One-iteration reconstruction algorithm for geometric inverse source problem

DOI10.1007/s41808-018-0015-4zbMath1497.65266OpenAlexW2790642915WikidataQ130194611 ScholiaQ130194611MaRDI QIDQ1753962

Mourad Hrizi, Maatoug Hassine

Publication date: 29 May 2018

Published in: Journal of Elliptic and Parabolic Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s41808-018-0015-4

zbMATH Keywords

topological optimizationtopological sensitivity analysisKohn-Vogelius formulationgeometric inverse source problem

Mathematics Subject Classification ID

Sensitivity, stability, well-posedness (49K40) Variational methods applied to PDEs (35A15) Perturbations in context of PDEs (35B20) Numerical methods for inverse problems for integral equations (65R32)

Related Items (6)

Shape optimization method for an inverse geometric source problem and stability at critical shape ⋮ Reconstruction and stability analysis of potential appearing in time‐fractional subdiffusion ⋮ A new reconstruction method for a parabolic inverse source problem ⋮ A non-iterative reconstruction method for an inverse problem modeled by a Stokes-Brinkmann equations ⋮ Reconstruction of contact regions in semiconductor transistors using Dirichlet-Neumann cost functional approach ⋮ A non-iterative reconstruction method for bioluminescence tomography

Cites Work

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• On the detection of several obstacles in 2D Stokes flow: topological sensitivity and combination with shape derivatives
• A new reconstruction method for the inverse potential problem
• Topological sensitivity analysis for the modified Helmholtz equation under an impedance condition on the boundary of a hole
• A new general mathematical framework for bioluminescence tomography
• Time domain topological gradient and time reversal analogy: an inverse method for ultrasonic target detection
• Functional analysis, Sobolev spaces and partial differential equations
• The shape and topological optimizations' connection
• Topological and shape gradient strategy for solving geometrical inverse problems
• Detection of point-forces location using topological algorithm in Stokes flows
• The Topological Asymptotic for PDE Systems: The Elasticity Case
• The extended adjoint method
• Topological derivative for multi-scale linear elasticity models applied to the synthesis of microstructures
• Topological Sensitivity Analysis for the Location of Small Cavities in Stokes Flow
• Mathematical theory and numerical analysis of bioluminescence tomography
• Direct algorithms for solving some inverse source problems in 2D elliptic equations
• Overlap domain decomposition method for bioluminescence tomography (BLT)
• Theoretical Numerical Analysis
• Determining conductivity by boundary measurements
• A Fast Local Level Set Method for Inverse Gravimetry
• Topological Sensitivity and Shape Optimization for the Stokes Equations
• Identification of a Core from Boundary Data
• Identification of Dislocations in Materials from Boundary Measurements
• A novel coupled complex boundary method for solving inverse source problems
• Bioluminescence tomography with optimized optical parameters
• From Differential Calculus to 0‐1 Topological Optimization
• The topological asymptotic expansion for the Quasi-Stokes problem
• A new reconstruction method for the inverse source problem from partial boundary measurements
• On Computing a Stable Least Squares Solution to the Inverse Problem for a Planar Newtonian Potential
• A source sensitivity approach for source localization in steady-state linear systems
• Inverse problems for partial differential equations

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