NURBS-Enhanced Finite Element Method (NEFEM)

Sevilla, Rubén; Fernández‐Méndez, Sonia; Huerta, Antonio

doi:10.1007/s11831-011-9066-5

Cited by 123 publications

(120 citation statements)

References 88 publications

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“…Nevertheless, p-FEM still suffers the same lack of consistency as isoparametric FEM, due to the definition of the polynomial shape functions in the reference element I, with local coordinates ξ. This is not the case for the recently proposed NEFEM [3].…”

Section: Exact Boundary Representationmentioning

confidence: 73%

“…This section recalls the basics of two formulations considering an exact boundary representation, p-FEM [1,4] and NEFEM [3]. In order to simplify the presentation and without loss of generality, curved physical subdomains, Ω e , are assumed to be triangles with one curved edge.…”

Section: Exact Boundary Representationmentioning

confidence: 99%

“…For the other direction, λ, no exact integration is feasible with standard quadratures due to the rational definition of the NURBS boundary. Numerical experiments reveal that Gauss-Legendre quadratures are a competitive choice in front of other quadrature rules such as trapezoidal and Simpson composite rules or Romberg's integration, see [3]. Numerical examples in Section 3.1 show the influence of the number of integration points in the accuracy of NEFEM computations.…”

Section: Exact Boundary Representationmentioning

confidence: 99%

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Comparison of high‐order curved finite elements

Sevilla

Fernández‐Méndez

Huerta

2011

Numerical Meth Engineering

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Several finite element techniques used in domains with curved boundaries are discussed and compared, with particular emphasis in two issues: the exact boundary representation of the domain and the consistency of the approximation. The influence of the number of integration points in the accuracy of the computation is also studied. Two dimensional numerical examples, solved with continuous and discontinuous Galerkin formulations, are used to test and compare all these methodologies. In every example shown, the recently proposed NURBS-enhanced finite element method (NEFEM) provides the maximum accuracy for a given spatial discretization, at least one order of magnitude more accurate than classical isoparametric finite element methods (FEM). Moreover, NEFEM outperforms Cartesian FEM and p-FEM, stressing the importance of the geometrical model as well as the relevance of a consistent approximation in finite element simulations.

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Section: Exact Boundary Representationmentioning

confidence: 73%

Section: Exact Boundary Representationmentioning

confidence: 99%

Section: Exact Boundary Representationmentioning

confidence: 99%

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Comparison of high‐order curved finite elements

Sevilla

Fernández‐Méndez

Huerta

2011

Numerical Meth Engineering

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“…We recall that the only available data regarding Ω 2 is the parametrization of the trimming curve that forms its boundary ∂Ω 2 . For the general case, existing techniques could be used to define a suitable quadrature rule: for instance, the standard sub-triangulation technique in the context of X-FEM [42], or the hierarchical element subdivision employed in the FCM [25,19,20], or the technique used in the NURBS Enhanced FEM [43]. Now, for most cases arising in the situation of geometric details, it seems that an exact NURBS domain may be simply constructed from the NURBS trimming curve by adding multiple interpolatory control points at the centre of the detail.…”

Section: Implementation: Computation Of the Interface Reaction Forcesmentioning

confidence: 99%

Local enrichment of NURBS patches using a non-intrusive coupling strategy: Geometric details, local refinement, inclusion, fracture

Bouclier

Passieux

Salaün

2016

Computer Methods in Applied Mechanics and Engineering

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OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in: http://oatao.univ-toulouse.fr/ Eprints ID : 14633 Highlights• We address the issue of modelling local phenomena in a NURBS patch with a global/local non-intrusive algorithm.• The approach provides simplicity and flexibility to treat any case of local enrichment in a NURBS patch.• We propose a strategy to handle non-conforming geometries.• We demonstrate the performance of the method on a range of two-dimensional linear elastic numerical examples. AbstractIn this work, we apply a non-intrusive global/local coupling strategy for the modelling of local phenomena in a NURBS patch. The idea is to consider the NURBS patch to be enriched as the global model. This results in a simple, flexible strategy: first, the global NURBS patch remains unchanged, which completely eliminates the need for costly re-parametrization procedures (even if the local domain is expected to evolve); then, easy merging of a linear NURBS code with any other existing robust codes suitable for the modelling of complex local behaviour is possible. The price to pay is the number of iterations of the non-intrusive solver but we show that this can be strongly reduced by means of acceleration techniques. The main development for NURBS is to be able to handle non-conforming geometries. Only slight changes in the implementation process, including the setting up of suitable quadrature rules for the evaluation of the interface reaction forces, are made in response to this issue. A range of numerical examples in two-dimensional linear elasticity are given to demonstrate the performance of the proposed methodology and its significant potential to treat any case of local enrichment in a NURBS patch simply.

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“…In practice this implies using NURBS to define the curved element faces, since any underlying CAD geometry is most likely represented with NURBS. A interesting isogeometric approach, referred to as the NURBS enhanced FE method (NEFEM) has recently been proposed by Sevilla, Fernández-Méndez, and Huerta [115] [114]. The NEFEM uses NURBS to define curved boundary faces such that they can conform exactly to a CAD definition, and NURBS to enhance the solution basis functions within each curved element.…”

Section: Isogeometric Approachesmentioning

confidence: 99%

Facilitating the Adoption of Unstructured High-Order Methods Amongst a Wider Community of Fluid Dynamicists

Vincent

Jameson

2011

Math. Model. Nat. Phenom.

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Abstract. Theoretical studies and numerical experiments suggest that unstructured high-order methods can provide solutions to otherwise intractable fluid flow problems within complex geometries. However, it remains the case that existing high-order schemes are generally less robust and more complex to implement than their low-order counterparts. These issues, in conjunction with difficulties generating high-order meshes, have limited the adoption of high-order techniques in both academia (where the use of low-order schemes remains widespread) and industry (where the use of low-order schemes is ubiquitous). In this short review, issues that have hitherto prevented the use of high-order methods amongst a non-specialist community are identified, and current efforts to overcome these issues are discussed. Attention is focused on four areas, namely the generation of unstructured high-order meshes, the development of simple and efficient time integration schemes, the development of robust and accurate shock capturing algorithms, and finally the development of high-order methods that are intuitive and simple to implement. With regards to this final area, particular attention is focused on the recently proposed flux reconstruction approach, which allows various well known high-order schemes (such as nodal discontinuous Galerkin methods and spectral difference methods) to be cast within a single unifying framework. It should be noted that due to the experience of the authors the review is directed somewhat towards aerodynamic applications and compressible flow. However, many of the discussions have a wider applicability. Moreover, the tone of the review is intended to be generally accessible, such that an extended scientific community can gain insight into factors currently pacing the adoption of unstructured high-order methods.

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NURBS-Enhanced Finite Element Method (NEFEM)

Cited by 123 publications

References 88 publications

Comparison of high‐order curved finite elements

Comparison of high‐order curved finite elements

Local enrichment of NURBS patches using a non-intrusive coupling strategy: Geometric details, local refinement, inclusion, fracture

Facilitating the Adoption of Unstructured High-Order Methods Amongst a Wider Community of Fluid Dynamicists

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