Determination of the thermal conductivity from the heat flux on the surface of a three-dimensional body

DOI10.1134/S096554252110002XzbMath1477.80005OpenAlexW3212829591MaRDI QIDQ2245888

V. I. Zubov, Alla F. Albu

Publication date: 15 November 2021

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s096554252110002x

zbMATH Keywords

optimal controlnonlinear problemsthree-dimensional heat equationcoefficient inverse problemsalternating direction schemesnumerical-optimization methods

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Heat equation (35K05) Inverse problems for PDEs (35R30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Optimization problems in thermodynamics and heat transfer (80M50) Finite difference methods applied to problems in thermodynamics and heat transfer (80M20) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32) Inverse problems in thermodynamics and heat transfer (80A23) Variational methods applied to problems in thermodynamics and heat transfer (80M30)

Related Items (4)

Inverse coefficient problems and fast automatic differentiation ⋮ On the uniqueness of identification the thermal conductivity and heat capacity of substance ⋮ Numerical study of stability of an algorithm for identifying the thermal conductivity in the three-dimensional case ⋮ Application of second-order optimization methods for solving an inverse coefficient problem in the three-dimensional statement

Cites Work

• Application of fast automatic differentiation for solving the inverse coefficient problem for the heat equation
• Generalized fast automatic differentiation technique
• Identification of thermal conductivity coefficient using a given temperature field
• Identification of the thermal conductivity coefficient in two dimension case
• On the stability of the algorithm of identification of the thermal conductivity coefficient
• Application of the fast automatic differentiation technique for solving inverse coefficient problems
• Choice of finite-difference schemes in solving coefficient inverse problems
• Identification of the thermal conductivity coefficient in the three-dimensional case by solving a corresponding optimization problem
• Identification of the thermal conductivity coefficient using a given surface heat flux
• The Numerical Solution of Parabolic and Elliptic Differential Equations
• On the Numerical Solution of Heat Conduction Problems in Two and Three Space Variables
• Stability theory of difference schemes and iterative methods

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