Mathematical Sciences: Scientific Computation in Mechanics

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An approach to scientific computation is proposed that incorporates research in numerical analysis, aspects of computer science, and solution of model problems in mechanics. Three research areas are the focus of the proposal: computational problems in incompressible fluid dynamics (including free-boundary problems, problems with variable density and high-order discretizations in three dimensions), computational chemistry (molecular dynamics simulations), and automated programming of scientific algorithms on parallel computers. The overall objective of the proposal is to improve the foundations for software for solving problems in science and technology that involve large scale, multidimensional models involving mechanics. The research will involve the development of new algorithms for several problems too difficult to solve by existing techniques. It will also include an analysis of each algorithm, yielding a rigorous justification that it accurately approximates the phenomena under study. Finally, the proposed research will involve prototype implementations of the algorithms in computer programs via techniques that can assure a robust and easliy maintained code. This research will improve computational modeling of many important industrial processes. One class involves such diverse things as making photographic film, sewing thread, extruded metals and Saran Wrap. Another involves biomedical applications, for example in the development of new pharmaceuticals. Another impacts the analysis of certain toxic gas spills.