中文摘要：

在CAD模型的性能模拟分析过程中,经常需要对计算域模型进行细化以提高模拟的精度.针对等几何分析这一新兴的模拟分析方法,提出一种新的细化方法,称之为r-p型细化方法.该细化方法包括2个步骤：首先通过极小化后验误差估计,对初始计算域的内部控制顶点的位置进行优化（即r型细化）;然后对通过r型细化得到的计算域模型进行升阶操作以增加自由度（即p型细化）.将r-p型细化方法应用于二维热传导问题的等几何模拟分析,通过实例验证了r-p型细化方法在等几何分析中的有效性,并与经典的h型细化方法进行了比较.

英文摘要：

In the simulation and analysis process of CAD models,some refinement operations are often performed to improve the simulation accuracy.In this paper,we propose a new refinement method called r-p-refinement for isogeometric analysis.There are mainly two steps in the proposed method.Firstly,we optimize the replacement of inner control points in initial computational domain by minimizing posteriori error estimation（r-refinement）.Secondly,the degree elevation is performed for the computational domain obtained after the first step to increase the degree of freedom（p-refinement）.The proposed r-p-refinement method is applied in the isogeometric analysis for two dimensional heat-conduction problems.The experimental results show the efficiency of r-p-refinement in isogeometric analysis.Comparison examples with h-refinement are also provided in this paper.