A collocated isogeometric finite element method based on Gauss–Lobatto Lagrange extraction of splines

Lam H. Nguyen, Dominik Schillinger

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

Generalizing the concept of Bézier extraction, we introduce an extraction operator that links C0 Gauss–Lobatto Lagrange functions with smooth splines. This opens the door for collocated isogeometric analysis that combines the accuracy of the Galerkin method with collocation-type formation and assembly procedures. We present the key ingredients of the technology, i.e. integration by parts and the weighted residual form, the interaction of Gauss–Lobatto Lagrange extraction with Gauss–Lobatto quadrature, and symmetrization with the ultra-weak formulation. We compare the new method with standard isogeometric Galerkin and isogeometric point-collocation methods for spline discretizations in three dimensions.

Original languageEnglish (US)
Pages (from-to)720-740
Number of pages21
JournalComputer Methods in Applied Mechanics and Engineering
Volume316
DOIs
StatePublished - Apr 1 2017

Bibliographical note

Funding Information:
We gratefully acknowledge support from the National Science Foundation (ACI-1565997). We also acknowledge the Minnesota Supercomputing Institute (MSI) of the University of Minnesota for providing computing resources that have contributed to the research results reported within this paper (https://www.msi.umn.edu/).

Keywords

  • Collocation
  • Gauss–Lobatto Lagrange extraction
  • Isogeometric analysis

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