Fast formation and assembly of finite element matrices with application to isogeometric linear elasticity

DOI10.1016/j.cma.2019.06.020zbMath1441.74244OpenAlexW2953761527MaRDI QIDQ1988213

R. R. Hiemstra, Francesco Calabrò, Thomas J. R. Hughes, Mattia Tani, Giancarlo Sangalli

Publication date: 16 April 2020

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2019.06.020

zbMATH Keywords

isogeometric analysisweighted quadraturesum factorizationcolumn assemblyrow assembly

Mathematics Subject Classification ID

Classical linear elasticity (74B05) Finite element methods applied to problems in solid mechanics (74S05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Computer-aided design (modeling of curves and surfaces) (65D17)

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Cites Work

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• Isogeometric collocation for elastostatics and explicit dynamics
• A simple algorithm for obtaining nearly optimal quadrature rules for NURBS-based isogeometric analysis
• Isogeometric divergence-conforming B-splines for the unsteady Navier-Stokes equations
• Finite element and NURBS approximations of eigenvalue, boundary-value, and initial-value problems
• GPU accelerated computation of the isogeometric analysis stiffness matrix
• Isogeometric boundary element analysis using unstructured T-splines
• Isogeometric shell analysis: the Reissner-Mindlin shell
• Efficient quadrature for NURBS-based isogeometric analysis
• Robustness of isogeometric structural discretizations under severe mesh distortion
• High order geometric methods with exact conservation properties
• Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows
• Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
• From \(h\) to \(p\) efficiently: implementing finite and spectral/hp element methods to achieve optimal performance for low- and high-order discretisations
• The role of continuity in residual-based variational multiscale modeling of turbulence
• Studies of refinement and continuity in isogeometric structural analysis
• A practical guide to splines
• Gauss quadrature for refineable weight functions
• Reduced Bézier element quadrature rules for quadratic and cubic splines in isogeometric analysis
• Isogeometric collocation: Neumann boundary conditions and contact
• Integration by interpolation and look-up for Galerkin-based isogeometric analysis
• Patient-specific isogeometric structural analysis of aortic valve closure
• Efficient matrix computation for tensor-product isogeometric analysis: the use of sum factorization
• Discrete spectrum analyses for various mixed discretizations of the Stokes eigenproblem
• The variational collocation method
• Optimal quadrature for univariate and tensor product splines
• Fast formation of isogeometric Galerkin matrices by weighted quadrature
• Optimal-order isogeometric collocation at Galerkin superconvergent points
• Optimal and reduced quadrature rules for tensor product and hierarchically refined splines in isogeometric analysis
• Reduced integration at superconvergent points in isogeometric analysis
• 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
• Duality and unified analysis of discrete approximations in structural dynamics and wave propagation: comparison of p-method finite elements with \(k\)-method NURBS
• Isogeometric finite element data structures based on Bézier extraction of NURBS
• Isogeometric finite element data structures based on Bézier extraction of T-splines
• Julia: A Fresh Approach to Numerical Computing
• ISOGEOMETRIC COLLOCATION METHODS
• Isogeometric Discrete Differential Forms in Three Dimensions
• Bernstein–Bézier Finite Elements of Arbitrary Order and Optimal Assembly Procedures
• Isogeometric Analysis
• ISOGEOMETRIC ANALYSIS: APPROXIMATION, STABILITY AND ERROR ESTIMATES FOR h-REFINED MESHES
• A General Algorithm for Nonnegative Quadrature Formulas
• Elasticity