The training of both undergraduate and graduate mathematics students can hardly be considered complete nowadays without their being exposed to the areas of applied mathematics and numerical analysis, and becoming familiar with computer simulations of the real world based on advanced mathematical models. In order to enhance training in this direction, the Department of Mathematics at the University of Wyoming will purchase a computer cluster that will be used for student training and research in several areas, including the simulation of fractal interface growth by interacting particles approximations, modeling of aircraft engine tonal noise under uncertain input, development of three-dimensional flow models for near-critical fluids, and analysis of parallel algorithms for massive graphs and convection-dominated reaction-diffusion problems. These projects are expected to advance the state of the art in a number of fields of high interest in the mathematical/numerical analysis community, such as: spectral element methods, large-scale solution of complex-valued linear systems, domain decomposition methods, analysis of stochastic processes and uncertainty, numerical simulation of such processes driven by Levy noise and spectral analysis of discrete Laplacian operators. They will entail the development of new computational algorithms, both sequential and parallel; new analytical/numerical models for the study of complex fluid physics including near-critical fluid flow and reaction-diffusion flow in porous media; new applications of stochastic analysis and uncertainty quantification; and innovative techniques for the study of large, complex network problems such as those arising on the Internet. The impact of this research will span several scientific disciplines, consistent with the University of Wyoming identification of interdisciplinary computational science as a critical area in its academic plan for 2004-2009. Existing research links between the Department of Mathematics and the Departments of Mechanical Engineering, Chemical and Petroleum Engineering and Computer Science will be enhanced by the presence of the cluster. The impacts also extend to problems of large social and technological interest. Aircraft noise modeling tools are of utmost importance in the design of current large transport aircraft and avoid the need for multi-million-dollar wind tunnel and flight experiments. Simulation of fractal interface growth is a first step toward the control of cutting-edge technological processes such as chemical vapor deposition. A better understanding of critical fluid flow is expected to have an impact in the areas of enhanced oil recovery and advanced materials manufacturing. Massive graph algorithms are needed to speed up processing of digital data in fields such as GIS, the World Wide Web and DNA banks. The use of bio-barriers to restrict flow of pollutants in porous media addresses a major nation-wide environmental concern. The acquisition of the cluster is coupled with a plan to develop a curriculum in computational science and high performance computing. The projects provide ideal topics for class learning and thesis research. They are expected to greatly enhance the training of mathematics students in the use of modern distributed parallel computers, as well as expose them to current areas of research in applied mathematics.
