THB-splines: The truncated basis for hierarchical splines

By Carlotta Giannelli, Bert Jüttler, Hendrik Speleers. Computer Aided Geometric Design, 2012

540 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanical Engineering

View Paper: https://www.semanticscholar.org/paper/a858aa68da617ad9d41de021f6807cc422002258

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In Computational Mechanics

In Mechanical Engineering

Citations in the corpus

Blended B-spline construction on unstructured quadrilateral and hexahedral meshes with optimal convergence rates in isogeometric analysis (2018, unknown): “Across the interface of the two submeshes, the truncation mechanism [32] is used to connect them.”
A geometrically exact isogeometric Kirchhoff plate: Feature‐preserving automatic meshing and C1 rational triangular Bézier spline discretizations (2018, background): “Multiplication of LT to the second equation in Equation (12) and rearranging terms yields LTλ(i+1) = wLTLd(i+1) − wLTG + LTλ(i), (13) where w = 1 ε is the weight.”
Isogeometric Collocation: Cost Comparison with Galerkin Methods and Extension to Adaptive Hierarchical NURBS Discretizations (2013, methodology): “A further simplification of the method can be achieved by exploiting the idea of truncated hierarchical NURBS [70,78] in the transition regions.”
Smooth cubic spline spaces on unstructured quadrilateral meshes with particular emphasis on extraordinary points: Geometric design and isogeometric analysis considerations (2017, background): “It should be clear that the framework is directly applicable to other locally refinable spline technologies, such as LR-splines [14] or (T)HB-splines [15], as long as the following two conditions are met: 67”
Optimal and reduced quadrature rules for tensor product and hierarchically refined splines in isogeometric analysis (2017, methodology): “Figure 18 plots the accuracy in terms of the relative error in the H1 semi-norm versus the number of degrees of freedom for uniform mesh refinement and local refinement through hierarchical B-splines.”
Integration by interpolation and look-up for Galerkin-based isogeometric analysis (2015, methodology): “First, we will explore the extension of the IIL approach to the case of non-uniform knot vectors and to hierarchical splines [18,25,28,34].”
Divergence-conforming discretization for Stokes problem on locally refined meshes using LR B-splines (2015, methodology): “Several techniques have been proposed to address this, among others are T-splines [36, 35], Hierarchical B-splines [21, 26], Truncated Hierarchical Bsplines [22] and Locally Refined (LR) B-splines [15].”