Mathematical Sciences: Scientific Computing in Mechanics

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Scott The investigator develops an approach to scientific computation 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 project: computational problems in incompressible fluid dynamics (including free--boundary problems and high-order, mixed method discretizations in two and three dimensions), diffusion acceleration techniques for particle transport, and algorithms for parallel computers. This research includes an analysis of each algorithm, yielding a rigorous justification that it accurately approximates the phenomenon under study. Finally, the research involves prototype implementations of the algorithms in computer programs via techniques that can assure a robust and easily maintained code. In collaboration with specialists in related disciplines, these computer programs are used to study basic physical phenomena in a variety of areas. The overall objective of the project is to improve the foundations for software for solving problems in science and technology that involve large scale, multidimensional models in continuum mechanics. These models are the basis for computer simulation used in engineering design in manufacturing processes, in environmental modeling and the development of remediation techniques, and in various aspects of biotechnology. The research involves the development of new algorithms for several problems too difficult to solve by existing techniques. It emphasizes the efficient use of high-performance computers in realistic simulations.