The nonlinear Landweber method applied to an inverse scattering problem for sound-soft obstacles in 3D

DOI10.1016/j.cpc.2011.07.023zbMath1308.76246OpenAlexW2011203048MaRDI QIDQ1943067

Andreas Kleefeld, Tzu-Chu Lin

Publication date: 15 March 2013

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cpc.2011.07.023

zbMATH Keywords

integral equationHelmholtz's equationtwo-grid methodinverse scatteringdomain derivativenonlinear Landweber method

Mathematics Subject Classification ID

Hydro- and aero-acoustics (76Q05) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21)

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Cites Work

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• Multigrid methods for boundary integral equations
• Grenz- und Sprungrelationen für Potentiale mit quadratsummierbarer Flächenbelegung
• Inverse acoustic and electromagnetic scattering theory.
• A modified Landweber iteration for solving parameter estimation problems
• A convergence analysis of the Landweber iteration for nonlinear ill-posed problems
• Convergence criteria of iterative methods based on Landweber iteration for solving nonlinear problems
• Fast methods for three-dimensional inverse obstacle scattering problems
• On the Landweber iteration for nonlinear ill-posed problems
• The Numerical Solution of the Three-Dimensional Inverse Scattering Problem for Time Harmonic Acoustic Waves
• The domain derivative and two applications in inverse scattering theory
• The Landweber iteration applied to inverse conductive scattering problems
• Local ill-posedness and source conditions of operator equations in Hilbert spaces
• Frechet differentiability of boundary integral operators in inverse acoustic scattering
• Two-Grid Iteration Methods for Linear Integral Equations of the Second Kind on Piecewise Smooth Surfaces in $\mathbb{R}^3 $
• Newton-Kantorovitch algorithm applied to an electromagnetic inverse problem
• Recent Developments in Inverse Acoustic Scattering Theory
• A Regularized Sampling Method for Solving Three-Dimensional Inverse Scattering Problems
• On the solution of three-dimensional inverse obstacle acoustic scattering problems by a regularized Newton method
• Frechet derivatives in inverse obstacle scattering
• Piecewise Polynomial Collocation for Boundary Integral Equations
• The Numerical Solution of Fredholm integral Equations of the Second Kind
• Linear integral equations