Scientific Computing Research Environments for the Mathematical Sciences

根据SCREMS计划，威廉和玛丽学院数学系将购买设备，用于建立一个致力于支持数学科学研究的计算网络。该奖项将为高带宽网络设备、用于数值计算的高性能计算机和一台文件服务器提供资金。这种设备与台式计算机一起为较小的计算提供平台，将为从事许多研究项目的教员研究人员和学生提供一个数字/文件服务器集群。这种设备将用于计算密集型研究项目，涉及广泛的应用数学。其中包括工程设计、数值数学、计算生物化学和运筹学的列举方法。具体包括：(1)偏微分方程组系统优化的有效途径，(2)分子构象的距离参数方法，(3)并行Hessenberg QR本征值算法，(4)计算遍历随机活动网络的准确时间分布和消除自举过程中的重采样误差。PiLeemis和两个以前的博士生写了APPL(一种概率编程语言)。这种基于Maple的语言被用来计算概率和执行随机变量的运算。APPL能够解决的许多问题的大小受到计算速度的限制，作为SCREMS拨款的一部分而获得的硬件所提供的速度对于解决实际遇到的大规模问题是至关重要的。

Under the SCREMS program, the Department of Mathematicsat the College of William & Mary will purchase equipmentfor the creation of a computing network dedicated to thesupport of research in the mathematical sciences. Theaward will provide funds for high-bandwidth networkingequipment, high-performance computers for numericalcalculations, and a file server. This equipment, togetherwith desktop machines providing platforms for smallercomputations, will provide a numerical/file server clusterfor the faculty investigators and students working on anumber of research projects. This equipment will be usedfor computationally intensive research projects spanninga wide range of applied mathematics. These includenumerical methods for engineering design, numericalmathematics, computational biochemistry, and operationsresearch. The projects specifically included in the grantare: (1) Efficient approaches to the optimization of systemsgoverned by partial differential equations, (2) distanceparameterized methods for molecular conformation, (3) aparallel Hessenberg QR eigenvalue algorithm, and (4) thecalculation of the exact distribution of the time totraverse a stochastic activity network and the eliminationof resampling error in bootstrapping. PI Leemis and two former doctoral students have writtenAPPL (A Probability Programming Language). This Maple-basedlanguage is used to compute probabilities and performoperations on random variables. The size of many problemsthat can be solved by APPL is limited by computing speed.The speed offered by the hardware obtained as part of theSCREMS grant is crucial to solving problems of the magnitudeencountered in practice.