Scientific Computing Research Environments for the Mathematical Sciences [SCREMS]

科罗拉多大学的数学系和应用数学系将进行研究工作，购买两个“计算引擎”，两个系各一个，将这些进步结合起来。在计算能力的进步中，有两个对我们感兴趣的问题至关重要：（i）内存容量的增加现在允许对一些在三维空间中随时间演化的物理现象进行现实的计算;以及（ii）增加的计算精度使得另外不可行的一类新的快速算法成为可行。一个项目的目标是开发快速和准确的算法来解决三维和更高维度的实际问题。这一发展过程中的两个主要工具是具有低分离秩的表示（分离变量的数值形式）。2）第二个项目的目标是原型新算法和开发新模型，用于中等到高雷诺数的流动。3）第三个研究项目，关于二维和三维颗粒介质的行为，借鉴经典的动力学理论，将其扩展到非弹性碰撞的情况，直接感兴趣的科学问题包括：（a）地球物理和天体物理的流体流动，由行星旋转，可变重力和磁力的竞争影响驱动;（B）颗粒流，如发生在雪崩或沙堆或滑坡;和（c）电磁波传播附近的不规则形体。 除了这些即时的应用，长期的目标是训练学生使用这些新机器。科罗拉多大学最近设立了两个新的研究生项目，旨在培训科学家和工程师掌握先进的计算方法。这两台机器将有助于使这些新项目更加有效。

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.