Numerical steepest descent method for Hankel type of hypersingular oscillatory integrals in electromagnetic scattering problems

DOI10.1155/2021/8021050OpenAlexW3184366017WikidataQ114069875 ScholiaQ114069875MaRDI QIDQ2244316

Qinghua Wu, Mengjun Sun

Publication date: 12 November 2021

Published in: Advances in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2021/8021050

Mathematics Subject Classification ID

Numerical analysis (65-XX) Optics, electromagnetic theory (78-XX)

Related Items (2)

Efficient algorithms for integrals with highly oscillatory Hankel kernels ⋮ New algorithms for approximating oscillatory Bessel integrals with Cauchy-type singularities

Cites Work

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• An improved algorithm for the evaluation of Cauchy principal value integrals of oscillatory functions and its application
• A new algorithm for Cauchy principal value and Hadamard finite-part integrals
• Quadrature rules with multiple nodes for evaluating integrals with strong singularities
• On uniform approximations to hypersingular finite-part integrals
• On the evaluation of Cauchy principal value integrals of oscillatory functions
• Definitions, properties and applications of finite-part integrals
• Hilbert and Hadamard transforms by generalized Chebyshev expansion
• Numerical evaluation of hypersingular integrals
• Sigmoidal transformations and the Euler-Maclaurin expansion for evaluating certain Hadamard finite-part integrals
• Uniform approximations to finite Hilbert transform and its derivative.
• Gauss-Jacobi quadratures for weakly, strongly, hyper- and nearly-singular integrals in boundary integral equation methods for domains with sharp edges and corners
• A fourth order product integration rule by using the generalized Euler-Maclaurin summation formula
• A method for the practical evaluation of the Hilbert transform on the real line
• Uniform approximation to finite Hilbert transform of oscillatory functions and its algorithm
• Clenshaw-Curtis-type quadrature rule for hypersingular integrals with highly oscillatory kernels
• Numerical methods for two classes of singularly oscillatory Bessel transforms and their error analysis
• Quadrature rules for weakly singular, strongly singular, and hypersingular integrals in boundary integral equation methods
• The superconvergence of Newton-Cotes rules for the Hadamard finite-part integral on an interval
• Asymptotics and numerical approximation of highly oscillatory Hilbert transforms
• An Automatic Quadrature for Cauchy Principal Value Integrals

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