U.S.-Czech Mathematics Research on Reliability Problems in Computational Mechanics

美捷数学关于计算力学可靠性问题的研究

• 批准号: 9724783
• 负责人: Ivo Babuska
• 金额: $ 5万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-10-01 至 2002-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9724783&HistoricalAwards=false
• 关键词: U.S.; Czech; Mathematics; Research; Reliability

INT 9724783 Babuska This U.S.-Czech mathematics project between Ivo Babuska of the University of Texas, Austin, and Michal Krizek of the Czech Mathematics Institute, Prague, will examine the problem of reliability in computational mathematics as it relates to mathematical models, available information used in such models (data), and the numerical procedures employed. Overall, this collaboration should yield work that will improve our ability to make engineering decisions based on the outcome of numerical computations. Using a stochastic approach and a worst case approach, the researchers intend to analyze the reliability of the numerical solution(s) by an a-posteriori estimation on the basis of the superconvergence theory. (The worst case approach involves working with a given set of admissible input data to find bounds for the information of interest.) Specifically, this project will test: 1) reliability of mathematical formulations with respect to engineering decisions; and 2) reliability of computed data of engineering importance that is derived by a numerical solution of the mathematical problem. Results are expected to be directly applicable to practical engineering calculations such as those associated with plasticity; elastoplastic torsion; and the Signorini contact problem with approximate friction. This applied mathematics project fulfills the program objective of advancing basic scientific knowledge by enabling leading experts in the United States and Central Europe to combine complementary talents and pool research resources in areas of mutual interest and competence. ??

INT 9724783 Babuska 这是德克萨斯大学奥斯汀分校的 Ivo Babuska 和布拉格捷克数学研究所的 Michal Krizek 之间的美国-捷克数学项目，将研究计算数学的可靠性问题，因为它与数学模型、模型中使用的可用信息（数据）以及所采用的数值程序有关。 总的来说，这种合作应该产生的成果将提高我们根据数值计算结果做出工程决策的能力。 研究人员打算使用随机方法和最坏情况方法，通过基于超收敛理论的后验估计来分析数值解的可靠性。 （最坏情况的方法涉及使用一组给定的可接受的输入数据来查找感兴趣信息的界限。）具体而言，该项目将测试：1）数学公式相对于工程决策的可靠性； 2) 通过数学问题的数值解得出的具有工程重要性的计算数据的可靠性。 结果预计可直接应用于实际工程计算，例如与塑性相关的计算；弹塑性扭转；以及具有近似摩擦力的 Signorini 接触问题。 该应用数学项目通过使美国和中欧的领先专家能够结合互补的人才并汇集共同感兴趣和能力领域的研究资源，实现了推进基础科学知识的计划目标。 ??