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

Gang Xu, Bernard Mourrain, André Galligo, Timon Rabczuk

Research output: Contribution to journalArticle

24 Citations (Scopus)

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 languageEnglish
Pages (from-to)1303-1313
Number of pages11
JournalComputational Mechanics
Volume54
Issue number5
DOIs
Publication statusPublished - 2014 Jan 1
Externally publishedYes

Fingerprint

NURBS
Trivariate
Reparameterization
Parameterization
Uniformity
Volumetric analysis
Isogeometric Analysis
NURBS Surface
Metric
Geometry
Dimensional Analysis
Control Points
Harmonic
Three-dimensional
Curve

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 journalArticle

Xu, Gang ; Mourrain, Bernard ; Galligo, André ; Rabczuk, Timon. / High-quality construction of analysis-suitable trivariate NURBS solids by reparameterization methods. In: Computational Mechanics. 2014 ; Vol. 54, No. 5. pp. 1303-1313.
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