A time-frequency method for acoustic scattering with trapping

A Fourier transform method is introduced for a class of hybrid time-frequency methods that solve the acoustic scattering problem in regimes where the solution exhibits both highly oscillatory behavior and slow decay in time. This extends the applicability of hybrid time-frequency schemes to domains with trapping regions. A fast sinc transform technique for managing highly oscillatory behavior and long time horizons is combined with a contour integration scheme that improves smoothness properties in the integrand.