Polynomial splines over hierarchical T-meshes

By J. Deng, Falai Chen, Xin Li, Chang Hu, Wei-hua Tong, Zhouwang Yang, Y. Feng. Graphical Models, 2008

367 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Graphics and Computer-Aided Design

View Paper: https://www.semanticscholar.org/paper/4b7b8c0443aa9e2c5a7e7059abfa761366f678b3

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In Computational Mechanics

In Computer Graphics and Computer-Aided Design

Citations in the corpus

A geometrically exact isogeometric Kirchhoff plate: Feature‐preserving automatic meshing and C1 rational triangular Bézier spline discretizations (2018, background): “Equations (15) and (16) can be used to solve the augmented Lagrangian system iteratively.”
Smooth cubic spline spaces on unstructured quadrilateral meshes with particular emphasis on extraordinary points: Geometric design and isogeometric analysis considerations (2017, background): “In a more recent work [36], some of the above mentioned problems are tackled by introducing C1 spline elements in the neighborhood of extraordinary points, albeit only in the context of PHT splines [13].”
T-spline based XIGA for fracture analysis of orthotropic media (2015, neutral): “Another alternative to T-splines are PHT-splines or RHT-splines that are based on hierarchical T-meshes [57].”
Rotation free isogeometric thin shell analysis using PHT-splines (2011, methodology): “[31], a basis function is represented by specifying its 16 Bézier ordinates in every cell within the support of the basis functions.”
Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids (2011, methodology): “As already mentioned in [21], the construction of PHT-spline basis functions is initiated from C continuous cubic B-splines.”
A two-dimensional Isogeometric Boundary Element Method for elastostatic analysis (2012, background): “[6,13] which have the attractive property that refinement can be achieved locally compared to the expensive global refinement achieved with NURBS due to the tensor product nature of the approximation.”
Isogeometric boundary-element analysis for the wave-resistance problem using T-splines (2014, methodology): “These alternatives may include hierarchical splines [25], T-splines [26,27], PHT-splines (Polynomial Splines over Hierarchical T-meshes) [28] and LR-splines (Locally Refined splines) [29].”
Isogeometric analysis: An overview and computer implementation aspects (2012, positive): “PHT-splines (polynomial spline over hierarchical T-meshes) have been extended to rational splines and applied in [94, 95] to problems in elasticity for continua and thin structures.”
THB-splines: The truncated basis for hierarchical splines (2012, background): “T–splines [17, 18] and PHT–splines [2] are defined over T–meshes, where T–junctions between axis aligned segments are allowed.”
Blended B-spline construction on unstructured quadrilateral and hexahedral meshes with optimal convergence rates in isogeometric analysis (2018, positive): “With a C1-continuous construction in the vicinity of extraordinary points in 2D, two methods were proposed based on degenerated bivariate Bézier patches [30]: one in the context of PHT-splines [31] with emphasis on refinability around extraordinary vertices [24], and the other from the isogeometric ”
Transfer learning enhanced physics informed neural network for phase-field modeling of fracture (2019, methodology): “For more information on modeling the geometry using NURBS and refinement using cross-insertion technique, we refer to [21, 22].”