A time-frequency method for acoustic scattering with trapping

2025/06/18 by Heather Wilber, Wietse Vaes, Wilber, Heather +4 · 1 citation
Computer Science · Earth and Planetary Sciences · Engineering · #65F05 #65M80 #65R20 #FOS: Mathematics #Image and Signal Denoising Methods #Microwave Imaging and Scattering Analysis #Numerical Analysis (math.NA) #Underwater Acoustics Research

paper · pdf · doi:10.48550/arxiv.2506.15165

openalex publication_date 2025/06/18 · openalex created_date 2025/10/19 · openalex updated_date 2026/08/01

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.

Citations

• Efficient time-domain scattering synthesis via frequency-domain singularity subtraction
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• Evaluation of resonances: adaptivity and AAA rational approximation of randomly scalarized boundary integral resolvents
• Zeta Correction: A New Approach to Constructing Corrected Trapezoidal Quadrature Rules for Singular Integral Operators
• Corrected Trapezoidal Rules for Boundary Integral Equations in Three Dimensions
• Solving Laplace problems with corner singularities via rational functions
• Chopping a Chebyshev Series
• Evaluation of layer potentials close to the boundary for Laplace and\n Helmholtz problems on analytic planar domains
• A direct solver with O(N) complexity for integral equations on\n one-dimensional domains

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