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

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 G. Xu College of Computer Science, Hangzhou Dianzi University, Hangzhou 310018, P.R.China E-mail: [email protected] B. Mourrain Galaad, INRIA Sophia-Antipolis, 2004 Route des Lucioles, 06902 Cedex, France E-mail: [email protected] A. Galligo University of Nice Sophia-Antipolis, 06108 Nice Cedex 02, France E-mail: [email protected] T. Rabczuk Institute of Structural Mechanics, Bauhaus-University Weimar, Marienstr. 15, D-99423 Weimar, Germany E-mail: [email protected] NURBS solid. Several examples with complicated geometry are presented to illustrate the effectiveness of proposed methods.