Advanced Isogeometric Design-through-analysis Concepts

我的博士项目的中心成果是一个等几何设计，通过分析方法的三维实体结构所描述的T样条CAD表面。它实现了等几何分析的所有关键优势，例如CAD几何形状的无缝集成，无需昂贵的网格生成，以及使用光滑的高阶B样条近似解场。拟议的项目扩展了目前的发展状态的两个重要方面：第一，现代预处理技术的强病态方程组进行了研究，以确定一个合适的方式，使本方法访问高效，易于并行化的迭代求解器。其次，将等几何分析设计方法与直接隐式时间积分法相结合，求解结构动力学瞬态问题。此外，我的博士研究还扩展到更先进的等几何概念，特别是等几何配置和T样条。该项目是与托马斯教授的研究小组合作进行的。德克萨斯大学奥斯汀分校计算工程与科学研究所（ICES）的休斯说。它继续成功的合作，这是在我在TUM博士工作期间发起的，包括2011年夏天在ICES进行的为期三个月的访问。本人谨此提议，申请2012年6月至11月6个月的资助

The central result of the my doctoral project is an isogeometric design-through-analysis methodology for three-dimensional solid structures described by T-spline CAD surfaces. It achieves all key benefits of isogeometric analysis, such as a seamless integration of the CAD geometry, no expensive mesh generation, and the use of smooth higher-order B-splines for the approximation of solution fields. The proposed project extends the present state of development by two important aspects: First, modern preconditioning techniques for strongly ill-conditioned systems of equations are studied to identify a suitable way to make the present approach accessible to efficient and easy-to-parallelize iterative solvers. Second, the isogeometric design-through-analysis methodology is combined with direct im-plicit time integration schemes for the solution of transient problems of structural dynamics. In addition, research is extended beyond my doctoral work to further advanced isogeometric concepts, in particular to isogeometric collocation and T-splines. The proposed project is carried out in collaboration with the group of Prof. Thomas J. R. Hughes at the Institute for Computational Engineering and Sciences (ICES) of the University of Texas at Austin. It continues the successful collaboration, which was initiated during my doctoral work at TUM, including a previous three month visit at ICES in summer 2011. With this proposal, I would like to apply for financial support for 6 months from June to November 2012