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

Lam H. Nguyen; Dominik Schillinger

doi:10.1016/j.cma.2016.09.036

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

Lam H. Nguyen, Dominik Schillinger

Civil, Environmental, and Geo- Engineering

Research output: Contribution to journal › Article › peer-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 language	English (US)
Pages (from-to)	720-740
Number of pages	21
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	316
DOIs	https://doi.org/10.1016/j.cma.2016.09.036
State	Published - 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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title = "A collocated isogeometric finite element method based on Gauss–Lobatto Lagrange extraction of splines",

abstract = "Generalizing the concept of B{\'e}zier 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.",

keywords = "Collocation, Gauss–Lobatto Lagrange extraction, Isogeometric analysis",

author = "Nguyen, {Lam H.} and Dominik Schillinger",

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/).",

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AU - Nguyen, Lam H.

AU - Schillinger, Dominik

N1 - 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/).

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N2 - 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.

AB - 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.

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