This grant provides funding for augmenting the computational resources in the Mathematics Department of the University of Florida. Four research projects which require the new resources are proposed: The first project on sparse matrix algorithms incorporates state of the art optimization strategies and multilevel heuristics into sparse matrix algorithms, with particular emphasis on techniques that can exploit and can be applied to parallel computing architectures. The second project aims to develop a new set of methods for solving partial differential equations on complicated structures. The third project centers around algorithms for the reconstruction of three dimensional tomographic images of internal regions of the human body. The fourth investigates nano-scale materials using simulations based on mathematically sound simplifications.
The success of the research activities will have impact beyond computational mathematics through collaborations in biomedical engineering, computer science, electrical engineering, and medicine. Specific applications considered include the simulation of lightning with potential benefits to air traffic control, the biomedical engineering of cardiac ablation technology potentially benefiting patients with arrhythmias, improved tomographic reconstruction algorithms for medical imaging potentially leading to better diagnostic tools, and better predictions for the properties of nano-scale materials which are challenging to fabricate with current technology. Students and young researchers will benefit from the new resources by rigorous training in mathematical courses combined with practical computational training using problems arising from large-scale applications.
