Numerical study of stability of an algorithm for identifying the thermal conductivity in the three-dimensional case. (English) Zbl 1531.65147
Summary: We consider the problem of identifying the temperature-dependent thermal conductivity of a material in the three-dimensional case. We numerically study the stability of the algorithm based on the fast automatic differentiation technique. We show that a perturbation of experimental data leads to a perturbation of the sought thermal conductivity of the same order.
MSC:
| 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 |
| 35K05 | Heat equation |
| 80A19 | Diffusive and convective heat and mass transfer, heat flow |
| 49M41 | PDE constrained optimization (numerical aspects) |
| 49N45 | Inverse problems in optimal control |
References:
| [1] | Zverev, VG; Gol’din, VD; Nazarenko, VA, Radiation-conduction heat transfer in fibrous heat-resistant insulation under thermal effect, High Temp., 46, 1, 108-114 (2008) · doi:10.1134/s10740-008-1015-0 |
| [2] | Alifanov, OM; Cherepanov, VV, Mathematical simulation of high-porosity fibrous materials and determination of their physical properties, High Temp., 47, 3, 438-447 (2009) · doi:10.1134/S0018151X09030183 |
| [3] | Vabishchevich, PN; Denisenko, AY, Numerical methods for solving the coefficient inverse problem, Comput. Math. Model., 3, 3, 261-267 (1992) · Zbl 1331.65134 · doi:10.1007/BF01133895 |
| [4] | Samarskii, AA; Vabishchevich, PN, Numerical Methods for Solving Inverse Problems of Mathematical Physics (2007), Berlin: de Gruyter, Berlin · Zbl 1136.65105 · doi:10.1515/9783110205794 |
| [5] | Czél, B.; Gróf, G., Simultaneous identification of temperature-dependent thermal properties via enhanced genetic algorithm, Int. J. Thermophys., 33, 1023-1041 (2012) · doi:10.1007/s10765-012-1226-9 |
| [6] | Albu, AF; Zubov, VI, Identification of the thermal conductivity coefficient in the three-dimensional case by solving a corresponding optimization problem, Comput. Math. Math. Phys., 61, 9, 1416-1431 (2021) · Zbl 1477.80006 · doi:10.1134/S0965542521090037 |
| [7] | Albu, AF; Zubov, VI, Determination of the thermal conductivity from the heat flux on the surface of a three-dimensional body, Comput. Math. Math. Phys., 61, 10, 1567-1581 (2021) · Zbl 1477.80005 · doi:10.1134/S096554252110002X |
| [8] | Evtushenko, YG, Computation of exact gradients in distributed dynamic systems, Optim. Methods Softw., 9, 45-75 (1998) · Zbl 0909.49013 · doi:10.1080/10556789808805686 |
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