: Modified inner products, their dispersion properties, and optimally blended schemes

Vladimir Puzyrev*, Quanling Deng, Victor Calo

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

43 Scopus citations


This paper introduces optimally-blended quadrature rules for isogeometric analysis and analyzes the numerical dispersion of the resulting discretizations. To quantify the approximation errors when we modify the inner products, we generalize the Pythagorean eigenvalue theorem of Strang and Fix. The proposed blended quadrature rules have advantages over alternative integration rules for isogeometric analysis on uniform and non-uniform meshes as well as for different polynomial orders and continuity of the basis. The optimally-blended schemes improve the convergence rate of the method by two orders with respect to the fully-integrated Galerkin method. The proposed technique increases the accuracy and robustness of isogeometric analysis for wave propagation problems.

Original languageEnglish (US)
Pages (from-to)421-443
Number of pages23
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - Jun 15 2017
Externally publishedYes

Bibliographical note

Funding Information:
This publication was made possible in part by the CSIRO Professorial Chair in Computational Geoscience at Curtin University, a National Priorities Research Program grant 7-1482-1-278 from the Qatar National Research Fund (a member of The Qatar Foundation), and by the European Union's Horizon 2020 Research and Innovation Program of the Marie Sklodowska-Curie grant agreement No. 644202. The J. Tinsley Oden Faculty Fellowship Research Program at the Institute for Computational Engineering and Sciences (ICES) of the University of Texas at Austin has partially supported the visits of VMC to ICES. The Spring 2016 Trimester on “Numerical methods for PDEs”, organized with the collaboration of the Centre Emile Borel at the Institut Henri Poincare in Paris supported VMC's visit to IHP in October, 2016. The authors would like to thank J. Tinsley Oden and two anonymous reviewers for their constructive suggestions, which helped to improve the manuscript.

Publisher Copyright:
© 2017 Elsevier B.V.


  • Eigenvalue problem
  • Finite elements
  • Isogeometric analysis
  • Numerical dispersion
  • Quadrature
  • Wave propagation

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications


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