U.S.-France (INRIA) Cooperative Research: Numerical Solutionor Partial Differential Equations in Engineering Problems

该奖项将支持美国和法国两组科学家在应用数学方面的合作研究，这两组科学家分别位于马里兰大学和法国国家信息科学与自动化研究所（INRIA）。美国小组将由伊沃·巴布斯卡教授领导；在法国方面，该项目将由罗昆古研究所的Michel Bernadou博士领导。马里兰大学和INRIA多年来一直致力于用有限元方法求解工程问题中出现的偏微分方程的数值解。INRIA开发了软件系统MODULEF；马里兰大学已经开发了新的理论方法和相关的计算机实现。因此，法国和美国的集团是互补的。拟议合作的主要目标是：a)开发一个科学框架，描述现有方法的相关特性，可用于评估其在实际计算中的有效性，并设计新的有效方法。b)评估计算结果的准确性和适应性程序的设计。c)开发重要工程问题的新数学公式，特别注意那些可用信息（输入数据）具有内在不确定性的问题。这项研究联合了美国和法国两组杰出的应用数学家。INRIA因其在计算机研究、自动化、数学和科学计算方面的专业知识而得到广泛认可；它提供了这些领域的基础研究与工业合作的良好结合。该奖项将允许在有限元理论和应用的重要领域继续进行富有成效的合作。

This award will support ongoing collaborative research in applied mathematics between two groups of U.S. and French scientists, based at the University of Maryland and at the French National Institute for Information Science and Automation (INRIA). The U.S. group will be led by Professor Ivo Babuska; on the French side the project will be led by Dr. Michel Bernadou, INRIA - Rocquencourt. The University of Maryland and INRIA have been working for many years on finite element methods for the numerical solution of partial differential equations that arise in engineering problems. INRIA has developed the software system MODULEF; new theoretical approaches and related computer implementations have been developed at the University of Maryland. Hence the French and U.S. groups complement each other. The major objectives of the proposed collaboration are: a) To develop a scientific framework characterizing the relevant properties of existing methods which can be used for the assessment of their effectiveness in practical computations, and to design new effective methods. b) To assess the accuracy of computed results and the design of adaptive procedures. c) To develop new mathematical formulations of important engineering problems, with special attention given to problems for which the available information (input data) has intrinsic uncertainties. This research joins two groups of outstanding U.S. and French applied mathematicians. INRIA is widely recognized for its concentration of expertise in computer research, automation, mathematics and scientific computing; it provides an excellent combination of fundamental research with industrial collaboration in these areas. This award will allow fruitful collaboration to continue in the important area of finite element theory and applications.