Fast formation of isogeometric Galerkin matrices by weighted quadrature
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Publication:2308985
DOI10.1016/j.cma.2016.09.013zbMath1439.65012arXiv1605.01238OpenAlexW2346926571MaRDI QIDQ2308985
Francesco Calabrò, Giancarlo Sangalli, Mattia Tani
Publication date: 6 April 2020
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1605.01238
Numerical computation using splines (65D07) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical integration (65D30)
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Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Tensor Decompositions and Applications
- A simple algorithm for obtaining nearly optimal quadrature rules for NURBS-based isogeometric analysis
- \textsc{GeoPDEs}: a research tool for isogeometric analysis of PDEs
- GPU accelerated computation of the isogeometric analysis stiffness matrix
- Explicit Gaussian quadrature rules for \(C^1\) cubic splines with symmetrically stretched knot sequences
- A new design for the implementation of isogeometric analysis in Octave and Matlab: GeoPDEs 3.0
- Some estimates for \(h\)-\(p\)-\(k\)-refinement in isogeometric analysis
- Efficient quadrature for NURBS-based isogeometric analysis
- Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
- Gaussian quadrature for splines via homotopy continuation: rules for \(C^2\) cubic splines
- A practical guide to splines
- Reduced Bézier element quadrature rules for quadratic and cubic splines in isogeometric analysis
- Integration by interpolation and look-up for Galerkin-based isogeometric analysis
- Variationally consistent domain integration for isogeometric analysis
- Selective and reduced numerical integrations for NURBS-based isogeometric analysis
- Efficient matrix computation for tensor-product isogeometric analysis: the use of sum factorization
- Bernstein-Bézier finite elements on tetrahedral-hexahedral-pyramidal partitions
- Optimal quadrature rules for odd-degree spline spaces and their application to tensor-product-based isogeometric analysis
- Isogeometric collocation: cost comparison with Galerkin methods and extension to adaptive hierarchical NURBS discretizations
- Computation of quadrature rules for integration with respect to refinable functions on assigned nodes
- Isogeometric Preconditioners Based on Fast Solvers for the Sylvester Equation
- Matrix Generation in Isogeometric Analysis by Low Rank Tensor Approximation
- A Nonlinear Optimization Procedure for Generalized Gaussian Quadratures
- Bernstein–Bézier Finite Elements of Arbitrary Order and Optimal Assembly Procedures
- Integrating Products of B-Splines
- Isogeometric Analysis
- Mathematical analysis of variational isogeometric methods
- Nonlinear Optimization, Quadrature, and Interpolation
- Generalized Gaussian Quadrature Rules for Systems of Arbitrary Functions
- Exploring Matrix Generation Strategies in Isogeometric Analysis
- ISOGEOMETRIC ANALYSIS: APPROXIMATION, STABILITY AND ERROR ESTIMATES FOR h-REFINED MESHES
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