等几何分析是一种基于CAD模型的精确几何表示进行模拟分析的新型技术。它的提出为实现CAD/CAE的无缝融合开辟了新途径，也为几何设计与计算领域提出了新的研究课题。本项目研究适合等几何分析的几何造型新理论和新方法,拟完成四项任务：1）研究基于有向图的CAD模型体参数化方法，解决复杂CAD模型的体参数化问题，拓展等几何分析的应用广度；2）研究基于体细分的CAD模型体参数化方法,建立体细分方法的基础理论，实现细分方法与等几何分析方法的有机结合；3）研究定义在三边/四边混合网格上的样条理论及其在等几何分析中的应用，提高等几何分析对拓扑复杂模型的通用性；4）构造适合分析的变次数T样条模型，并研究其在等几何分析中的应用，提高模拟分析的自适应性。通过本项目的研究，有望解决制约等几何分析发展的瓶颈问题,为等几何分析方法在CAD产品模拟仿真中的应用提供坚实的几何基础，并进一步将其推向实用。

Isogeometric analysis(IGA for short) is a new method to perform simulation and analysis based on the exact geometry representation of CAD model. It provides a new way to realize the seamless integration of CAD/CAE, and also some new topics for the field of geometric design and computation. This project will focus on new theory and methods of geometric modeling, which are suitable for isogeometric analysis, and has four tasks: 1). investigate the volume parameterization method of CAD model based on the concept of directed graph to sovle the volume parameterization problem of CAD model with complex shape and increase the application of isogeometric analysis in practice; 2) construct the volume parameterization of CAD model by subdivision volume method, and build the theory framework of subdivision volume to realize the connection between isogeometry and subdivision method; 3) study the spline theory defined on mixed meshes consisting of triangles and rectangles and its application in isogeometric analysis to improve the universality of IGA for models with arbitrary topology; 4) construct analysis-suitable T-spline model with variable degrees and study its application in isogeometric analysis to improve the adaptivity of IGA. By the proposed research in this project, we can solve the bottleneck problems in the development of isogeometric analysis, provide solid theory foundation and technique support for the application of isogeometric analysis in the simulation of CAD product, and increase its application in practice.