U.S.-China Cooperative Research: Finite Element Superconvergence in Computational Mechanics

本奖项支持DMS 9626193项目的扩展研究，包括与计算数学研究所中国科学与工程计算国家实验室的研究人员的合作。德克萨斯理工大学的张志民打算与中国科学院科学与工程计算国家实验室主任石忠慈合作。美国PI计划让一名美国本科生和一名美国研究生参与该项目。学生们将与P.I.一起到中国进行研究访问，以发展他们自己在计算数学方面的研究。本项目的主要目的是研究有限元计算中的导数超收敛及其恢复。这种研究在计算力学中具有根本性的重要性，因为工程师们对更有效地估计应力、应变能等的方法感兴趣。目前，工程中使用的大多数商业代码都要求具有自适应能力，以便以最有效的方式进行计算。这种自适应设计需要超收敛知识。本研究结果将对结构力学中出现的大规模科学计算问题产生重大影响。中方将由国家自然科学基金提供支持。

9605050 Zhang This award supports extension of work funded under DMS 9626193 to include cooperation with researchers at China's National Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics. Zhimin Zhang, Texas Tech University, intends to pursue collaboration with Shi Zhongci, Director of the National Laboratory for Scientific and Engineering Computing, Chinese Academy of Sciences, Beijing. The U.S. PI plans to involve one U.S. undergraduate and one U.S. graduate student in the project. The students will join the P.I. in research visits to China to develop their own research in computational mathematics. The primary objective of this project is the study of derivative superconvergence and its recovery in finite element computations. Such study is of fundamental importance in computational mechanics in that engineers are interested in more effective ways to estimate stress, strain energy, etc. At present, most commercial codes used in engineering are required to have adaptive capabilities which allow computations to be performed in the most efficient way. Knowledge of superconvergence is necessary for this adaptivity design. The results of this research will have significant impact on large-scale scientific computing problems arising in structural mechanics. Support on the Chinese side will be provided by the National Natural Science Foundation.