ISOGEOMETRIC COLLOCATION METHODS

By Ferdinando Auricchio, L. Beirão da Veiga, Thomas J. R. Hughes, Alessandro Reali, Giancarlo Sangalli. 2010

399 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/b9259eb819163b509c9f506e29069876e9111745

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In Computational Mechanics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Isogeometric analysis: An overview and computer implementation aspects (2012, background): “(iv) In an attempt to compete with low order FEs with one-point quadrature that are extensively used in industrial applications, isogeometric collocation methods were developed [90, 91].”
Three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS (2012, methodology): “(2009) for an application to isogeometric analysis in the context of the boundary element method and Aurrichio et al. (2010) for further applications in addition to the use of Demko abscissae.”
Isogeometric collocation for three-dimensional geometrically exact shear-deformable beams (2016, methodology): “IGA-C is a new promising method introduced in [23] based on the discretization of the strong form of the governing equations.”
Meshfree Methods: Progress Made after 20 Years (2017, neutral): “…2004); (cid:129) GRKCM: gradient RKCM (Chi et al. 2013); (cid:129) HPC: hp clouds (Duarte and Oden 1996b, a); (cid:129) IGC: isogeometric collocation (Auricchio et al. 2010); (cid:129) IGA: isogeometric analysis (Cottrell et al. 2009; Hughes et al. 2005); (cid:129) KC: kernel contact (Chi et al.…”
Isogeometric boundary element analysis using unstructured T-splines (2013, methodology): “Collocation at Greville abscissae has been shown to be an accurate choice in the context of collocated isogeometric boundary element [63, 64] and finite element methods [97, 98].”
Mathematical analysis of variational isogeometric methods* (2014, methodology): “Finally, again thanks to the regularity of splines, an isogeometric collocation method may be implemented, as proposed by Auricchio et al. (2010b) and Schillinger et al. (2013), for example, although its mathematical understanding is still incomplete.”
Fast formation and assembly of finite element matrices with application to isogeometric linear elasticity (2019, methodology): “Firstly, collocating the strong form of the equations [4, 5, 21] is a 35 viable alternative to the Galerkin method that decreases the formation and assembly time by orders of magnitude at the expense of decreased accuracy per degree of freedom and sub-optimal convergence rates [42].”
Integration by interpolation and look-up for Galerkin-based isogeometric analysis (2015, methodology): “Consequently, our method restores the appeal of the Galerkin approach by making its performance similar to the recently established isogeometric collocation method [1,19,29].”