Characterization of T-splines with reduced continuity order on T-meshes

Buffa, Annalisa; Cho, D.; Kumar, Mukesh

doi:10.1016/j.cma.2011.09.005

Cited by 20 publications

(13 citation statements)

References 28 publications

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“…Inspired by similar results for T-splines [5], we now test duplicate knot lines. The effect of splitting the elements using both double and triple knot lines is here shown in Figure 36 and 37.…”

Section: Resultsmentioning

confidence: 99%

“…Regarding adaptive refinement of isogeometric finite elements there have been some recent attempts using T-splines and hierarchical B-splines, see [5,7,21,22]. It is common to mark those elements (knotspan) with highest energy error and subdivide into into four new elements by inserting a cross (ignoring large aspect ratio elements for now) through the element center.…”

Section: Adaptive Refinement Of Isogeometric Finite Elementsmentioning

confidence: 99%

“…The synthetic case denoted Diagonal Refinement is chosen as it illustrates very well the spreading effect of the refinement schemes and has been addressed by other researchers in the isogeometric community ( [5,7,13]). The first Poisson example denoted L-shape is chosen as it has a point singularity at the boundary that causes reduced convergence rate when performing uniform refinement.…”

Section: Preliminariesmentioning

confidence: 99%

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Isogeometric analysis using LR B-splines

Johannessen

Kvamsdal

Dokken

2014

Computer Methods in Applied Mechanics and Engineering

241

165

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The recently proposed locally refined B-splines, denoted LR B-splines, by Dokken et al. [6] may have the potential to be a framework for isogeometric analysis to enable future interoperable computer aided design and finite element analysis. In this paper, we propose local refinement strategies for adaptive isogeometric analysis using LR B-splines and investigate its performance by doing numerical tests on well known benchmark cases. The theory behind LR B-spline is not presented in full details, but the main conceptual ingredients are explained and illustrated by a number of examples.

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Section: Resultsmentioning

confidence: 99%

Section: Adaptive Refinement Of Isogeometric Finite Elementsmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

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Isogeometric analysis using LR B-splines

Johannessen

Kvamsdal

Dokken

2014

Computer Methods in Applied Mechanics and Engineering

241

165

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“…Design and numerical benchmarking of isogeometric methods for advection dominated or reaction dominated problems can be found in [14,24,28] and [48].…”

Section: Remark 36mentioning

confidence: 99%

An Introduction to the Numerical Analysis of Isogeometric Methods

Veiga

Buffa

Sangalli

et al. 2016

SEMA SIMAI Springer Series

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This paper gives an introduction to isogeometric methods from a mathematical point of view, with special focus on some theoretical results that are part of the mathematical foundation of the method. The aim of this work is to serve as a complement to other existing references in the field, that are more engineering oriented, and to provide a reference that can be used for didactic purposes. We analyse variational techniques for the numerical resolutions of PDEs using isogeometric methods, that is, based on splines or NURBS, and we provide optimal approximation and error estimates for scalar elliptic problems. The theoretical results are demonstrated by some numerical examples. We also present the definition of structure-preserving discretizations with splines, a generalization of edge and face finite elements, also with approximation estimates and some numerical tests for time harmonic Maxwell equations in a cavity.

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“…Examples are T-splines [3,5], hierarchical splines [12,38], LR-splines [8,18], and splines on triangulations [17,34,35].…”

Section: Introductionmentioning

confidence: 99%

Optimizing domain parameterization in isogeometric analysis based on Powell–Sabin splines

Speleers

Manni

2015

Journal of Computational and Applied Mathematics

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Please cite this article as: H. Speleers, C. Manni, Optimizing domain parameterization in isogeometric analysis based on Powell-Sabin splines, Journal of Computational and Applied Mathematics (2015), http://dx. AbstractWe address the problem of constructing a high-quality parameterization of a given planar physical domain, defined by means of a finite set of boundary curves. We look for a geometry map represented in terms of Powell-Sabin B-splines. Powell-Sabin splines are C 1 quadratic splines defined on a triangulation, and thus the parameter domain can be any polygon.The geometry map is generated by the following three-step procedure. First, the shape of the parameter domain and a corresponding triangulation are determined, in such a way that its number of corners matches the number of corners of the physical domain. Second, the boundary control points related to the Powell-Sabin B-spline representation are chosen so that they parameterize the boundary curve of the physical domain. Third, the remaining inner control points are obtained by solving a nimble optimization problem based on the Winslow functional.The proposed domain parameterization procedure is illustrated numerically in the context of isogeometric Galerkin discretizations based on Powell-Sabin splines. It turns out that the flexibility rising from the generality of the parameter domain has a beneficial effect on the quality of the parameterization and also on the accuracy of the computed approximate solution.

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Characterization of T-splines with reduced continuity order on T-meshes

Cited by 20 publications

References 28 publications

Isogeometric analysis using LR B-splines

Isogeometric analysis using LR B-splines

An Introduction to the Numerical Analysis of Isogeometric Methods

Optimizing domain parameterization in isogeometric analysis based on Powell–Sabin splines

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