Scientific Computing Research Environments for the Mathematical Sciences

在SCREMS项目下，威廉玛丽学院数学系将购买设备，用于创建一个专门用于支持数学科学研究的计算网络。该合同将为高带宽网络设备、用于数值计算的高性能计算机和文件服务器提供资金。该设备与台式计算机一起为小型计算提供平台，将为从事大量研究项目的教师调查员和学生提供数字/文件服务器集群。该设备将用于计算密集型研究项目，涵盖广泛的应用数学。这些包括工程设计、数值数学、计算生物化学和运筹学的数值方法。具体包括的项目包括：(1)偏微分方程控制的系统优化的有效方法，(2)分子构象的距离参数化方法，(3)并行Hessenberg QR特征值算法，以及(4)遍历随机活动网络的精确时间分布的计算和自举中重采样误差的消除。PI Leemis和两位前博士生编写了appl（一种概率编程语言）。这种基于maple的语言用于计算概率并对随机变量执行操作。应用程序应用程序可以解决的许多问题的规模受到计算速度的限制。作为crems拨款的一部分，获得的硬件提供的速度对于解决实践中遇到的重大问题至关重要。

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.