Scientific Computing Research Environments for the Mathematical Sciences

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ABSTRACTThe Department of Mathematics of the University of Alabama at Birmingham will purchase and assemble onsite a 25 node dual Pentium III Beowulf cluster using commodity personal computer technology. The cluster will be dedicated to support of research in the mathematical sciences. The equipment will be used in particular for the following mathematics research projects based in the Departments of Mathematics and Physics at the University of Alabama at Birmingham and the Departments of Mathematics at the University of Alabama in Huntsville and the University of Alabama (Tuscaloosa): Inverse Problems: Ian Knowles. This project centers on the development of computational algorithms for elliptic inverse problems for groundwater modeling and medical imaging. Modeling Coupled Katabatic/Ice/Ocean Processes Related to the Energy and Carbon Budget in the High Latitude Southern Ocean: Richard T. McNider. It is the purpose of this project to test and further develop simplified two-dimensional coupled atmospheric, ocean, ice and biological models to elucidate the role of physical factors in Antarctic sea ice distribution and heat flux exchange and, ultimately, to address CO_2 exchange between the atmosphere and ocean. Coupled Stochastic Differential Equations: Ryoichi Kawai. When a number of nonlinear dynamical elements interact with each other in the presence of multiplicative noise, ordered phases appear via symmetry breaking noise-induced phase transitions, whereas the same system does not exhibit any interesting behavior in the absence of noise; this phenomenon is investigated computationally. Stability of Interfacial Flows: D. Halpern and A.L. Frenkel. The stability of thin films coating a capillary tube or a planar wall subject to a time-dependent forcing is investigated computationally . Intermediate Shocks for Magnetohydrodynamics: Yanni Zeng. This project is to study the nonlinear stability of intermediate shock waves occurring in magnetohydrodynamics.