Bézier extraction and adaptive refinement of truncated hierarchical NURBS

Hennig, Paul; Müller, Sebastian; Kästner, Markus

doi:10.1016/j.cma.2016.03.009

Cited by 82 publications

(88 citation statements)

References 32 publications

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“…In detail, we use a Bézier extraction framework that has been developed to implement the THB‐spline basis in a standard finite element code . For this purpose we start from a multilevel nested mesh that results from uniform h ‐refinement and integrate the system matrices by applying Bézier extraction to active elements that contribute to the hierarchical approximation, Figure .…”

Section: Diffuse Formulation Of Embedded Interface Problemsmentioning

confidence: 99%

“…However, the application of the hℓ ‐adaptive refinement strategy, where the interface width ℓ and the element size h are reduced simultaneously, allows for an improved convergence to the sharp interface solution and a good resolution of the local stress and strain fields. For this purpose, an adaptive refinement strategy for truncated hierarchical (TH) B‐splines is applied …”

Section: Introductionmentioning

confidence: 99%

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A diffuse modeling approach for embedded interfaces in linear elasticity

et al. 2019

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In this contribution, we present a diffuse modeling approach to embed material interfaces into nonconforming meshes with a focus on linear elasticity. For this purpose, a regularized indicator function is employed that describes the distribution of the different materials by a scalar value. The material in the resulting diffuse interface region is redefined in terms of this indicator function and recomputed by a homogenization of the adjacent material parameters. The applied homogenization method fulfills the kinematic compatibility across the interface and the static equilibrium at the interface. In addition, an hℓ‐adaptive refinement strategy based on truncated hierarchical B‐spline is applied to provide an appropriate and efficient approximation of the diffuse interface region. We justify mathematically and demonstrate numerically that the applied approach leads to optimal convergence rates in the far field for one‐dimensional problems. A two‐dimensional example illustrates that the application of the hℓ‐adaptive refinement strategy allows for a clear reduction of the error in the near and far field and a good resolution of the local stress and strain fields at the interface. The use of a higher continuous B‐spline basis leads to efficient computations due to the higher continuity of the diffuse interface model.

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Section: Diffuse Formulation Of Embedded Interface Problemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A diffuse modeling approach for embedded interfaces in linear elasticity

et al. 2019

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“…The refinement is driven by a predictor‐corrector scheme . Adaptive methodologies for brittle fracture have also been proposed in the framework of isogeometric analysis …”

Section: Introductionmentioning

confidence: 99%

A hybridizable discontinuous Galerkin phase‐field model for brittle fracture with adaptive refinement

Muixí

Ferran

Fernández‐Méndez

2019

Numerical Meth Engineering

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Summary In this paper, we propose an adaptive refinement strategy for phase‐field models of brittle fracture, which is based on a novel hybridizable discontinuous Galerkin (HDG) formulation of the problem. The adaptive procedure considers standard elements and only one type of h‐refined elements, dynamically located along the propagating cracks. Thanks to the weak imposition of interelement continuity in HDG methods, and in contrast with other existing adaptive approaches, hanging nodes or special transition elements are not needed, which simplifies the implementation. Various numerical experiments, including one branching test, show the accuracy, robustness, and applicability of the presented approach to quasistatic phase‐field simulations.

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“…For adaptive refinement, the optimal convergence rate is obtained in the asymptotic limit . In general, the error level for adaptive refinement is lower than that for uniform refinement because adaptive refinement smoothens the stress gradient.…”

Section: Numerical Examplesmentioning

confidence: 99%

The role of Bézier extraction in adaptive isogeometric analysis: Local refinement and hierarchical refinement

Borst

Chen

2017

Numerical Meth Engineering

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SummaryWe present 2 adaptive refinement techniques, namely, adaptive local refinement and adaptive hierarchical refinement, for isogeometric analysis. An element-wise point of view is adopted, exploiting Bézier extraction, which facilitates the implementation of adaptive refinement in isogeometric analysis. Locally refined and hierarchical T-splines are used for the description of the geometry as well as for the approximation of the solution space in the analysis. The refinement is conducted with the aid of a subdivision operator, which is computed by again exploiting the Bézier extraction operator. The concept and algorithm of an element-based adaptive isogeometric analysis are illustrated.Numerical examples are given to examine the accuracy, the convergence, and the condition number.

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Bézier extraction and adaptive refinement of truncated hierarchical NURBS

Cited by 82 publications

References 32 publications

A diffuse modeling approach for embedded interfaces in linear elasticity

A diffuse modeling approach for embedded interfaces in linear elasticity

A hybridizable discontinuous Galerkin phase‐field model for brittle fracture with adaptive refinement

The role of Bézier extraction in adaptive isogeometric analysis: Local refinement and hierarchical refinement

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