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 |
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Pages (from-to) | 1303-1313 |
Number of pages | 11 |
Journal | Computational Mechanics |
Volume | 54 |
Issue number | 5 |
DOIs | |
Publication status | Published - 2014 Oct 8 |
Bibliographical note
Publisher Copyright:© 2014, Springer-Verlag Berlin Heidelberg.
Keywords
- Boundary reparameterization
- Isogeometric analysis
- Uniformity metric
- Volumetric parameterization
ASJC Scopus subject areas
- Computational Mechanics
- Ocean Engineering
- Mechanical Engineering
- Computational Theory and Mathematics
- Computational Mathematics
- Applied Mathematics