On the Spectrum of Volume Integral Operators in Acoustic Scattering

DOI10.1007/978-3-319-16727-5_11zbMath1336.65191arXiv1412.8685OpenAlexW2273665882MaRDI QIDQ2799374

Martin Costabel

Publication date: 11 April 2016

Published in: Integral Methods in Science and Engineering (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.8685

zbMATH Keywords

acoustic scatteringessential spectrumHelmholtz equationvolume integral equationdouble layer potential boundary integral operator

Mathematics Subject Classification ID

Boundary element methods applied to problems in fluid mechanics (76M15) Hydro- and aero-acoustics (76Q05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Boundary element methods for boundary value problems involving PDEs (65N38)

Related Items (7)

Stable and efficient FEM-BEM coupling with OSRC regularisation for acoustic wave transmission ⋮ Frequency-robust preconditioning of boundary integral equations for acoustic transmission ⋮ Volume integral equations and single-trace formulations for acoustic wave scattering in an inhomogeneous medium ⋮ On the energetic Galerkin boundary element method applied to interior wave propagation problems ⋮ Volume integral equations for electromagnetic scattering in two dimensions ⋮ A stable 3D energetic Galerkin BEM approach for wave propagation interior problems ⋮ Fast, Adaptive, High-Order Accurate Discretization of the Lippmann--Schwinger Equation in Two Dimensions

Cites Work

• The essential spectrum of the volume integral operator in electromagnetic scattering by a homogeneous body
• Volume and surface integral equations for electromagnetic scattering by a dielectric body
• An integral equation approach and the interior transmission problem for Maxwell's equations
• A direct boundary integral equation method for transmission problems
• T-coercivity for scalar interface problems between dielectrics and metamaterials
• Spectral Properties for the Magnetization Integral Operator
• The operator equations of Lippmann–Schwinger type for acoustic and electromagnetic scattering problems inL²
• Boundary Integral Operators on Lipschitz Domains: Elementary Results

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