等几何分析为产品设计与仿真的无缝集成提供了新途径.计算域参数化是等几何分析领域的重要研究课题,但目前计算域参数化的相关工作主要面向静态等几何分析问题,为克服这一局限性,本项目针对时间相关的动态等几何分析问题,提出“时变参数化”这一概念,共包括三项研究内容:1)研究基于控制顶点重定位的时变参数化方法,在不增加自由度的前提下,提高等几何分析求解时间相关动态问题的精度;2)研究基于局部加细样条模型的时变参数化方法,自适应地进行动态局部加细与局部加粗,以保证在适当的自由度数目下,尽可能提高仿真精度,实现精度和效率的最佳平衡;3)建立定义在球面任意拓扑四边网格上的样条理论框架,以此为基础研究面向流形曲面上动态PDE问题的时变参数化方法.通过本项目的研究,可提高动态等几何分析的精度和计算效率,使其在CAD产品的多学科物理动态仿真中得到更广泛的应用.

Isogeometric analysis provides a new way to realize seamless integration of product design and numerical simulation. Parameterization of computational domain is an important research topic in the field of isogeometric analysis.Till this moment, however, the related work on parameterization of computational domain only focus on static problems with isogeometric analysis. To overcome this limitation, this project will propose the concept of “time-varying parameterization” for time-dependent dynamic isogeometric analysis. The proposed project has three major tasks: (1) to investigate the time-varying parameterization method by redistributing the interior control points, to improve the simulation accuracy of time-varying isogeometric analysis without increasing the degree of freedom; (2) to investigate the time-varying parameterization method based on local-refinement spline model, in which adaptive local refinement and local de-refinement can be performed to improve the simulation accuracy as much as possible with proper degree of freedom, and the best balance between accuracy and efficiency can be achieved; 3) to build the theory framework of spline model defined on spherical quad mesh with arbitrary topology,and to investigate the time-varying parameterization for dynamic PDE problems on manifold surfaces.With the proposed research in this project,we expect to improve the simulation accuracy and computational efficiency of isogeometric analysis,and extend the applications of isogeometric analysis on CAD products in the field of multidisciplinary physical dynamic simulation.