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

Bézier basis; Finite element mesh; Finite element method; Quality of curved elements; Stiffness matrix; Curved elements; Efficient computation; Finite element meshes; Key feature; Point wise; Quality measures; Shape quality; Sharp bounds

Abstract :

[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. 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. © 2018 Elsevier Ltd

Disciplines :

Electrical & electronics engineering

Author, co-author :

Johnen, Amaury ; Université de Liège - ULiège > Institut Montefiore > ACE

Geuzaine, Christophe ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Applied and Computational Electromagnetics (ACE)

Toulorge, Thomas; Cemef - Mines ParisTech, rue Claude Daunesse 1, Sophia-Antipolis, France

Remacle, Jean-François; Université Catholique de Louvain - UCL > Institute of Mechanics, Materials and Civil Engineering (iMMC), Avenue Georges Lemaitre 4, Louvain-la-Neuve, Belgium

Language :

English

Title :

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

Publication date :

2018

Journal title :

Computer-Aided Design

ISSN :

0010-4485

Publisher :

Elsevier Ltd

Volume :

103

Pages :

24-33

Peer reviewed :

Peer Reviewed verified by ORBi

Funders :

ASRF, Applied Scientific Research Fund; 635962, Horizon 2020; UCL, University College London; DLR, Deutsches Zentrum für Luft- und Raumfahrt; 1017074

Available on ORBi :

since 22 April 2021

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