Scientific Computing Research Environments for the Mathematical Sciences

数学科学的科学计算研究环境(DMS-0532160)合作PI：M.Holmes，D.Schwendeman，J.Mitchell和E.GiladiRensselaer理工学院数学科学系这个项目涉及购买和使用高速多处理器计算集群，以：1.使计算密集型研究项目能够解决复杂的数学建模和优化问题，特别包括在化学反应流、数学生物学、数值优化和波散射研究中出现的多尺度问题。显著增强伦塞勒数学科学研究生计算课程，并继续努力吸引女性和其他代表性不足的群体加入我们的研究计划。拟议的设备将在几个方面有利于我们的研究项目。这些设备将(I)使我们能够继续我们的研究工作，以开发和测试使用并行计算的新的数值方法，(Ii)为我们的毕业生开辟新的研究领域，以及(Iii)对于运行已经在我们较小的四处理器系统上工作的生产代码是必不可少的。这些新的研究途径将加强我们在计算数学方面的研究生教育和职业发展，并将成为REUS(本科生研究经验)等外展活动的基础。该集群将立即产生影响的具体项目包括：在复合重叠网格上开发自适应网格加密方法，用于多尺度模拟爆炸和爆轰介质中的化学反应流动；负责耳蜗声传导的非线性、三维、机电过程的计算模拟；基于多面体和非多面体割平面方法的并行算法的开发，以解决大规模的半定和整数规划问题；以及在中频区求解复杂现实三维目标散射问题的渐近-数值混合算法的发展。在更广泛的层面上，计算集群将为我们提供开发可扩展算法的能力，这些算法对于分析科学和工程应用中出现的某些复杂数学问题是必不可少的，它将为我们提供一个计算实验室，为我们的学生和博士后的准备和计算经验提供宝贵的资源。因此，计算集群的更广泛影响将作为一种工具，用于我们的学生和博士后的职业发展，通过出版物和讲座传播我们的计算研究的新结果，以及发展新的跨学科合作。

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.