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Numerical reconstruction of a non-smooth heat flux in the inverse radial heat conduction problem. (English) Zbl 1448.65141
Summary: When gun barrels are multiple fired, monitoring the non-smooth heat flux of the gun with the additional input data makes it possible to identify the corrosion of the gun. Based on this background, we study the identification of the non-smooth heat flux in a 1-dimensional heat transfer system. Aiming to overcome the non-smoothness of the unknown heat flux and to simplify the choice of regularization parameter, we transform the inverse problem to a constraint optimization problem and prove the existence and convergence properties of the regularization solution. Then an algorithm based on minimizing the data-match term and penalty term alternatively is proposed. Finally, a numerical experiment supports our regularization scheme quantitatively, especially for input data with high noise level.
65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
80A23 Inverse problems in thermodynamics and heat transfer
80M50 Optimization problems in thermodynamics and heat transfer
65K10 Numerical optimization and variational techniques
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65J20 Numerical solutions of ill-posed problems in abstract spaces; regularization
35K05 Heat equation
49J20 Existence theories for optimal control problems involving partial differential equations
49N45 Inverse problems in optimal control
Full Text: DOI
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