LTB: Accurate Computational Methods for Very Large Dynamical Systems

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Foundational principles of the theory of dynamical systems, such as the closing lemma and the Poincare recurrence theorem, suggest that dynamics can be understood quite generally in terms of periodic motions. This project will use those principles as a beacon and develop numerical methods that elucidate the dynamics of systems with more than a million degrees of freedom using accurate computations of steady solutions, traveling waves, periodic motions, and relative periodic motions. These methods will be applied to fluid turbulence at low and moderate Reynolds numbers and to the technologically important transition-to-turbulence problem. This project will advance the instruction of computational science by training students to be skillful at using and creating scientific software.