A hierarchical approach to adaptive local refinement in isogeometric analysis

By Anh-Vu Vuong, Carlotta Giannelli, Bert Jüttler, Bernd Simeon. 2011

466 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/7c3862d9c10ef6a4d7860d90b63c2c580b2afb03

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Extended isogeometric analysis based on PHT‐splines for crack propagation near inclusions (2017, unknown): “Bi = [ Ri,x1 0 0 Ri,x2 Ri,x2 Ri,x1 ] , Bi = [ (Ri),x1 H 0 0 (Ri),x2 H (Ri),x2 H (Ri),x1 H ] , (28)”
THB-splines: The truncated basis for hierarchical splines (2012, methodology): “In particular, the modified support definition (2) — firstly considered in [20] — allows for refinement close to ∂Ω, which was not covered by the original construction presented in [11].”
Isogeometric Collocation: Cost Comparison with Galerkin Methods and Extension to Adaptive Hierarchical NURBS Discretizations (2013, methodology): “For hierarchical refinement in the framework of the Galerkin method (see for example [122,69,70]), these problems do not occur.”
A new isogeometric topology optimization using moving morphable components based on R-functions and collocation schemes (2018, methodology): “Many researchers devote to using various new modeling techniques, such as T-splines [33,34], hierarchical B-Splines [35,36] in the IGA and apply it to the fluid, fluid–solid interaction [37,38], beams and shells [39–42], fracture [43] and many other mechanical analysis fields.”
Image-based goal-oriented adaptive isogeometric analysis with application to the micro-mechanical modeling of trabecular bone (2015, background): “[12,23] for details, including a proof of global linear independence of H p.”
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].”
An Isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and T-spline CAD surfaces (2012, methodology): “A straightforward approach, introduced for B-spline FEA by Kraft [33] and Höllig [35] and recently extended to isogeometric analysis by Vuong and coworkers [37], is the application of the two-scale relation Equation (10) to all basis functions with support in the knot span element under consideratio”
Phase‐field modeling and simulation of fracture in brittle materials with strongly anisotropic surface energy (2015, background): “However, recent advances in T-splines [51] and hierarchical B-splines [52] alleviate the rigidity of these methods and may soon become accessible in 3D [53].”
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 contact: a review (2014, methodology): “Multivariate B-splines are generated through the tensor product of univariate B-splines.”
Divergence-conforming discretization for Stokes problem on locally refined meshes using LR B-splines (2015, background): “For T-splines consider [5, 16, 33, 37, 38], for Hierarchical B-splines consider [30, 39, 8, 34], and for LR-splines see [25, 27].”
Isogeometric analysis: An overview and computer implementation aspects (2012, unknown): “The idea is based on the fact that any B-splines basis can be written as a linear combination of Bernstein polynomials.”