中文摘要：

三变量体参数化是进行三维等几何分析求解的首要步骤,论文提出了基于模板的由边界曲面生成B样条参数体的新方法。首先给出了插值边界曲面的Coons体的参数表达式,再由该表达式的离散表示,内部控制顶点可表示为边界控制顶点的线性组合。然后由其离散表示可得到Coons模板,并将Coons模板推广到统一形式,为内部控制顶点的生成提供了更多选择。论文通过热传导问题的实例对由不同的模板所得到的不同体参数化结果及其对等几何分析结果的影响进行了比较分析。

英文摘要：

Volume parameterization is the key step in three-dimensional isogeometric analysis. In this paper, we propose discrete Coons method for B-spline parametric volume generation from given boundary surfaces. The parametric formula of Coons volume interpolating the boundary surfaces is firstly presented. From the discrete version of this formula, for B-spline volume generation, the inner control points can be obtained by the linear combination of the boundary control points. Furthermore, the discrete coons mask is generalized into a unified form in the mask, which provides various choices for the generation of inner control points. The volume parameterization obtained from different mask and their influences on the result of isogeometric analysis are also compared by an example for heat conduction problems.