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
N1 - Funding Information:
The authors wish to thank the reviewers for their constructive suggestions. Gang Xu is partially supported by the National Nature Science Foundation of China (Nos. 61004117, 61272390, 61272300), the Scientific Research Foundation for the Returned Overseas Chinese Scholars from State Education Ministry ([2012]1707), and the Open Project Program of the State Key Lab of CAD & CG (No. A1406), Zhejiang University. Timon Rabczuk is supported by the European Union Initial Training Network (ITN) INSIST from the Framework Programme 7 (No. 289361) “ Integrating Numerical Simulation and Geometric Design Technology ”.
Publisher Copyright:
© 2014, Springer-Verlag Berlin Heidelberg.
PY - 2014/10/8
Y1 - 2014/10/8
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
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 -