Mathematical Research at FSU
Optimization, Control and Sensitivity Analysis
Dr. Gallivan and collaborators develop optimization algorithms for functions defined on manifolds. These algorithms are important in the fields of biomedical signal processing, feature extraction, wireless telecommunication systems, sonar and radar systems. In particular, Dr. Gallivan and his group develop algorithms for the optimum representation of large amounts of data.
Dr. Hussaini and collaborators develop numerical algorithms for optimization, control, and sensitivity analysis in fluid mechanics (optimal placement of wind turbines, airfoil shape optimization) and power grid network topology. Dr. Hussaini develops improved techniques for uncertainty quantification. Quantification of parametric uncertainty in simulations is based on probability tools such as Monte Carlo techniques and polynomial chaos. This research includes improving the efficiency of these techniques for practical applications. Model form uncertainty analysis employs evidence theory tools to study uncertainty associated with auxiliary models such as turbulence models in aerodynamic simulations. In regard to network topology, network research relates to quantifying survivability/reliability inherent in a given network topology, developing new topologies of enhanced survivability to multiple faults, and creating structural analysis tools for detecting and isolating faults. Current applications focus on the integrated power system in an all-electric ship and communication systems.