Gang Xu, Bernard Mourrain, André Galligo, Timon Rabczuk. Abstract High-quality volumetric parameterization of computational domain plays an important role in threedimensional 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
Xu et al. proposed a two-stage scheme to construct the analysis-suitable NURBS volumetric parameterization by a uniformity-improved boundary reparameterization method REF .
High-quality construction of analysis-suitable trivariate NURBS solids by reparameterization methods
Computational Mechanics
Mathematics