Analysis-suitable volume parameterization of multi-block computational domain in isogeometric applications

作者：Xu, Gang^*; Mourrain, Bernard; Duvigneau, Regis; Galligo, Andre

来源：CAD Computer Aided Design, 2013, 45(2): 395-404.

DOI：10.1016/j.cad.2012.10.022

• Isogeometric analysis
• Volume parameterization
• Multi-block computational domain
• Heat conduction

Parameterization of the computational domain is a key step in isogeometric analysis just as mesh generation is in finite element analysis. In this paper, we study the volume parameterization problem of the multi-block computational domain in an isogeometric version, i.e., how to generate analysis-suitable parameterization of the multi-block computational domain bounded by B-spline surfaces. Firstly, we show how to find good volume parameterization of the single-block computational domain by solving a constraint optimization problem, in which the constraint condition is the injectivity sufficient conditions of B-spline volume parameterization, and the optimization term is the minimization of quadratic energy functions related to the first and second derivatives of B-spline volume parameterization. By using this method, the resulting volume parameterization has no self-intersections, and the isoparametric structure has good uniformity and orthogonality. Then we extend this method to the multi-block case, in which the continuity condition between the neighbor B-spline volumes should be added to the constraint term. The effectiveness of the proposed method is illustrated by several examples based on the three-dimensional heat conduction problem.

• 出版日期2013-2
• 单位INRIA; 杭州电子科技大学