Efficient quadrature for NURBS-based isogeometric analysis

By Thomas J. R. Hughes, Alessandro Reali, Giancarlo Sangalli. 2010

559 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Computer Graphics and Computer-Aided Design

View Paper: https://www.semanticscholar.org/paper/daee2d9374c6e5e13e288fd3bd9d218127e254f6

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In Computational Mechanics

In Computational Theory and Mathematics

In Computer Graphics and Computer-Aided Design

Citations in the corpus

Isogeometric analysis of plane-curved beams (2016, methodology): “By referring to [3] for some guidelines about the number of Gauss points to be used for efficient quadrature, here we resort to a simple rule suggested by some numerical tests and validated by the numerical results presented in the next section.”
Efficient isogeometric NURBS-based solid-shell elements: Mixed formulation and B-method (2013, unknown): “[47] and Auricchio et al.”
Constitutive models for strongly curved beams in the frame of isogeometric analysis (2016, background): “[3] provide some guidelines about the choice of the number of Gauss points for an efficient quadrature rule.”
Three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS (2012, background): “[28] for a recent discussion of efficient quadrature schemes appropriate for isogeometric analysis.”
Isogeometric boundary element analysis using unstructured T-splines (2013, methodology): “In future work, we plan on developing adaptive quadrature schemes which properly account for nearly singular and singular integrals and which take advantage of the smoothness of the underlying T-spline basis [110].”
Optimal and reduced quadrature rules for tensor product and hierarchically refined splines in isogeometric analysis (2017, methodology): “3 Contributions of this work We continue the study initiated in [29] in search of optimal quadrature rules for tensor product NURBS and hierarchically refined splines in isogeometric analysis.”
The variational collocation method (2016, background): “Reduced quadrature rules have been extensively investigated in the field of finite elements and, in particular, in isogeometric methods [53, 54].”
A large deformation frictional contact formulation using NURBS‐based isogeometric analysis (2011, background): “[20] for a recent discussion of efficient quadrature schemes appropriate for isogeometric analysis.”
An isogeometric analysis approach to gradient damage models (2011, methodology): “Numerical integration of NURBS for analysis purposes was studied in [24] and remains an active topic of research.”