University - Industry Cooperative Research Programs in the Mathematical Sciences: Rensselaer-Rockwell Senior Research Fellowship

该奖项支持罗克韦尔科学中心的Barna Bihari博士和伦斯勒理工学院数学科学系的Donald Schwendeman教授发起的一项合作研究计划。该研究将于1997-98学年和随后的夏季在伦斯勒进行，并计划开展后续合作活动。研究的重点将放在非线性守恒律数值解的多分辨率格式上。具体任务将包括在一般曲线网格上实现高阶多维ENO方案，研究和实现高阶边界条件，研究和实现误差估计和自适应，以及将这些方法应用于与工业赞助商高度相关的计算流体动力学（CFD）问题。计划开展广泛的研究和教学活动，包括成立一个守恒定律数值方法研究活动小组，这将集中于该奖项发起的教师和学生的研究工作。通过与这个研究小组和伦斯勒的其他项目，如科学计算研究中心（SCOREC）的互动，合作将产生广泛的影响。除了为伦斯勒带来新的活跃研究领域外，这一合作项目还将丰富现有项目。伦斯勒的教学活动将通过与数学系学生和计算科学与工程专业学生的互动而受益。Bihari博士的合作还将通过诸如工业数学问题研讨会（MPI）等项目，加强正在进行的鼓励学术界与工业界互动的努力。该合同包括罗克韦尔公司的大量费用分摊。该项目由MPS多学科活动办公室（OM A）和数学科学部（DMS）联合支持。

This award supports the initiation of a collaborative research program between Dr. Barna Bihari of the Rockwell Science Center and Professor Donald Schwendeman of the Department of Mathematical Sciences at Rensselaer Polytechnic Institute. The research will be performed at Rensselaer during the academic year, 1997-98, and the subsequent summer, with follow-up collaborative activity planned. The focus of the research will be on multiresolution schemes for the numerical solution of nonlinear conservation laws. Specific tasks will include the implementation of high-order multidimensional ENO schemes on general curvilinear grids, the study and implementation of high-order boundary conditions, the study and implementation of error estimates and adaptivity, and the application of these methods to highly relevant computational fluid dynamics (CFD) problems to the industrial sponsor. A wide range of research and teaching activity is planned including the formation of a research activity group on numerical methods for conservation laws which will focus the research efforts of faculty and students initiated by this award. Through the interaction with this research group and with other programs at Rensselaer, such as the Scientific Computation Research Center (SCOREC), the collaboration will have a broad impact. In addition to bringing new areas of active research to Rensselaer, this collaborative program will enrich existing programs. A benefit to the teaching activity at Rensselaer will occur through the interaction with students in the math department and with students involved in the Computational Science and Engineering program. Dr. Bihari's collaboration will also enhance the ongoing effort to encourage academic-industry interaction through programs such as the Workshop on Mathematical Problems in Industry (MPI). This award includes significant cost sharing by Rockwell. This project is jointly supported by the MPS Office of Multidisciplinary Activities (OM A) and the Division of Mathematical Sciences (DMS).