Abstract
High-quality volumetric parameterization of computational domain plays an important role in three-dimensional isogeometric analysis. Reparameterization technique can improve the distribution of isoparametric curves/surfaces without changing the geometry. In this paper, using the reparameterization method, we investigate the high-quality construction of analysis-suitable NURBS volumetric parameterization. Firstly, we introduce the concept of volumetric reparameterization, and propose an optimal Möbius transformation to improve the quality of the isoparametric structure based on a new uniformity metric. Secondly, from given boundary NURBS surfaces, we present a two-stage scheme to construct the analysis-suitable volumetric parameterization: in the first step, uniformity-improved reparameterization is performed on the boundary surfaces to achieve high-quality isoparametric structure without changing the shape; in the second step, from a new variational harmonic metric and the reparameterized boundary surfaces, we construct the optimal inner control points and weights to achieve an analysis-suitable NURBS solid. Several examples with complicated geometry are presented to illustrate the effectiveness of proposed methods.
| Original language | English |
|---|---|
| Pages (from-to) | 1303-1313 |
| Number of pages | 11 |
| Journal | Computational Mechanics |
| Volume | 54 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - 2014 Jan 1 |
| Externally published | Yes |
Fingerprint
ASJC Scopus subject areas
- Computational Theory and Mathematics
- Mechanical Engineering
- Ocean Engineering
- Applied Mathematics
- Computational Mathematics
Cite this
High-quality construction of analysis-suitable trivariate NURBS solids by reparameterization methods. / Xu, Gang; Mourrain, Bernard; Galligo, André; Rabczuk, Timon.
In: Computational Mechanics, Vol. 54, No. 5, 01.01.2014, p. 1303-1313.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - High-quality construction of analysis-suitable trivariate NURBS solids by reparameterization methods
AU - Xu, Gang
AU - Mourrain, Bernard
AU - Galligo, André
AU - Rabczuk, Timon
PY - 2014/1/1
Y1 - 2014/1/1
N2 - High-quality volumetric parameterization of computational domain plays an important role in three-dimensional isogeometric analysis. Reparameterization technique can improve the distribution of isoparametric curves/surfaces without changing the geometry. In this paper, using the reparameterization method, we investigate the high-quality construction of analysis-suitable NURBS volumetric parameterization. Firstly, we introduce the concept of volumetric reparameterization, and propose an optimal Möbius transformation to improve the quality of the isoparametric structure based on a new uniformity metric. Secondly, from given boundary NURBS surfaces, we present a two-stage scheme to construct the analysis-suitable volumetric parameterization: in the first step, uniformity-improved reparameterization is performed on the boundary surfaces to achieve high-quality isoparametric structure without changing the shape; in the second step, from a new variational harmonic metric and the reparameterized boundary surfaces, we construct the optimal inner control points and weights to achieve an analysis-suitable NURBS solid. Several examples with complicated geometry are presented to illustrate the effectiveness of proposed methods.
AB - High-quality volumetric parameterization of computational domain plays an important role in three-dimensional isogeometric analysis. Reparameterization technique can improve the distribution of isoparametric curves/surfaces without changing the geometry. In this paper, using the reparameterization method, we investigate the high-quality construction of analysis-suitable NURBS volumetric parameterization. Firstly, we introduce the concept of volumetric reparameterization, and propose an optimal Möbius transformation to improve the quality of the isoparametric structure based on a new uniformity metric. Secondly, from given boundary NURBS surfaces, we present a two-stage scheme to construct the analysis-suitable volumetric parameterization: in the first step, uniformity-improved reparameterization is performed on the boundary surfaces to achieve high-quality isoparametric structure without changing the shape; in the second step, from a new variational harmonic metric and the reparameterized boundary surfaces, we construct the optimal inner control points and weights to achieve an analysis-suitable NURBS solid. Several examples with complicated geometry are presented to illustrate the effectiveness of proposed methods.
KW - Boundary reparameterization
KW - Isogeometric analysis
KW - Uniformity metric
KW - Volumetric parameterization
UR - http://www.scopus.com/inward/record.url?scp=84919439794&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84919439794&partnerID=8YFLogxK
U2 - 10.1007/s00466-014-1060-y
DO - 10.1007/s00466-014-1060-y
M3 - Article
AN - SCOPUS:84919439794
VL - 54
SP - 1303
EP - 1313
JO - Computational Mechanics
JF - Computational Mechanics
SN - 0178-7675
IS - 5
ER -