Lagrange extraction and projection for NURBS basis functions: A direct link between isogeometric and standard nodal finite element formulations

Dominik Schillinger, Praneeth K. Ruthala, Lam H. Nguyen

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

Abstract

We introduce Lagrange extraction and projection that link a C0 nodal basis with a smooth B-spline basis. Our technology is equivalent to Bézier extraction and projection but offers an alternative implementation based on the interpolatory property of nodal basis functions. The Lagrange extraction operator can be constructed by simply evaluating B-spline basis functions at nodal points and eliminates the need for introducing Bernstein polynomials as new shape functions. The Lagrange projection operator is defined as the inverse of the Lagrange extraction operator and directly relates function values at nodal points to element-level B-spline coefficients of a local interpolant. For geometries based on polynomial B-splines, our technology allows the implementation of isogeometric analysis in standard nodal finite element codes with simple algorithms and minimal intrusion.

Original languageEnglish (US)
Pages (from-to)515-534
Number of pages20
JournalInternational Journal for Numerical Methods in Engineering
Volume108
Issue number6
DOIs
StatePublished - Nov 9 2016

Bibliographical note

Publisher Copyright:
Copyright © 2016 John Wiley & Sons, Ltd.

Keywords

  • Bézier extraction
  • Lagrange extraction
  • isogeometric analysis
  • local projection

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