Polynomial splines over locally refined box-partitions

By T. Dokken, T. Lyche, Kjell Fredrik Pettersen. Computer Aided Geometric Design, 2013

411 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/fe2ccb263da54967d83d9fdff90968ed6fa7e89a

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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.”
Digital Twin: Values, Challenges and Enablers From a Modeling Perspective (2019, methodology): “One popular method for local reﬁnement is the Locally Reﬁned B-splines (LR B-Splines), see [85] and [86].”
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].”
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”
Conformal solid T-spline construction from boundary T-spline representations (2013, methodology): “In addition, the presented method is not restricted to NURBS and T-splines, it can also apply to models using Locally Refined B-splines [4].”
Mathematical analysis of variational isogeometric methods* (2014, background): “LRsplines (Dokken et al. 2013) and hierarchical splines (Vuong et al. 2011) were proposed more recently in the isogeometric literature, and represent a valid alternative to T-splines.”
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].”