Iterative methods for solving the exterior Dirichlet problem for the Helmholtz equation with applications to the inverse scattering problem for low frequency acoustic waves

DOI10.1016/0022-247X(80)90261-9zbMath0444.35023MaRDI QIDQ1144725

David Colton, Rainer Kress

Publication date: 1980

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

Dirichlet problemintegral equationwave numberfundamental solutioniterative methodsHelmholtz equationexterior Dirichlet probleminverse scattering problemlow frequency acoustic waves

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Inverse problems for PDEs (35R30) Theoretical approximation in context of PDEs (35A35) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (9)

A method for solving the inverse elastic scattering problem via low- frequency moments ⋮ The exterior dirichlet problem for the Laplace equation ⋮ Inverse scattering for an accoustically soft scatterer in the low-frequency region ⋮ Remarks on the inverse scattering problem for low frequency acoustic waves ⋮ On an exterior Laplace equation problem with Robin boundary condition ⋮ Solution of the Dirichlet problem for the Laplace equation. ⋮ Justification of the collocation method for an integral equation of the exterior Dirichlet problem for the Laplace equation ⋮ On constructing the solution to the exterior Dirichlet problem for the Helmholtz equation ⋮ Stable methods for determining the surface impedance of an obstacle from low frequency far field data

Cites Work

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• On Neumann's method for the exterior Neumann problem for the Helmholtz equation
• The Dirichlet problem for the Helmholtz equation
• The inverse scattering problem for a cylinder
• On the limiting behaviour of solutions to boundary integral equations associated with time harmonic wave equations for small frequencies
• The direct and inverse scattering problems for an arbitrary cylinder: Dirichlet boundary conditions
• Can One See the Shape of a Surface?
• The Low-Frequency Scalar Dirichlet Scattering by a General Ellipsoid
• Low Frequency Scattering by Spheroids and Disks 1. Dirichlet Problem for a Prolate Spheroid

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