Computational Mechanics

, Volume 54, Issue 5, pp 1303–1313 | Cite as

High-quality construction of analysis-suitable trivariate NURBS solids by reparameterization methods

  • Gang Xu
  • Bernard Mourrain
  • André Galligo
  • Timon Rabczuk
Original Paper


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.


Isogeometric analysis Volumetric parameterization  Boundary reparameterization Uniformity metric 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Gang Xu
    • 1
  • Bernard Mourrain
    • 2
  • André Galligo
    • 3
  • Timon Rabczuk
    • 4
  1. 1.College of Computer ScienceHangzhou Dianzi UniversityHangzhouPeople’s Republic of China
  2. 2.GalaadINRIA Sophia-AntipolisSophia-Antipolis CedexFrance
  3. 3.University of Nice Sophia-AntipolisNice Cedex 02France
  4. 4.Institute of Structural MechanicsBauhaus-University WeimarWeimarGermany

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