Shadow boundary effects in hybrid numerical-asymptotic methods for high-frequency scattering

DOI10.1017/S0956792515000315zbMath1383.65148arXiv1409.3776MaRDI QIDQ4594557

D. P. Hewett

Publication date: 24 November 2017

Published in: European Journal of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.3776

zbMATH Keywords

Fresnel integralboundary element methoddiffractionmesh refinementhigh frequency scattering

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Diffraction, scattering (78A45) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Boundary element methods for boundary value problems involving PDEs (65N38) Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) (33B20)

Related Items (8)

Spectral Galerkin boundary element methods for high-frequency sound-hard scattering problems ⋮ Wavenumber-explicit regularity estimates on the acoustic single- and double-layer operators ⋮ A hybrid numerical-asymptotic boundary element method for high frequency scattering by penetrable convex polygons ⋮ Fast hybrid numerical-asymptotic boundary element methods for high frequency screen and aperture problems based on least-squares collocation ⋮ Wavenumber-explicit analysis for the Helmholtz \(h\)-BEM: error estimates and iteration counts for the Dirichlet problem ⋮ Galerkin boundary element methods for high-frequency multiple-scattering problems ⋮ A sharp relative-error bound for the Helmholtz \(h\)-FEM at high frequency ⋮ Thin-layer solutions of the Helmholtz equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Computing Fresnel integrals via modified trapezium rules
• A fully discrete Galerkin method for high frequency exterior acoustic scattering in three dimensions
• Local solutions to high-frequency 2D scattering problems
• A high frequency boundary element method for scattering by a class of nonconvex obstacles
• A hybrid numerical-asymptotic boundary integral method for high-frequency acoustic scattering
• Tangent ray diffraction and the pekeris caret function
• Thin-Layer Solutions of the Helmholtz and Related Equations
• Numerical-asymptotic boundary integral methods in high-frequency acoustic scattering
• A new frequency-uniform coercive boundary integral equation for acoustic scattering
• On Asymptotic Series for Functions Occurring in the Theory of Diffraction of Waves by Wedges
• A frequency-independent boundary element method for scattering by two-dimensional screens and apertures
• A High Frequency $hp$ Boundary Element Method for Scattering by Convex Polygons
• Hybrid numerical-asymptotic approximation for high-frequency scattering by penetrable convex polygons
• Plane-wave basis finite elements and boundary elements for three-dimensional wave scattering
• A Galerkin Boundary Element Method for High Frequency Scattering by Convex Polygons
• Scalar wave diffraction by tangent rays.

This page was built for publication: Shadow boundary effects in hybrid numerical-asymptotic methods for high-frequency scattering