Condition number estimates for combined potential boundary integral operators in acoustic scattering

DOI10.1216/JIE-2009-21-2-229zbMath1167.35030OpenAlexW1966793029MaRDI QIDQ2389591

Marko Lindner, Ivan G. Graham, Simon N. Chandler-Wilde, Stephen Langdon

Publication date: 17 July 2009

Published in: Journal of Integral Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/jie-2009-21-2-229

zbMATH Keywords

integral equationacoustic scatteringcondition numbers

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Hydro- and aero-acoustics (76Q05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Linear operators on function spaces (general) (47B38) Integral operators (47G10) Numerical methods for partial differential equations, boundary value problems (65N99)

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Cites Work

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• On the condition number of boundary integral operators for the exterior Dirichlet problem for the Helmholtz equation
• Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains
• Potential techniques for boundary value problems on \(C^1\)-domains
• Boundary integral solution of the exterior Helmholtz problem
• Boundary value problems and Hardy spaces associated to the Helmholtz equation in Lipschitz domains
• A hybrid numerical-asymptotic boundary integral method for high-frequency acoustic scattering
• Über das Dirichletsche Außenraumproblem für die Helmholtzsche Schwingungsgleichung
• Zur Dirichletschen Randwertaufgabe des Außenraumes der Schwingungsgleichung
• On the spectrum of the electric field integral equation and the convergence of the moment method
• Condition number estimates for combined potential integral operators in acoustics and their boundary element discretisation
• Wave-Number-Explicit Bounds in Time-Harmonic Scattering
• On the Acoustic Single Layer Potential: Stabilization and Fourier Analysis
• On the choice of the coupling parameter in boundary integral formulations of the exterior acoustic problem
• Surface scattering in three dimensions: an accelerated high–order solver
• Uniqueness in inverse obstacle scattering with conductive boundary conditions
• MINIMIZING THE CONDITION NUMBER OF BOUNDARY INTEGRAL OPERATORS IN ACOUSTIC AND ELECTROMAGNETIC SCATTERING
• A Galerkin Boundary Element Method for High Frequency Scattering by Convex Polygons
• A Refined Galerkin Error and Stability Analysis for Highly Indefinite Variational Problems
• Quadrature methods for multivariate highly oscillatory integrals using derivatives
• The application of integral equation methods to the numerical solution of some exterior boundary-value problems
• Inverse acoustic and electromagnetic scattering theory