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Explore a detailed lecture on nonlinear phase averaging techniques in highly oscillatory PDEs delivered by Professor Beth Wingate from the University of Exeter. Discover how these mathematical techniques address computational challenges in atmospheric and oceanic modeling, where wave motions like inertial-gravity and sound waves require increasingly smaller time steps as spatial resolution improves. Learn about innovative time-parallel numerical methods that enable larger, accurate time steps through phase averaging, inspired by fast singular limits mapping. Examine the practical implications for climate modeling, where current explicit atmosphere models must balance horizontal resolution against simulation timeframes. Delve into the combination of mapping and phase averaging as a coarse propagator for parareal, supported by various examples. Conclude with insights into three new research directions: multi-level parareal convergence proof, mean-corrected phase averaging mapping, and applications on spherical geometries.
