Scientific Computing Research Environments for the Mathematical Sciences [SCREMS]

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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.