[en] 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. Based on previous work presented by Johnen et al. (Journal of Computational Physics 233:359–372, 2013, [1]); Johnen and Geuzaine (Journal of Computational Physics 299:124–129, 2015, [2]), the computation of the minimum of the pointwise qualities is efficient. The key feature is to expand polynomial quantities into Bézier bases which allows to compute sharp bounds on the minimum of the pointwise quality measures.
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Johnen, A.; Institute of Mechanics, Materials and Civil Engineering (iMMC), Université catholique de Louvain, Louvain-la-Neuve, Belgium
Geuzaine, Christophe ; Université de Liège - ULiège > Montefiore Institute of Electrical Engineering and Computer Science
Toulorge, T.; Cenaero, Gosselies, Belgium
Remacle, J.-F.; Institute of Mechanics, Materials and Civil Engineering (iMMC), Université catholique de Louvain, Louvain-la-Neuve, Belgium
Language :
English
Title :
Quality Measures for Curvilinear Finite Elements
Publication date :
2021
Main work title :
Notes on Numerical Fluid Mechanics and Multidisciplinary Design
Publisher :
Springer Science and Business Media Deutschland GmbH
A. Johnen is mandated by the Belgian Fund for Scientific Research (F.R.S.-FNRS). This research project was funded in part by the Walloon Region under WIST 3 grant 1017074 (DOMHEX) and by TILDA project.
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