Local refinement of analysis-suitable T-splines

Scott, Michael A.; Li, Xin; Sederberg, Thomas W.; Hughes, Thomas J.R.

doi:10.1016/j.cma.2011.11.022

Cited by 325 publications

(203 citation statements)

References 49 publications

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“…One of the most noteworthy is the development of new splines that enable local refinement: hierarchical B-splines and NURBS [13,14], LRB-splines [15], T-splines [16,17] and multigrid-based NURBS [18]. Among these strategies, T-splines seem to have gathered considerable momentum in both the computational geometry and analysis communities since they also appear suitable to address trimmed multi-patch geometries.…”

Section: Introductionmentioning

confidence: 99%

Local enrichment of NURBS patches using a non-intrusive coupling strategy: Geometric details, local refinement, inclusion, fracture

Bouclier

Passieux

Salaün

2016

Computer Methods in Applied Mechanics and Engineering

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OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in: http://oatao.univ-toulouse.fr/ Eprints ID : 14633 Highlights• We address the issue of modelling local phenomena in a NURBS patch with a global/local non-intrusive algorithm.• The approach provides simplicity and flexibility to treat any case of local enrichment in a NURBS patch.• We propose a strategy to handle non-conforming geometries.• We demonstrate the performance of the method on a range of two-dimensional linear elastic numerical examples. AbstractIn this work, we apply a non-intrusive global/local coupling strategy for the modelling of local phenomena in a NURBS patch. The idea is to consider the NURBS patch to be enriched as the global model. This results in a simple, flexible strategy: first, the global NURBS patch remains unchanged, which completely eliminates the need for costly re-parametrization procedures (even if the local domain is expected to evolve); then, easy merging of a linear NURBS code with any other existing robust codes suitable for the modelling of complex local behaviour is possible. The price to pay is the number of iterations of the non-intrusive solver but we show that this can be strongly reduced by means of acceleration techniques. The main development for NURBS is to be able to handle non-conforming geometries. Only slight changes in the implementation process, including the setting up of suitable quadrature rules for the evaluation of the interface reaction forces, are made in response to this issue. A range of numerical examples in two-dimensional linear elasticity are given to demonstrate the performance of the proposed methodology and its significant potential to treat any case of local enrichment in a NURBS patch simply.

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Section: Introductionmentioning

confidence: 99%

Local enrichment of NURBS patches using a non-intrusive coupling strategy: Geometric details, local refinement, inclusion, fracture

Bouclier

Passieux

Salaün

2016

Computer Methods in Applied Mechanics and Engineering

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“…This provides the capacity of making unstructured meshes and local refinements. For more details about the T-spline or NURBS theory, the reader is refereed to [47,55,[72][73][74][75].…”

Section: Associated To Each Vertexmentioning

confidence: 99%

“…Moreover, unlike the NURBS, T-splines allow local refinements and unstructured meshes this makes their use attractive for the engineering analyses. In this direction, Scott et al [55] and Li et al [56] formulated the analysis-suitable T-spline in which necessary mathematical properties of the basis (as linear independence) are guaranteed to be used in IGA. However, the implementation of T-spline in the IGA requires a more advanced development.…”

Section: Introductionmentioning

confidence: 99%

A 3d Isogeometrical Boundary Element Analysis for Non-Linear Gravity Wave Propagation

Maestre¹,

Pallarès²,

Cuesta³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. In this paper we describe a three-dimensional Isogeometric BEM in the time domain based on the T-spline and Non Uniform Rational B-Splines (NURBS) basis to study the free surface behavior. Traditionally, the Lagrange polynomials have been used to discretize the geometry and the BEMs variables. The Lagrange basis are discontinues across the elements although the physical variables are continuous. In dynamics problems with high mesh distortions this approach can produce numerical instabilities that can be quickly propagated. This problem could be overcome using T-spline or NURB basis. The main advantages of this approach are: (1) the control of the continuity and smoothness of the T-spline and NURBS basis, which makes the model numerically stable without the need of artificial smooth techniques;(2) the high order geometrical approximation by non-rational splines;(3) the refinement capabilities without affecting the geometry and BEM's variables; and (4) the direct integration with computer aid geometrical design tools. We use the concept of the Bézier extraction operation which provides an element point of view of the T-Spline and NURBS similar to the traditional finite element. The boundary integral Equation is solved at each time step by the GMRES algorithm and the time marching scheme is performed with a fourth-order Runge-Kutta method to update the model. Additionally, the hydrodynamic force is calculated by an auxiliary boundary equation. Some numerical benchmark examples are analysed to show the accuracy and the stability of the method 7967 J. Maestre, J. Pallarés and I. Cuesta

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“…In particular, the linear independence of the T-spline blending functions can be guaranteed only by considering a restricted subset of Tsplines [1,13,16]. In order to allow this, a more involved algorithm -which reduces, but still does not eliminate, the unwanted propagation of the refinement -has to be considered and has been studied in [16].…”

Section: Neverthelessmentioning

confidence: 99%

THB-splines: The truncated basis for hierarchical splines

Giannelli

Jüttler

Speleers

2012

Computer Aided Geometric Design

427

402

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The construction of classical hierarchical B-splines can be suitably modified in order to define locally supported basis functions that form a partition of unity. We will show that this property can be obtained by reducing the support of basis functions defined on coarse grids, according to finer levels in the hierarchy of splines. This truncation not only decreases the overlapping of supports related to basis functions arising from different hierarchical levels, but it also improves the numerical properties of the corresponding hierarchical basis -which is denoted as truncated hierarchical B-spline (THB-spline) basis. Several computed examples will illustrate the adaptive approximation behavior obtained by using a refinement algorithm based on THB-splines.

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Local refinement of analysis-suitable T-splines

Cited by 325 publications

References 49 publications

Local enrichment of NURBS patches using a non-intrusive coupling strategy: Geometric details, local refinement, inclusion, fracture

Local enrichment of NURBS patches using a non-intrusive coupling strategy: Geometric details, local refinement, inclusion, fracture

A 3d Isogeometrical Boundary Element Analysis for Non-Linear Gravity Wave Propagation

THB-splines: The truncated basis for hierarchical splines

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