Reduced Bézier element quadrature rules for quadratic and cubic splines in isogeometric analysis

By Dominik Schillinger, Shaikh Jahangir Hossain, Thomas J. R. Hughes. 2014

140 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanical Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/0f8670f7edc5d86dec7028ecd7e3acc5f00f2a03

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In Computational Mechanics

In Mechanical Engineering

In Mechanics of Materials

Citations in the corpus

Optimal and reduced quadrature rules for tensor product and hierarchically refined splines in isogeometric analysis (2017, methodology): “However, numerical evidence [44] suggest that these conditions may not be necessary.”
Integration by interpolation and look-up for Galerkin-based isogeometric analysis (2015, background): “A variety of reduced Bézier element quadrature rules for isogeometric discretizations of low degree have been investigated in [30].”
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].”
Reduced integration at superconvergent points in isogeometric analysis (2018, background): “The source term provided as in [4]: b(x, r ) = 16r2 sin(x) − 68 sin(x) + x(8r2 − 68) cos(x) (19)”
Fast formation and assembly of finite element matrices with application to isogeometric linear elasticity (2019, unknown): “Several other works have focussed on making Galerkin more efficient by employing specialized or reduced quadrature rules 40 [6, 8, 25, 27, 33, 34, 43] and employing fast formation routines such as sum factorization [3, 15, 22, 40] or table lookup [37].”
A parameter-free variational coupling approach for trimmed isogeometric thin shells (2017, background): “The accuracy of a discretized elastostatic boundary value problem predominantly depends on the accuracy of the lowest eigenvalues, which can be shown by a spectral representation of the solution coefficients [76].”