Scientific Computing Research Environments for the Mathematical Sciences [SCREMS]

科罗拉多大学数学系和应用数学系将进行研究，购买两个“计算引擎”，每个系一个，结合这些进步。随着计算能力的不断进步，第二个问题对这里感兴趣的问题是至关重要的：(I)增加的内存大小现在允许对一些在三维空间维度上随时间演变的物理现象进行真实的计算；以及(Ii)计算精度的提高使一类新的快速算法成为可能，否则这些算法是不可行的。1)一个项目的目标是开发快速而准确的算法来解决三维和更高维度的实际问题。这一发展中的两个主要工具是低分离等级的表示(分离变量的数值版本)。2)第二个项目的目标是为中到高雷诺数流动设计新的算法原型和开发新的模型。3)第三个研究项目，关于二维和三维的颗粒介质的行为，利用经典的运动学理论，将其扩展到非弹性碰撞的情况，并给出诸如应力和颗粒能量的宏观量的显式表达式。直接感兴趣的科学问题包括：(A)地球物理和天体物理流体流动，由行星自转、可变重力和磁力的竞争影响驱动；(B)颗粒流，例如在雪崩、沙堆或山体滑坡中出现的颗粒流；(C)电磁波在不规则形状的物体附近传播。除了这些眼前的应用，长远的目标是训练学生很好地使用这些新机器。科罗拉多大学最近创建了两个新的研究生项目，旨在培训科学家和工程师使用先进的计算方法。这两台机器将有助于使这些新项目更有效。

The Departments of Mathematics and Applied Mathematics atthe University of Colorado will conduct research effortsthat will purchase two "compute engines", one for each oftwo departments, that incorporate these advances. Amongadvances in computing capacity two are crucial for theproblems of interest here: (i) increased size of memory nowallows for realistic computations of some physical phenomenathat evolve in time in three spatial dimensions; and (ii) increased computational precision makes feasible anew class of fast algorithms that were infeasible otherwise.1) A goal of one project is the development of fast andaccurate algorithms for solving practical problems indimensions three and higher. The two main tools in thisdevelopment are representations with a low separation rank(a numerical version of separation of variables).2) A goal of a second project is prototyping new algorithmsand developing new models for moderate to high Reynoldsnumber flows.3) A third research project, on the behavior of a granularmedium in two and three dimensions, draws on the classicalkinetic theory, extending it to the case of inelasticcollisions, and gives explicit expression for macroscopicquantities such as stress and granular energy.Scientific problems of immediate interest include:(a) geophysical and astrophysical fluid flows, driven bythe competing influences of planetary rotation, variablegravity, and magnetic forces; (b) granular flows, such asoccur in avalanches or sand-piles or landslides; and (c)electromagnetic wave propagation near irregularly shapedbodies. Aside from these immediate applications, alonger-term goal is to train students to use these newmachines well. The University of Colorado recentlycreated two new graduate programs, designed to trainscientists and engineers in advanced computational methods.These two machines will help to make these new programsmore effective.