The generation of arbitrary order curved meshes for 3D finite element analysis

Xie, Zhong Qiu; Sevilla, Rubén; Hassan, O.; Morgan, K.

doi:10.1007/s00466-012-0736-4

Cited by 122 publications

(128 citation statements)

References 32 publications

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“…The a posteriori approach has been previously used with success for Bspline mappings [7,6,30,28,43], and for iso-parametric elements [44,32,34,48,16,12,33]. Next, we highlight the two main types of approaches to generate high-order tetrahedral meshes by means of an a posteriori approach.…”

Section: Related Workmentioning

confidence: 99%

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Distortion and quality measures for validating and generating high-order tetrahedral meshes

Gargallo-Peiró

Roca

Peraire

et al. 2014

Engineering with Computers

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A procedure to quantify the distortion (quality) of a high-order mesh composed of curved tetrahedral elements is presented. The proposed technique has two main applications. First, it can be used to check the validity and quality of a high-order tetrahedral mesh. Second, it allows the generation of curved meshes composed of valid and high-quality high-order tetrahedral elements. To this end, we describe a method to smooth and untangle high-order tetrahedral meshes simultaneously by minimizing the proposed mesh distortion. Moreover, we present a p-continuation procedure to improve the initial configuration of a high-order mesh for the optimization process. Finally, we present several results to illustrate the two main applications of the proposed technique.

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Section: Related Workmentioning

confidence: 99%

“…On the one hand, in [32,48] two techniques to generate curved meshes by means of a solid mechanics analogy are presented (non-linear and linear elasticity, respectively). On the other hand, the curving of the mesh in the a posteriori approach can also be achieved by the optimization of a distortion (quality) measure.…”

Section: Related Workmentioning

confidence: 99%

Distortion and quality measures for validating and generating high-order tetrahedral meshes

Gargallo-Peiró

Roca

Peraire

et al. 2014

Engineering with Computers

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“…Jacobian measure, that is a standard measure of the smoothness of the element representation mapping, see [57,35,36,37].…”

Section: High-order Curved Meshingmentioning

confidence: 99%

“…is widely used to assess the validity of the high-order mesh elements [57,35,36,37], and it quantifies the variation of the Jacobian of the representation mapping. In fact, it quantifies the linearity of the representation mapping, being 1 only for constant Jacobian matrices, that is, for linear elements.…”

Section: Validation Of the Smoothness Of The Representation Mappingmentioning

confidence: 99%

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A distortion measure to validate and generate curved high‐order meshes on CAD surfaces with independence of parameterization

Gargallo-Peiró

Roca

Peraire

et al. 2015

Numerical Meth Engineering

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A framework to validate and generate curved nodal high-order meshes on CAD surfaces is presented. The proposed framework is of major interest to generate meshes suitable for thin-shell and 3D finite element analysis with unstructured high-order methods. First, we define a distortion (quality) measure for high-order meshes on parameterized surfaces that we prove to be independent of the surface parameterization. Second, we derive a smoothing and untangling procedure based on the minimization of a regularization of the proposed distortion measure. The minimization is performed in terms of the parametric coordinates of the nodes to enforce that the nodes slide on the surfaces. Moreover, the proposed algorithm repairs invalid curved meshes (untangling), deals with arbitrary polynomial degrees (high-order), and handles with low-quality CAD parameterizations (independence of parameterization). Third, we use the optimization procedure to generate curved nodal high-order surface meshes by means of an a posteriori approach. Given a linear mesh, we increase the polynomial degree of the elements, we curve them to match the geometry, and we optimize the location of the nodes to ensure mesh validity. Finally, we present several examples to demonstrate the features of the optimization procedure, and to illustrate the surface mesh generation process.high-order methods; high-order mesh generation; quality measure; mesh optimization; curved elements; CAD ; parameterized surfaces 1

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A method for computing curved meshes via the linear elasticity analogy, application to fluid dynamics problems

Abgrall

Dobrzynski

Froehly

2014

Numerical Methods in Fluids

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SUMMARYWe propose and analyze an algorithm for the robust construction of curved meshes in two and three dimensions. The meshes are made of curved simplexes. The algorithm starts from a mesh made of straight simplexes, and using a linear elasticity analogy applied on well‐chosen data, one can generate a curved mesh. Note that if the initial mesh has a boundary layer, this method allows to conserve it on the final mesh. This algorithm is used on several airfoils in two and three dimensions, including a turbulent M6 wing. Copyright © 2014 John Wiley & Sons, Ltd.

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The generation of arbitrary order curved meshes for 3D finite element analysis

Cited by 122 publications

References 32 publications

Distortion and quality measures for validating and generating high-order tetrahedral meshes

Distortion and quality measures for validating and generating high-order tetrahedral meshes

A distortion measure to validate and generate curved high‐order meshes on CAD surfaces with independence of parameterization

A method for computing curved meshes via the linear elasticity analogy, application to fluid dynamics problems

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