Numerical evaluation of oscillatory integrals via automated steepest descent contour deformation

DOI10.1016/j.jcp.2024.112787arXiv2307.07261OpenAlexW4391152061MaRDI QIDQ6126570

Daan Huybrechs, A. Gibbs, D. P. Hewett

Publication date: 9 April 2024

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2307.07261

zbMATH Keywords

saddle point methodoscillatory quadraturenumerical steepest descent methodintegrals with coalescing saddles

Mathematics Subject Classification ID

Numerical approximation and computational geometry (primarily algorithms) (65Dxx) Approximations and expansions (41Axx) Approximations and expansions (41-XX)

Cites Work

• A Gaussian quadrature rule for oscillatory integrals on a bounded interval
• Computing the zeros, maxima and inflection points of Chebyshev, Legendre and Fourier series: solving transcendental equations by spectral interpolation and polynomial rootfinding
• Problem of whispering gallery waves in a neighborhood of a simple zero of the effective curvature of the boundary
• An adaptive contour code for the numerical evaluation of the oscillatory cuspoid canonical integrals and their derivatives.
• Contour integral solutions of the parabolic wave equation
• Fast hybrid numerical-asymptotic boundary element methods for high frequency screen and aperture problems based on least-squares collocation
• Asymptotic Approximations of Integrals
• A Sparse Discretization for Integral Equation Formulations of High Frequency Scattering Problems
• Computing Highly Oscillatory Integrals
• The kissing polynomials and their Hankel determinants
• Exactness of Quadrature Formulas
• Searchlight asymptotics for high-frequency scattering by boundary inflection
• A Numerical Method for Oscillatory Integrals with Coalescing Saddle Points
• The Topology of the Level Curves of Harmonic Functions with Critical Points
• Unnamed Item