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

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.
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Computational Mechanics, Springer Verlag, 2014, 54 (5), pp.1303-1313. 〈10.1007/s00466-014-1060-y〉
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Gang Xu, Bernard Mourrain, André Galligo, Timon Rabczuk. High-quality construction of analysis-suitable trivariate NURBS solids by reparameterization methods. Computational Mechanics, Springer Verlag, 2014, 54 (5), pp.1303-1313. 〈10.1007/s00466-014-1060-y〉. 〈hal-00922544v2〉

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