Goal-adaptive Isogeometric Analysis with hierarchical splines

Kuru, G.; Verhoosel, Clemens V.; Zee, van der Kg Kristoffer; Brummelen, van Eh Harald

doi:10.1016/j.cma.2013.11.026

Cited by 68 publications

(63 citation statements)

References 42 publications

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“…However, to allow for adaptive refinement, several extensions of the B-spline model have recently emerged, e.g. analysis-suitable T-splines, 40,5 hierarchical splines, 45,26,32 or LR-splines 18,30 ; see also Refs. 31 and 28 for a comparison of (1.5)…”

Section: Adaptivity In Isogeometric Analysismentioning

confidence: 99%

Adaptive IGAFEM with optimal convergence rates: Hierarchical B-splines

Gantner

Haberlik

Praetorius

2017

Math. Models Methods Appl. Sci.

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We consider an adaptive algorithm for finite element methods for the isogeometric analysis (IGAFEM) of elliptic (possibly non-symmetric) second-order partial differential equations in arbitrary space dimension d ≥ 2. We employ hierarchical B-splines of arbitrary degree and different order of smoothness. We propose a refinement strategy to generate a sequence of locally refined meshes and corresponding discrete solutions. Adaptivity is driven by some weighted residual a posteriori error estimator. We prove linear convergence of the error estimator (respectively, the sum of energy error plus data oscillations) with optimal algebraic rates. Numerical experiments underpin the theoretical findings.

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Section: Adaptivity In Isogeometric Analysismentioning

confidence: 99%

Adaptive IGAFEM with optimal convergence rates: Hierarchical B-splines

Gantner

Haberlik

Praetorius

2017

Math. Models Methods Appl. Sci.

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“…[12,23] for details, including a proof of global linear independence of H p . Using the hierarchical basis (18) we can now create the finite dimensional approximation space for the primal problem (15) as…”

Section: Hierarchical Spline Discretizationmentioning

confidence: 99%

“…The second novelty of this work is the usage of goal-oriented adaptive analysis [22] in the context of the scan-based isogeometric finite cell method. This aspect of our work builds on the recent work in [23], where goaloriented isogeometric analysis is considered in the context of tensor-product B-splines. The usage of adaptive methods is of paramount importance in the context of three-dimensional scan-based geometric models, since manual refinement operations are impractical.…”

Section: Introductionmentioning

confidence: 99%

Image-based goal-oriented adaptive isogeometric analysis with application to the micro-mechanical modeling of trabecular bone

Verhoosel

Zwieten

Rietbergen

et al. 2015

Computer Methods in Applied Mechanics and Engineering

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104

166

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“…The application to other adaptive algorithms such as a goal-oriented hp-adaptive algorithm [32,35], adaptivity in a high continuity space [7,11,23], or adaptivity in time domain [10] is straightforward.…”

Section: Introductionmentioning

confidence: 99%

Goal-oriented adaptivity using unconventional error representations for the 1D Helmholtz equation

Darrigrand

Pardo

Muga

2015

Computers & Mathematics with Applications

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In this work, the error of a given output functional is represented using bilinear forms that are different from those given by the adjoint problem. These representations can be employed to design novel h, p, and hp energy-norm and goal-oriented adaptive algorithms. Numerical results in 1D show that, for wave propagation problems, the advantages of this new representation are notorious when selecting the Laplace equation as the dual problem. Specifically, the upper bounds of the new error representation are sharper than the classical ones used in both energy-norm and goal-oriented adaptive methods, especially when the dispersion (pollution) error is significant.

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Goal-adaptive Isogeometric Analysis with hierarchical splines

Cited by 68 publications

References 42 publications

Adaptive IGAFEM with optimal convergence rates: Hierarchical B-splines

Adaptive IGAFEM with optimal convergence rates: Hierarchical B-splines

Image-based goal-oriented adaptive isogeometric analysis with application to the micro-mechanical modeling of trabecular bone

Goal-oriented adaptivity using unconventional error representations for the 1D Helmholtz equation

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