等几何分析作为一种有效求解精确几何上微分方程数值解的方法，近年来已成为国际研究的一个热点。其中计算域的参数化在基于等几何分析的数值求解中是一个关键性的问题。不同于经典的等几何分析的参数化研究，本项目从实际应用背景出发拟研究以求解一般计算域上定义的微分方程数值解为目标的参数化方法。项目主要结合试探函数光滑性研究计算域内部参数化的生成算法以及协同网格加细的计算域边界参数化算法，并进行数值仿真测试。研究主要是基于申请人前期在样条、参数化以及微分方程求解中的相关研究经历，并且相关工作已有了一定的工作积累，有望完成研究目标。本项目的研究将为在等几何分析框架中一般计算域上的物理仿真奠定基础。

Isogeometric analysis, which is one of international researching focuses recently , is an effective numerical method to solve PDEs over computational domains with an exact boundary representation. Parameterizations play a key role for solving PDEs problems in the framework of Isogeometric analysis. Different from classical parameterization in Isogeometric analysis, the proposed project intends to work on design parameterizations for general computational domains in order to obtain more accurate numerical solutions of PDEs. The topics of this project come from a practice background with application value. They include design interior parameterizations with consideration the smoothness of test functions, modification boundary parameterizations during refining parametric meshes and the solving PDEs-based numerical tests. Our research builds on the applicant’s research experience on splines, parameterizations and solving PDEs within IGA technique. We have obtained some research accumulation about these research topics, and hence it is reasonable to expect that we will reach the research objects. These research works will setup a solid foundation for computation numerical solutions of PDEs on a general computational domain.