Adaptive Mode Decomposition Methods

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This proposal intends to take two fairly diverse areas, combustion and nonlinear dynamics of shells, and apply a similar numerical method (domain decomposition) to both areas. Each area is represented by a well known researcher, Belytschko- shells & Bayliss-combustion, and in the application of the method an expert in numerical optimization, Nocedal, will contribute to the effort. This proposal is a nice example of interdisciplinary research within a university. Using domain decomposition as a connection the three researchers will cooperate to make advances not only in their individual areas, but also in parallel processing. The original proposal was for a three year effort. Due to the uncertain program funding, and the heavy future commitment, this proposal is recommended for only two years as a standard grant. As discussed with the PI's, a number of other cost reductions have been included: the visiting professor has not been approved; the disc upgrade has not been included; the networking request has been denied; most important, the number of graduate students has been reduced from three to two. It is felt that by this last action that the three faculty members will have to coordinate their research in order to best occupy these two students.