Acquisition of a High-Performance Parallel Computer for Mathematical Sciences and Applications

科罗拉多大学丹佛分校(CU-Denver)计算数学中心(CCM)从事数学科学研究和应用，涉及科学计算的各个领域，包括模型开发、离散化方法、数值线性代数、优化算法和应用统计学。由于这些计算密集型研究领域中的每一个领域的前沿都在不断进步，因此保持能够满足日益增长的需求的高性能计算设施是至关重要的。CCM是校园里唯一专门进行大规模并行计算的站点。除了支持研究活动外，CCM还在大学的教学任务中发挥关键作用。许多计算机科学和应用数学的高级课程都严重依赖CCM计算机。而CCM设施对我们数学诊所项目的成功至关重要。计算密集型领域的研究和教学活动正日益受到CCM过时的计算服务器的限制。因此，迫切需要升级CCM的计算能力。这项建议旨在通过描述教师和学生使用的下列研究项目和应用来证明对新的并行计算机的需求：极大特征值问题的数值解；声波散射、区域分解和子结构以及分布式并行编程；确定性和随机次表层流动的并行欧拉-拉格朗日和混合方法；环境恢复的地下水模拟；验证新的膨胀多孔介质数学模型；非光滑方程的数值解；选项的价值估计；大气模型；海量数据集的统计方法；流体问题的精确有限元方法的发展。我们已经确定了基于英特尔的处理器Beowulf集群系统来满足我们的计算需求。每个ITS 32节点都有两个PIII 733 MHz处理器和2 GB的RAM。这个具有GB总内存的强大集群不仅将处理提案中描述的跨学科研究，还将向CCM的其他用户开放，包括所有教职员工、博士后学者、来访者和数学系的学生以及计算机科学系和加州大学丹佛分校工程学院的附属教职员工和学生。

Acquisition of a High-Performance Parallel Computer for Mathematical Sciences andApplicationsThe Center for Computational Mathematics (CCM) at the University of Colorado at Denver(CU-Denver) engages in mathematical sciences research and applications covering diverse areas of scientific computation, including model development, discretization methods, numerical linear algebra, optimization algorithms and applied statistics. Because the frontiers in each of these computationally intensive research areas continue to advance, it is essential to maintain high performance computing facilities capable of meeting ever increasing demands. The CCM is the only specialized site on campus for large-scale parallel computations. In addition to supporting research activities, the CCM also fulfills a critical role in the teaching mission of the University. Numerous advanced courses in Computer Science and Applied Mathematics rely heavily on the CCM computers. And the CCM facilities are vital to the success of our Mathematics Clinic Program. Research and teaching activities in computationally intensive areas are becoming increasingly limited by the CCM's outdated computational servers. There is therefore a pressing need to upgrade the computing capabilities of the CCM. This proposal aims to demonstrate the need for a new parallel computer by describing the following research projects and applications that will result from its use by faculty and students:Numerical Solution of Extremely Large Eigenvalue Problems; Acoustic Scattering, Domain Decomposition and Substructuring, and Distributed ParallelProgramming;Parallel Eulerian-Lagrangian and Mixed Methods for Deterministic and Stochastic SubsurfaceFlows;Groundwater Modeling for Environmental Restoration;Validating New Mathematical Models for Swelling Porous Media;Numerical Solutions of Nonsmooth Equations;Estimation of the Value of Options;Atmospheric Models;Statistical Methodology for Massive Data Sets;Development of Accurate Finite Element Methods for Fluids Problems. We have identified the 64 processor Beowulf Intel-based cluster system to meet our computing needs. Each its 32 nodes has two PIII 733MHz processors and 2 GB of RAM. This powerful cluster with 64 GB total memory will handle not only the cross-disciplinary research described in the proposal, but will also be available to other users of CCM, including all faculty, postdoctoral scholars, visitors and students from the Department of Mathematics as well as affiliated faculty and students in the Department of Computer Science and the School of Engineering at CU-Denver.