Error-estimate-based adaptive integration for immersed isogeometric analysis

Divi, Sai C.; Verhoosel, Clemens V.; Auricchio, Ferdinando; Reali, Alessandro; Brummelen, E. Harald van

doi:10.1016/j.camwa.2020.03.026

Cited by 38 publications

(39 citation statements)

References 48 publications

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“…A myriad of advanced integration techniques has been developed to reduce the computational burden associated with the integration of trimmed elements; see, e.g., Refs. [42][43][44][45]. Nitsche's method [46] has been demonstrated to be a reliable technique to impose essential boundary conditions along immersed boundaries, e.g., [23,[47][48][49], and various techniques have been developed to construct a parametrization of immersed boundaries to impose boundary conditions [49][50][51][52].…”

Section: Introductionmentioning

confidence: 99%

Topology-preserving scan-based immersed isogeometric analysis

Divi

Verhoosel

Auricchio

et al. 2022

Computer Methods in Applied Mechanics and Engineering

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Section: Introductionmentioning

confidence: 99%

Topology-preserving scan-based immersed isogeometric analysis

Divi

Verhoosel

Auricchio

et al. 2022

Computer Methods in Applied Mechanics and Engineering

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“…For all E ∈ E act h , let K E be the element of Q h such that (E ∩ Γ N ) ⊂ ∂(K E ∩ Ω), and note that by the shape regularity of Q h , h K E h E . Then for the first term of (28), using the scaled trace inequality (12), properties ( 14) and ( 15) of the Scott-Zhang-type operator, and by the continuous extension property (21),…”

Section: An a Posteriori Error Estimator On Trimmed Geometriesmentioning

confidence: 99%

“…To obtain a unified end-to-end methodology between geometric design and analysis, it is thus crucial to properly address the challenges coming from the treatment of trimmed models in the analysis [6][7][8]. Several results have succeeded to overcome some of the issues arising from the analysis on trimmed geometries, such as the need for a reparametrization of the cut elements for integration purposes [9][10][11][12][13][14], or the need of stabilization techniques to recover the well-posedness of the differential problem and the accuracy of its numerical solution [15][16][17]. However, much work remains to be done.…”

Section: Introductionmentioning

confidence: 99%

An a posteriori error estimator for isogeometric analysis on trimmed geometries

Buffa¹,

Chanon²,

Vázquez³

2021

Preprint

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Trimming consists of cutting away parts of a geometric domain, without reconstructing a global parametrization (meshing). It is a widely used operation in computer aided design, which generates meshes that are unfitted with the described physical object. This paper develops an adaptive mesh refinement strategy on trimmed geometries in the context of hierarchical B-spline based isogeometric analysis. A residual a posteriori estimator of the energy norm of the numerical approximation error is derived, in the context of Poisson equation. The reliability of the estimator is proven, and the effectivity index is shown to be independent from the number of hierarchical levels and from the way the trimmed boundaries cut the underlying mesh. In particular, it is thus independent from the size of the active part of the trimmed mesh elements. Numerical experiments are performed to validate the presented theory.

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“…We provide a brief review of these types of methods below. For more complete short surveys of quadrature strategies for arbitrary geometries, see [14,15,16].…”

Section: Introductionmentioning

confidence: 99%

“…Because the boundary is approximated by straight-sided geometry, these methods can only achieve low-order convergence to the correct integral with respect to total number of quadrature points. Much work has been done on optimizing these low-order methods [16,19]. However, the fundamentally low convergence precludes the possibility of high accuracy integration.…”

Section: Introductionmentioning

confidence: 99%

High-accuracy mesh-free quadrature for trimmed parametric surfaces and volumes

Gunderman,

Weiss,

Evans

2021

Preprint

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This work presents a high-accuracy, mesh-free, generalized Stokes theorem-based numerical quadrature scheme for integrating functions over trimmed parametric surfaces and volumes. The algorithm relies on two fundamental steps: (1) We iteratively reduce the dimensionality of integration using the generalized Stokes theorem to line integrals over trimming curves, and (2) we employ numerical antidifferentiation in the generalized Stokes theorem using high-order quadrature rules. The scheme achieves exponential convergence up to trimming curve approximation error and has applications to computation of geometric moments, immersogeometric analysis, conservative field transfer between high-order curvilinear meshes, and initialization of multi-material simulations. We compare the quadrature scheme to commonly-used quadrature schemes in the literature and show that our scheme is much more efficient in terms of number of quadrature points used. We provide an open-source implementation of the scheme in MATLAB as part of QuaHOG, a software package for Quadrature of High-Order Geometries.

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Error-estimate-based adaptive integration for immersed isogeometric analysis

Cited by 38 publications

References 48 publications

Topology-preserving scan-based immersed isogeometric analysis

Topology-preserving scan-based immersed isogeometric analysis

An a posteriori error estimator for isogeometric analysis on trimmed geometries

High-accuracy mesh-free quadrature for trimmed parametric surfaces and volumes

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