A time-frequency method for acoustic scattering with trapping

TL;DR

This paper introduces a Fourier transform-based hybrid time-frequency method to solve acoustic scattering problems in trapping regions, effectively handling oscillatory behavior and long time horizons with improved computational techniques.

Contribution

It extends hybrid time-frequency schemes to trapping domains and combines a fast sinc transform with contour integration for enhanced accuracy and efficiency.

Findings

Successfully models acoustic scattering in trapping regions.

Handles highly oscillatory solutions over long time periods.

Improves computational smoothness and efficiency.

Abstract

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.