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

Gang Xu, Bernard Mourrain, André Galligo, Timon Rabczuk

Research output: Contribution to journalArticlepeer-review

46 Citations (Scopus)


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 languageEnglish
Pages (from-to)1303-1313
Number of pages11
JournalComputational Mechanics
Issue number5
Publication statusPublished - 2014 Oct 8

Bibliographical note

Publisher Copyright:
© 2014, Springer-Verlag Berlin Heidelberg.


  • 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


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