A new non-iterative singular sources method for the reconstruction of piecewise constant media.

DOI10.1007/s00211-004-0524-yzbMath1061.65120OpenAlexW1998348293MaRDI QIDQ704793

Roland W. E. Potthast

Publication date: 19 January 2005

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-004-0524-y

zbMATH Keywords

acoustic scatteringinverse scatteringsingular sources method

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Hydro- and aero-acoustics (76Q05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Inverse problems (including inverse scattering) in optics and electromagnetic theory (78A46)

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Cites Work

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• Multidimensional inverse spectral problem for the equation \(-\Delta \psi -(v(x)-Eu(x))\psi =0\)
• Reconstructions from boundary measurements
• Inverse acoustic and electromagnetic scattering theory.
• Recovery of singularities for formally determined inverse problems
• Stability estimates and reconstructions in inverse acoustic scattering using singular sources
• On the denseness of Herglotz wave functions and electromagnetic Herglotz pairs in Sobolev spaces
• On the numerical solution of a three-dimensional inverse medium scattering problem
• The MUSIC-algorithm and the factorization method in inverse scattering theory for inhomogeneous media
• A Novel Method for Solving the Inverse Scattering Problem for Time-Harmonic Acoustic Waves in the Resonance Region
• A Novel Method for Solving the Inverse Scattering Problem for Time-Harmonic Acoustic Waves in the Resonance Region II
• Elliptic Partial Differential Equations of Second Order
• Reconstruction of an obstacle from the scattering amplitude at a fixed frequency
• A point source method for inverse acoustic and electromagnetic obstacle scattering problems
• Characterization of the shape of a scattering obstacle using the spectral data of the far field operator
• Iterative method for multi-dimensional inverse scattering problems at fixed frequencies
• A simple method using Morozov's discrepancy principle for solving inverse scattering problems
• A  range test  for determining scatterers with unknown physical properties
• The No Response Test---A Sampling Method for Inverse Scattering Problems
• Recent Developments in Inverse Acoustic Scattering Theory
• A simple method for solving inverse scattering problems in the resonance region
• A fast new method to solve inverse scattering problems
• Enclosing a polygonal cavity in a two-dimensional bounded domain from Cauchy data
• A propagation-backpropagation method for ultrasound tomography
• Recovery of the potential from fixed-energy scattering data

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