SCREMS: Developing Computational Mathematics at the University of Florida

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This grant provides funding for augmenting the computational resourcesin the Mathematics Department of the University of Florida. Fourresearch projects which require the new resources are proposed: Thefirst project on sparse matrix algorithms incorporates state of theart optimization strategies and multilevel heuristics into sparsematrix algorithms, with particular emphasis on techniques that canexploit and can be applied to parallel computing architectures. Thesecond project aims to develop a new set of methods for solvingpartial differential equations on complicated structures. The thirdproject centers around algorithms for the reconstruction of threedimensional tomographic images of internal regions of the humanbody. The fourth investigates nano-scale materials using simulationsbased on mathematically sound simplifications.The success of the research activities will have impact beyondcomputational mathematics through collaborations in biomedicalengineering, computer science, electrical engineering, andmedicine. Specific applications considered include the simulation oflightning with potential benefits to air traffic control, thebiomedical engineering of cardiac ablation technology potentiallybenefiting patients with arrhythmias, improved tomographicreconstruction algorithms for medical imaging potentially leading tobetter diagnostic tools, and better predictions for the properties ofnano-scale materials which are challenging to fabricate with currenttechnology. Students and young researchers will benefit from the newresources by rigorous training in mathematical courses combined withpractical computational training using problems arising fromlarge-scale applications.