中文摘要：

等几何分析方法为实现CAD/CAE阶段几何数据的无缝融合提供了新途径,但其求解精度和效率依赖于计算域参数化的质量.为提高优化效率,提出局部r细化方法,即通过局部优化内部部分控制顶点的位置提高等几何分析方法的求解精度.首先利用残值法得到计算域上每个子面片所对应的局部误差指示子;然后根据平均标记策略选择需要进行优化的面片集合,从而确定需要进行优化的控制顶点集合;最后通过极小化标记曲面片上的误差指示子得到所标记的内部控制顶点的最优分布.文中将局部r细化和基于节点插入操作的h细化结合起来,提出Dr局部细化方法.通过二维Poisson方程求解的若干实例,验证了所提出的局部优化方法在等几何分析中的有效性.

英文摘要：

The iso-geometric analysis method provides a new way to realize the seamless integration of geometric data representation in CAD/CAE. However, its accuracy and efficiency strongly depend on the parameterization of the computational domain. In order to improve its optimization efficiency, a local refinement method is proposed in this paper. In our method, the local position optimization of interior partial control points is used to improve the simulation accuracy. Firstly the local error indicator is obtained on each sub-patch by applying a residual-based approach. Then the set of sub- patches to be refined are obtained by a mean-value marking method to determine the set of inner control points to be optimized. Finally the optimal distribution of inner control points is obtained by minimizing the sum of local error indicators using a nonlinear optimization method. A local h-r- refinement is also proposed by combining local r-refinement with h-refinement method based on knot insertion. Several examples for two-dimensional Poisson equation solving are presented to show the efficiency of the proposed local optimization method in iso-geometric analysis.