Inverse thermal imaging in materials with nonlinear conductivity by material and shape derivative method

DOI10.1002/mma.1533zbMath1242.49092OpenAlexW1530370207MaRDI QIDQ3106282

Ivan Cimrák

Publication date: 20 December 2011

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.1533

zbMATH Keywords

sensitivity analysislevel set methodshape optimizationspeed method

Mathematics Subject Classification ID

Sensitivity, stability, well-posedness (49K40) Numerical optimization and variational techniques (65K10) Inverse problems in optimal control (49N45) Sensitivity analysis for optimization problems on manifolds (49Q12) PDEs in connection with control and optimization (35Q93)

Related Items (4)

Nonlinear magnetoquasistatic interface problem in a permanent-magnet machine with stochastic partial differential equation constraints ⋮ Detecting damage in thin plates by processing infrared thermographic data with topological derivatives ⋮ Piecewise Constant Level Set Algorithm for an Inverse Elliptic Problem in Nonlinear Electromagnetism ⋮ Application of the topological derivative to post-processing infrared time-harmonic thermograms for defect detection

Cites Work

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• Level set method for the inverse elliptic problem in nonlinear electromagnetism
• The transmission problem for quasi-linear elliptic second order equations in a conical domain. I, II
• Finite element methods for semilinear elliptic and parabolic interface problems
• Uniqueness of weak solution for nonlinear elliptic equations in divergence form
• Non-coercive linear elliptic problems
• Classical solvability and linear schemes for the approximate solution of the diffraction problem for quasilinear equations of parabolic and elliptic type
• The finite element method for elliptic equations with discontinuous coefficients
• Level-set function approach to an inverse interface problem
• Adjoint variable method for time‐harmonic Maxwell equations
• Central WENO Schemes for Hamilton–Jacobi Equations on Triangular Meshes
• Direct Algorithms for Thermal Imaging of Small Inclusions

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