Numerical algorithm for two-dimensional inverse acoustic problem based on Gel'fand–Levitan–Krein equation

DOI10.1515/jiip.2011.016zbMath1279.35066OpenAlexW2328089678MaRDI QIDQ2874488

Maxim A. Shishlenin, Sergey I. Kabanikhin

Publication date: 30 January 2014

Published in: jiip (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/jiip.2011.016

zbMATH Keywords

numerical methodsinverse acoustic problemGel'fand-Levitan-Krein equation

Mathematics Subject Classification ID

Inverse problems in geophysics (86A22) Inverse problems for PDEs (35R30) Wave equation (35L05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32)

Related Items (10)

On justification of the Gelfand-Levitan-Krein method for a two-dimensional inverse problem ⋮ Untangling the nonlinearity in inverse scattering with data-driven reduced order models ⋮ Solving of the coefficient inverse problem for a nonlinear singularly perturbed two-dimensional reaction-diffusion equation with the location of moving front data ⋮ Robust nonlinear processing of active array data in inverse scattering via truncated reduced order models ⋮ PDE-based numerical method for a limited angle x-ray tomography ⋮ On \(t\)-local solvability of inverse scattering problems in two-dimensional layered media ⋮ Numerics of acoustical 2D tomography based on the conservation laws ⋮ Solution of an inverse scattering problem for the acoustic wave equation in three-dimensional media ⋮ Asymptotic analysis of solving an inverse boundary value problem for a nonlinear singularly perturbed time-periodic reaction-diffusion-advection equation ⋮ The inverse scattering problem in a nonstationary medium

Cites Work

• A global uniqueness theorem for an inverse boundary value problem
• Inverse boundary value problems and a theorem of Gel'fand and Levitan
• The Gelfand-Levitan, the Marchenko, and the Gopinath-Sondhi integral equations of inverse scattering theory, regarded in the context of inverse impulse-response problems
• An inverse problem for the wave equation in the half plane
• A discrete Gel'fand-Levitan method for band-matrix inverse eigenvalue problems
• An economical method for the numerical solution of convolution equations
• Dynamical variant of the BC-method: theory and numerical testing
• Boundary control in reconstruction of manifolds and metrics (the BC method)
• Iteration methods for solving a two dimensional inverse problem for a hyperbolic equation
• Boundary control and Gel'fand–Levitan–Krein methods in inverse acoustic problem

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