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

该奖项将支持正在进行的合作研究， 美国和法国两组科学家之间的数学， 在马里兰州大学和法国国家研究所 信息科学与自动化（INRIA） 美团 将由Ivo Babuska教授领导;在法国方面， 该项目将由INRIA - Rocquencourt的Michel Bernadou博士领导。 马里兰州大学和INRIA一直在为许多 年的有限元方法的数值解， 偏微分方程在工程问题中的应用 INRIA开发了软件系统MODULEF;新的理论 已经开发了一些方法和相关的计算机实现 在马里兰州大学。 因此，法国和美国的集团 相辅相成。 建议的主要目标 合作是： （a）制定一个科学框架， 现有方法的属性，这些属性可用于 评估其在实际计算中的有效性，以及 设计新的有效方法。 B）评估计算结果的准确性， 设计适应性程序。 （c）发展重要的新数学公式 工程问题，特别注意问题 可用信息（输入数据）具有固有的 不确定性 这项研究加入了两组杰出的美国和法国 应用数学家 INRIA因其 集中在计算机研究、自动化、 数学和科学计算;它提供了一个很好的 基础研究与产业合作相结合 在这些领域。 该奖项将使富有成效的合作， 继续在有限元理论的重要领域， 应用.

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.