Efficient computation of the minimum of shape quality measures on curvilinear finite elements

Amaury Johnen 1, 2 Christophe Geuzaine 2 Thomas Toulorge 3 Jean-François Remacle 1
1 Institute of Mechanics, Materials and Civil Engineering Université catholique de Louvain
2 Department of Electrical Engineering and Computer Science
3 CEMEF - Centre de Mise en Forme des Matériaux
Abstract : We present a method for computing robust shape quality measures defined for finite elements of any order and any type, including curved pyramids. The measures are heuristically defined as the minimum of the pointwise quality of curved elements. Three pointwise qualities are considered: the ICN that is related to the conditioning of the stiffness matrix for straight-sided simplicial elements, the scaled Jacobian that is defined for quadrangles and hexahedra, and a new shape quality that is defined for triangles and tetrahedra. The computation of the minimum of the pointwise qualities is based on previous work presented by Johnen et al. (2013) and Johnen and Geuzaine (2015) and is very efficient. The key feature is to expand polynomial quantities into Bézier bases which allow to compute sharp bounds on the minimum of the pointwise quality measures.
Keywords : Finite element method Finite element mesh Quality of curved elements Bézier basis
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https://hal-mines-paristech.archives-ouvertes.fr/hal-01784552
Contributeur : Magalie Prudon <>
Soumis le : jeudi 3 mai 2018 - 15:41:48
Dernière modification le : lundi 12 novembre 2018 - 10:54:31

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Amaury Johnen, Christophe Geuzaine, Thomas Toulorge, Jean-François Remacle. Efficient computation of the minimum of shape quality measures on curvilinear finite elements. Computer-Aided Design, Elsevier, 2018, pp.In Press. ⟨10.1016/j.cad.2018.03.001⟩. ⟨hal-01784552⟩

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