Inverse coefficient problems and fast automatic differentiation

An approach to solving the problem of determining the thermal conductivity of a substance based on the results of observing the dynamics of the temperature field is proposed. The consideration is based on the Dirichlet boundary value problem for the three-dimensional nonstationary heat equation. The...

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Bibliographic Details
Published inJournal of inverse and ill-posed problems Vol. 30; no. 3; pp. 447 - 460
Main Authors Evtushenko, Yury, Zubov, Vladimir, Albu, Alla
Format Journal Article
LanguageEnglish
Published Berlin De Gruyter 01.06.2022
Walter de Gruyter GmbH
Subjects
49J20
Boundary value problems
Differentiation
Dirichlet problem
fast automatic differentiation
Heat conductivity
Heat transfer
Inverse coefficient problems
nonlinear problems
Optimal control
Temperature distribution
Thermal conductivity
Thermodynamics
three-dimensional heat equation
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Summary:An approach to solving the problem of determining the thermal conductivity of a substance based on the results of observing the dynamics of the temperature field is proposed. The consideration is based on the Dirichlet boundary value problem for the three-dimensional nonstationary heat equation. The effectiveness of the proposed approach is based on the application of the Fast Automatic Differentiation technique. The required thermal conductivity coefficient is determined as the solution to the formulated optimal control problem.
ISSN:0928-0219
1569-3945
DOI:10.1515/jiip-2021-0075