Efficient matrix computation for isogeometric discretizations with hierarchical B-splines in any dimension
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Publication:2060109
DOI10.1016/j.cma.2021.114210OpenAlexW3208271869MaRDI QIDQ2060109
Bert Jüttler, Maodong Pan, Felix Scholz
Publication date: 13 December 2021
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.2021.114210
complexityisogeometric analysishierarchical B-splinesassembling matriceslooking up and sum-factorizationspline projection
Numerical computation using splines (65D07) Numerical interpolation (65D05) Complexity and performance of numerical algorithms (65Y20)
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Cites Work
- Unnamed Item
- A simple algorithm for obtaining nearly optimal quadrature rules for NURBS-based isogeometric analysis
- THB-splines: The truncated basis for hierarchical splines
- GPU accelerated computation of the isogeometric analysis stiffness matrix
- Efficient quadrature for NURBS-based isogeometric analysis
- \(n\)-widths, sup-infs, and optimality ratios for the \(k\)-version of the isogeometric finite element method
- Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
- Effortless quasi-interpolation in hierarchical spaces
- Isogeometric analysis of structural vibrations
- Complexity of hierarchical refinement for a class of admissible mesh configurations
- Reduced Bézier element quadrature rules for quadratic and cubic splines in isogeometric analysis
- Isogeometric analysis: mathematical and implementational aspects, with applications
- Integration by interpolation and look-up for Galerkin-based isogeometric analysis
- Efficient matrix computation for tensor-product isogeometric analysis: the use of sum factorization
- Partial tensor decomposition for decoupling isogeometric Galerkin discretizations
- Matrix-free weighted quadrature for a computationally efficient isogeometric \(k\)-method
- Suitably graded THB-spline refinement and coarsening: towards an adaptive isogeometric analysis of additive manufacturing processes
- Sum factorization techniques in isogeometric analysis
- The surrogate matrix methodology: low-cost assembly for isogeometric analysis
- Adaptive isogeometric analysis on two-dimensional trimmed domains based on a hierarchical approach
- Fast formation of isogeometric Galerkin matrices via integration by interpolation and look-up
- Local (T)HB-spline projectors via restricted hierarchical spline fitting
- Mathematical foundations of isogeometric analysis. Abstracts from the workshop held July 14--20, 2019
- An efficient solver for space-time isogeometric Galerkin methods for parabolic problems
- Efficient matrix assembly in isogeometric analysis with hierarchical B-splines
- Quadrature rules in the isogeometric Galerkin method: state of the art and an introduction to weighted quadrature
- Efficient mass and stiffness matrix assembly via weighted Gaussian quadrature rules for B-splines
- Refinement algorithms for adaptive isogeometric methods with hierarchical splines
- The variational collocation method
- 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
- Low rank tensor methods in Galerkin-based isogeometric analysis
- Space-time isogeometric analysis of parabolic evolution problems
- Dispersion-minimizing quadrature rules for \(C^1\) quadratic isogeometric analysis
- A black-box low-rank approximation algorithm for fast matrix assembly in isogeometric analysis
- Approximation in FEM, DG and IGA: a theoretical comparison
- Hierarchical spline spaces: quasi-interpolants and local approximation estimates
- THB-splines: an effective mathematical technology for adaptive refinement in geometric design and 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
- Adaptive isogeometric methods with hierarchical splines: Error estimator and convergence
- ISOGEOMETRIC COLLOCATION METHODS
- Efficient Computer Manipulation of Tensor Products
- Adaptive IGAFEM with optimal convergence rates: Hierarchical B-splines
- Isogeometric Analysis
- Mathematical analysis of variational isogeometric methods
- Sharp error estimates for spline approximation: Explicit constants, n-widths, and eigenfunction convergence
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