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

• Published in: Computer aided design Vol. 103; pp. 24 - 33
• Main Authors: Johnen, A., Geuzaine, C., Toulorge, T., Remacle, J.-F.
• Format: Journal Article Web Resource
• Language: English
• Published: Amsterdam Elsevier Ltd 01.10.2018; Elsevier BV
• Subjects: Bézier basis; Curved elements; Efficient computation; Electrical & electronics engineering; Engineering, computing & technology; Finite element analysis; Finite element mesh; Finite element meshes; Finite element method; Heuristic; Ingénierie électrique & électronique; Ingénierie, informatique & technologie; Key feature; Measurement techniques; Point wise; Pyramids; Quality measures; Quality of curved elements; Shape quality; Sharp bounds; Stiffness matrix; Triangles; Finite element method; Finite element mesh; Quality of curved elements; Bézier basis
• ISSN: 0010-4485; 1879-2685
• DOI: 10.1016/j.cad.2018.03.001

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. •We present a new shape quality measure for straight-sided simplicial elements.•We present an algorithm to compute shape quality measures on curved elements.•We consider three shape quality measures (the new one, the scaled Jacobian and the ICN measure).•We show that the computation of the presented measures is efficient.