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

被引：3
|
作者：
Johnen, A. [1 ,2 ]
Geuzaine, C. [1 ]
Toulorge, T. [3 ]
Remacle, J. -F. [2 ]
机构：
[1] Univ Liege, Dept Elect Engn & Comp Sci, Grande Traverse 10, B-4000 Liege, Belgium
[2] Catholic Univ Louvain, Inst Mech Mat & Civil Engn iMMC, Ave Georges Lemaitre 4, B-1348 Louvain La Neuve, Belgium
[3] Cemef Mines ParisTech, Rue Claude Daunesse 1, F-06904 Sophia Antipolis, France
来源：
COMPUTER-AIDED DESIGN | 2018年 / 103卷
基金：
欧盟地平线“2020”;
关键词：
Finite element method; Finite element mesh; Quality of curved elements; Bezier basis; HEXAHEDRAL MESH GENERATION; P-VERSION; GEOMETRICAL VALIDITY; JACOBIAN MATRIX; INITIAL MESHES; CURVED MESHES; FRAMEWORK; DOMAINS; DECOMPOSITION; OPTIMIZATION;
D O I：
10.1016/j.cad.2018.03.001
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
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 Bezier bases which allow to compute sharp bounds on the minimum of the pointwise quality measures. (C) 2018 Elsevier Ltd. All rights reserved.
引用
收藏
页码：24 / 33
页数：10
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