Bézier projection: a unified approach for local projection and quadrature-free refinement and coarsening of NURBS and T-splines with particular application to isogeometric design and analysis
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Publication:1797969
DOI10.1016/j.cma.2014.07.014zbMath1425.65035arXiv1404.7155OpenAlexW2034297781MaRDI QIDQ1797969
K. Tew, D. C. Thomas, John A. Evans, Emily. J. Evans, Michael A. Scott
Publication date: 22 October 2018
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1404.7155
quasi-interpolationisogeometric analysisBézier extractionlocal projectionlocal refinement and coarseningspline reconstruction
Numerical computation using splines (65D07) Numerical smoothing, curve fitting (65D10) Computer-aided design (modeling of curves and surfaces) (65D17)
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Uses Software
Cites Work
- Unnamed Item
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- Isogeometric fluid structure interaction analysis with emphasis on non-matching discretizations, and with application to wind turbines
- Analysis-suitable T-splines are dual-compatible
- An isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and T-spline CAD surfaces
- Converting an unstructured quadrilateral mesh to a standard T-spline surface
- A hierarchical approach to adaptive local refinement in isogeometric analysis
- On linear independence of T-spline blending functions
- Convergence of an efficient local least-squares fitting method for bases with compact support
- Local refinement of analysis-suitable T-splines
- The Bernstein polynomial basis: a centennial retrospective
- THB-splines: The truncated basis for hierarchical splines
- Strongly stable bases for adaptively refined multilevel spline spaces
- Finite element and NURBS approximations of eigenvalue, boundary-value, and initial-value problems
- An isogeometric continuum shell element for non-linear analysis
- Isogeometric spline forests
- Acoustic isogeometric boundary element analysis
- Isogeometric large deformation frictionless contact using T-splines
- Isogeometric boundary element analysis using unstructured T-splines
- From NURBS to NURPS geometries
- Isogeometric analysis of trimmed NURBS geometries
- On the degree elevation of Bernstein polynomial representation
- Integrals of Bernstein polynomials: an application for the solution of high even-order differential equations
- Quasi-interpolation in isogeometric analysis based on generalized B-splines
- Generalized B-splines as a tool in isogeometric analysis
- Isogeometric analysis using T-splines
- Adaptive isogeometric analysis by local \(h\)-refinement with T-splines
- Analysis-aware modeling: understanding quality considerations in modeling for isogeometric analysis
- \(n\)-widths, sup-infs, and optimality ratios for the \(k\)-version of the isogeometric finite element method
- Knot removal for B-spline curves
- A phase-field description of dynamic brittle fracture
- Isogeometric analysis with Powell-Sabin splines for advection-diffusion-reaction problems
- Isogeometric methods for computational electromagnetics: B-spline and T-spline discretizations
- Trigonometric generalized T-splines
- Degree elevation of B-spline curves
- A fast and accurate algorithm for solving Bernstein-Vandermonde linear systems
- Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
- Isogeometric analysis of structural vibrations
- Studies of refinement and continuity in isogeometric structural analysis
- Near-best univariate spline discrete quasi-interpolants on nonuniform partitions
- The dual basis functions for the Bernstein polynomials
- Least squares approximation of Bézier coefficients provides best degree reduction in the \(L_2\)-norm
- Polynomial degree reduction in the \(L_2\)-norm equals best Euclidean approximation of Bézier coefficients
- Bases of T-meshes and the refinement of hierarchical B-splines
- Isogeometric boundary-element analysis for the wave-resistance problem using T-splines
- An arbitrary Lagrangian-Eulerian finite element method for transient dynamic fluid-structure interactions
- Spline approximation by quasiinterpolants
- Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces
- Polynomial splines over locally refined box-partitions
- A unified matrix representation for degree reduction of Bézier curves
- Some properties of LR-splines
- Modified T-splines
- Isogeometric collocation: cost comparison with Galerkin methods and extension to adaptive hierarchical NURBS discretizations
- On calculating with B-splines
- Fast degree elevation and knot insertion for B-spline curves
- Isogeometric structural shape optimization
- ANALYSIS-SUITABLE T-SPLINES OF ARBITRARY DEGREE: DEFINITION, LINEAR INDEPENDENCE AND APPROXIMATION PROPERTIES
- An isogeometric analysis approach to gradient damage models
- Isogeometric finite element data structures based on Bézier extraction of NURBS
- An isogeometric approach to cohesive zone modeling
- Isogeometric finite element data structures based on Bézier extraction of T-splines
- A generalized finite element formulation for arbitrary basis functions: From isogeometric analysis to XFEM
- CHARMS
- Isogeometric Analysis
- On the Numerical Condition of Bernstein-Bezier Subdivision Processes
- Algorithms and Data Structures for Truncated Hierarchical B–splines
- Analysis-suitable T-splines: Characterization, refineability, and approximation
- ISOGEOMETRIC ANALYSIS: APPROXIMATION, STABILITY AND ERROR ESTIMATES FOR h-REFINED MESHES
- Polynomial least squares fitting in the Bernstein basis