Identification of the thermal conductivity coefficient in the three-dimensional case by solving a corresponding optimization problem

DOI10.1134/S0965542521090037zbMath1477.80006OpenAlexW3206710076MaRDI QIDQ2245906

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/s0965542521090037

zbMATH Keywords

optimal controlnonlinear problemsthree-dimensional heat equationcoefficient inverse problemsnumerical optimization methodsalternating direction schemes

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) PDEs in connection with classical thermodynamics and heat transfer (35Q79)

Related Items (5)

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 ⋮ Determination of the thermal conductivity from the heat flux on the surface of a three-dimensional body ⋮ Application of second-order optimization methods for solving an inverse coefficient problem in the three-dimensional statement

Cites Work

• Unnamed Item
• Identification of thermal conductivity coefficient using a given temperature field
• Application of the fast automatic differentiation technique for solving inverse coefficient problems
• Choice of finite-difference schemes in solving coefficient inverse problems
• Numerical methods for solving inverse problems of mathematical physics.
• 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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