Two numerical methods for an inverse problem for the 2-D Helmholtz equation

DOI10.1016/S0021-9991(02)00023-2zbMath1016.65078OpenAlexW2009462223MaRDI QIDQ1869843

Thomas R. Lucas, Michael V. Klibanov, Yuriy A. Gryazin

Publication date: 28 April 2003

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0021-9991(02)00023-2

zbMATH Keywords

numerical resultsinverse problemconjugate gradient methodHelmholtz equationpreconditionerselliptic systemssubsurface imagingland minesmarching finite-difference scheme

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Finite difference methods for boundary value problems involving PDEs (65N06) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21)

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A meshless method for some inverse problems associated with the Helmholtz equation ⋮ Analysis of multi-frequency subspace migration weighted by natural logarithmic function for fast imaging of two-dimensional thin, arc-like electromagnetic inhomogeneities ⋮ A PDE-based inverse solver for diffusion tomography using multiple continuous wave sources ⋮ Identifying the wavenumber for the inverse Helmholtz problem using an enriched finite element formulation ⋮ Boundary knot method for the Cauchy problem associated with the inhomogeneous Helmholtz equation ⋮ Parameter identification in Helmholtz-type equations with a variable coefficient using a regularized DRBEM

Uses Software

• symrcm

Cites Work

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• A practical guide to splines
• GMRES computation of high frequency electrical field propagation in land mine detection
• Numerical Solution of a Subsurface Imaging Inverse Problem
• Three-dimensional inverse scattering for the wave equation: weak scattering approximations with error estimates
• Computational Methods for Integral Equations
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Numerical Linear Algebra for High-Performance Computers
• Optical tomography in medical imaging
• Imaging the diffusion coefficient in a parabolic inverse problem in optical tomography
• Numerical Solution of a Parabolic Inverse Problem in Optical Tomography Using Experimental Data
• A fast and accurate imaging algorithm in optical/diffusion tomography
• A shape reconstruction method for electromagnetic tomography using adjoint fields and level sets
• Inverse problems for a perturbed dissipative half-space
• A propagation-backpropagation method for ultrasound tomography
• A nonlinear inversion method for 3D electromagnetic imaging using adjoint fields