<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" id="d1e2004" altimg="si2.gif"><mml:mi>h</mml:mi></mml:math>- and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" id="d1e2009" altimg="si267.gif"><mml:mi>p</mml:mi></mml:math>-adaptivity driven by recovery and residual-based error estimators for PHT-splines applied to time-harmonic acoustics

Videla, Javier; Anitescu, Cosmin; Khajah, Tahsin; Bordas, Stéphane P.A.; Atroshchenko, Elena

doi:10.1016/j.camwa.2018.12.026

Cited by 49 publications

(10 citation statements)

References 61 publications

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“…the requirement of iso-parametric approximation. In [15], GIFT was applied to problems of heat conduction and linear elasticity, in [18] -to time-harmonic acoustics, where it was shown that NURBS geometry and PHT-splines as solution basis yield optimal convergence rate and lead to computational savings in comparison with NURBS-based IGA and PHT-splines based IGA. Computational savings are associated with avoiding geometry refinement and utilizing adaptive local refinement of the solution.…”

Section: Discussionmentioning

confidence: 99%

“…These beneficial features made the recovered-based error estimator widely applied in engineering [22]. In [18] a comparison between residual-based and recovery-based error estimators was recently done in the context of the Helmholtz equation, leading in both cases to similar results. In this work, we propose a recovery-based error estimator based on the stress definition in the framework of the Kirchhoff-Love theory.…”

Section: A Posteriori Error Estimatormentioning

confidence: 99%

“…Application of GIFT for time harmonic acoustics is given in the work of Videla et al [18]. In the present work, we will pair NURBS geometries with a PHT-splines solution basis to model fracture mechanics problems under the Kirchhoff-Love plate theory.…”

Section: Geometry Independent Field Approximation (Gift)mentioning

confidence: 99%

“…Anitescu et al [12] proposed a recovery-based error estimator for PHT-splines based on 2D and 3D linear elasticity. This definition was extended by Videla et al [18] in the context of the Helmholtz equation. In the following section, the procedure to obtain the recovery-based error estimator is adapted to Kirchhoff-Love plate theory.…”

Section: Recovery-based Error Estimator and Adaptive Mesh Refinementmentioning

confidence: 99%

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Application of PHT-splines in bending and vibration analysis of cracked Kirchhoff–Love plates

Videla

Contreras

Nguyễn

et al. 2020

Computer Methods in Applied Mechanics and Engineering

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In this work, we present an eXtended Geometry Independent Field approximaTion (X-GIFT) formulation for cracked Kirchhoff-Love plates. The plate geometry is modelled by Non-Uniform Rational B-Splines (NURBS) while the solution is approximated by Polynomial Splines over Hierarchical T-meshes (PHT-splines) and enriched by the Heaviside function and crack tip asymptotic expansions. The adaptive refinement is driven by a recovery-based error estimator. The formulation is employed for bending and vibration analysis. We compare different strategies for refinement, enrichment and evaluation of fracture parameters. The obtained results are shown to be in a good agreement with the reference solutions.

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Section: Discussionmentioning

confidence: 99%

Section: A Posteriori Error Estimatormentioning

confidence: 99%

Section: Geometry Independent Field Approximation (Gift)mentioning

confidence: 99%

Section: Recovery-based Error Estimator and Adaptive Mesh Refinementmentioning

confidence: 99%

See 2 more Smart Citations

Application of PHT-splines in bending and vibration analysis of cracked Kirchhoff–Love plates

Videla

Contreras

Nguyễn

et al. 2020

Computer Methods in Applied Mechanics and Engineering

Self Cite

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“…Within this framework, NURBS are used as basis functions but are truncated. The performance of B-splines FEM and adaptive PHT-spline IGA for solving exterior time-harmonic acoustic problems were studied in [38,39]. In particular, it was shown that the pollution error is well controlled for a fixed discretization density and order of the basis functions p � 3.…”

Section: Introductionmentioning

confidence: 99%

Non Uniform Rational B-Splines and Lagrange approximations for time-harmonic acoustic scattering: accuracy and absorbing boundary conditions

Dsouza

Khajah

Antoine

et al. 2021

Mathematical and Computer Modelling of Dynamical Systems

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The paper aims to evaluate the performance of the Lagrange-based finite element method and the non-uniform rational B-splines isogeometric analysis of time-harmonic acoustic exterior scattering problems using high-order local absorbing boundary conditions, in particular based on the Karp's and Wilcox's far-field expansions. The analysis of accuracy and convergence of both methods is achieved by observing the effect of the order of the approximating polynomial, the number of degrees of freedom, the wave number, and the absorbing boundary conditions tuning parameters. It is concluded that, regardless of the polynomial order, IGA provides a higher accuracy per degree of freedom compared to the traditional Lagrange-based finite element method.

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Subdivision based isogeometric analysis for geometric flows

Pan

Rabczuk

Chen

2021

Numerical Meth Engineering

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We present a new isogeometric analysis (IGA) approach based on extended Loop subdivision scheme for solving various geometric flows defined on subdivision surfaces. The studied flows include the second-order, fourth-order, and sixth-order geometric flows, such as averaged mean curvature flow, constant mean curvature flow, and minimal mean-curvature-variation flow, which are generally derived by minimizing the associate energy functionals with L 2 -gradient flow respectively. The geometric flows are discretized by means of subdivision based IGA, where the finite element space is formulated by the limit form of the extended Loop subdivision for different initial control meshes. The basis functions, consisting of quartic box-splines corresponding to each subdivided control mesh, are utilized to represent the geometry exactly. For the cases of the evolution of open surfaces with any shape boundary, high-order continuous boundary conditions derived from the mixed variational forms of the geometric flows should be implemented to be consistent with the isogeometric concept. For time discretization, we adopt an adaptive semi-implicit Euler scheme. By several numerical experiments, we study the convergence behaviors of the proposed approach for solving the geometric flows with high-order boundary conditions. Moreover, the numerical results also show the accuracy and efficiency of the proposed method.

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h- and p-adaptivity driven by recovery and residual-based error estimators for PHT-splines applied to time-harmonic acoustics

Cited by 49 publications

References 61 publications

Application of PHT-splines in bending and vibration analysis of cracked Kirchhoff–Love plates

Application of PHT-splines in bending and vibration analysis of cracked Kirchhoff–Love plates

Non Uniform Rational B-Splines and Lagrange approximations for time-harmonic acoustic scattering: accuracy and absorbing boundary conditions

Subdivision based isogeometric analysis for geometric flows

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