2015
DOI: 10.1002/nme.5162
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A distortion measure to validate and generate curved high‐order meshes on CAD surfaces with independence of parameterization

Abstract: 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… Show more

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Cited by 30 publications
(19 citation statements)
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References 58 publications
(126 reference statements)
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“…1(a)). For this reason, the 3D surface mesh is optimized maximizing the elemental quality presented in [12,13] and imposing the nodes position over the exact topography to avoid lost of real geometry representation, using the process presented in [14,15]. Fig.…”
Section: Hybrid Mesh Generationmentioning
confidence: 99%
See 1 more Smart Citation
“…1(a)). For this reason, the 3D surface mesh is optimized maximizing the elemental quality presented in [12,13] and imposing the nodes position over the exact topography to avoid lost of real geometry representation, using the process presented in [14,15]. Fig.…”
Section: Hybrid Mesh Generationmentioning
confidence: 99%
“…However, this iterative scheme diverged in some of the tested complex cases, even using relaxation methods. Herein, introducing (15) in (14) we rewrite the iterative problem in terms of U ∞ and we translate it into solving the non-linear equation…”
Section: Actuator Disc Modelmentioning
confidence: 99%
“…To overcome this drawback, we use the regularized distortion measure introduced in Escobar et al and Garanzha and Kaporin for linear elements, in which σ is replaced by hfalse(σfalse)=12()σ+σ2+4δ2, where δ is a small parameter that depends on the problem and can be calculated according to Escobar et al and Gargallo‐Peiró et al This regularization is also used for optimizing curved high‐order meshes. ()…”
Section: Surface Insertion Algorithmmentioning
confidence: 99%
“…In a standard high-order finite element formulation, measures involving the Jacobian of the isoparametric mapping have been extensively used [29,77], in particular the so-called scaled Jacobian. This measure only quantifies volumetric deformations and alternative measures that exploit different modes of deformation and account for shape, skewness and degeneracy of elements have only been recently considered [27,28]. However, it is worth noting that not all of these quality measures can be regarded as independent quantities.…”
Section: Mesh Quality Measuresmentioning
confidence: 99%
“…Next, the quality of the generated meshes in terms of different measures is studied, namely the measures defined in Equation (27) that are defined in terms of the invariants in Equation (17). The two anisotropic mesh quality measures Q 4 and Q 5 are dropped from the comparison because they are only valid for the transversely isotropic material model, which has been shown to produce low quality meshes in the examples considered.…”
Section: Mesh Around the Sd7003 Aerofoilmentioning
confidence: 99%