Scientific Computing Research Environments for the Mathematical Sciences

数学科学的科学计算研究环境

• 批准号: 0532160
• 负责人: Mark Holmes
• 金额: $ 10万
• 依托单位: Rensselaer Polytechnic Institute
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-09-15 至 2007-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0532160&HistoricalAwards=false
• 关键词: Scientific; Computing; Research; Environments; Mathematical; Scientific; Computing; Research; Environments; Mathematical

Scientific Computing Research Environmentsfor the Mathematical Sciences (DMS-0532160)Co-PIs: M. Holmes, D. Schwendeman, J. Mitchell and E. GiladiDepartment of Mathematical Sciences, Rensselaer Polytechnic InstituteThis project involves the purchase and use of a high-speed multiprocessor computing cluster to:1. Enable computationally intensive research projects to address complex mathematical modelingand optimization issues, including, in particular, multi-scale problems arising in thestudy of chemically reacting flows, mathematical biology, numerical optimization, and wavescattering.2. Significantly enhance graduate computational courses in the Mathematical Sciences at Rensselaerand expand our continuing efforts to attract women and other under-represented groupsinto our research programs.The proposed equipment will benefit our research projects in several ways. The equipment will (i)enable us to proceed with our research efforts directed towards the development and testing of newnumerical methods using parallel computing, (ii) open up new areas for research for our graduatestudents, and (iii) be essential for running production codes already working on our smaller fourprocessor system. These new avenues of research will strengthen our graduate student educationand career development in computational mathematics, and will become the basis for outreachactivities such as REUs (Research Experiences for Undergraduates).The specific projects for which the cluster will have immediate impact involve: the developmentof adaptive mesh refinement methods on composite overlapping grids for multiscale simulations ofchemically reacting flows in exploding and detonating media; the computational modeling of thenonlinear, three-dimensional, electromechanical processes responsible for transduction of soundin the cochlea; the development of parallel algorithms based on polyhedral and non-polyhedralcutting plane methods for solving large-scale semidefinite and integer programming problems; andthe development of hybrid asymptotic-numeric algorithms for solving scattering problems fromcomplex realistic three-dimensional objects, in the mid frequency regime. On a broader level, thecomputing cluster will provide us with the ability to develop scalable algorithms that are essential foranalyzing certain complex mathematical problems that arise in science and engineering applications,and it will provide us with a computational laboratory that will serve as an invaluable resourcefor the preparation and computational experience of our students and post-docs. As a result, thebroader impact of the computing cluster will be as a tool used in the career development of ourstudents and post-docs, the dissemination of the new results of our computational research throughpublications and talks, and the development of new interdisciplinary collaborations.

Scientific Computing Research Environmentsfor the Mathematical Sciences (DMS-0532160)Co-PIs: M. Holmes, D. Schwendeman, J. Mitchell and E. GiladiDepartment of Mathematical Sciences, Rensselaer Polytechnic InstituteThis project involves the purchase and use of a high-speed multiprocessor computing cluster to:1.启用计算密集型研究项目，以解决复杂的数学建模和优化问题，特别是在化学反应流，数学生物学，数值优化和波动播放的术中引起的多尺度问题。2。伦斯莱德（Rensselaerand）的数学科学中的研究生计算课程显着增强了我们的持续努力，以吸引妇女和其他代表性不足的研究计划。拟议的设备将以几种方式使我们的研究项目受益。设备（i）将使我们能够使用并行计算来开发和测试新数方法，（ii）为毕业生开放新领域，（iii）对于运行已经在我们较小的四个处理器系统上运行的生产代码至关重要的研究工作。 These new avenues of research will strengthen our graduate student educationand career development in computational mathematics, and will become the basis for outreachactivities such as REUs (Research Experiences for Undergraduates).The specific projects for which the cluster will have immediate impact involve: the developmentof adaptive mesh refinement methods on composite overlapping grids for multiscale simulations ofchemically reacting flows in exploding and detonating media;负责导致耳蜗转导的三维，机电过程的计算建模；基于多面体和非多层缩放平面方法的平行算法的开发，用于解决大规模的半决赛和整数编程问题；以及在中间频率状态下，杂种渐近算法的开发，用于解决散射问题的散射问题。在更广泛的层面上，计算集群将使我们能够开发可扩展的算法，这些算法是必不可少的，这些算法是科学和工程应用中某些复杂的数学问题的必定性，并且它将为我们提供一个计算实验室，这些计算实验室将作为我们的学生的准备和计算体验和docs的计算经验。结果，计算集群的影响力将是一种用于我们的学生和事后职业发展的工具，我们的计算研究遍历和谈判的新结果以及新的跨学科合作的发展。