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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2008, Volume 11, Number 1, Pages 41–51 (Mi sjvm32)  
This article is cited in 34 scientific papers (total in 34 papers)

The gradient-based method for solving the inverse coefficient heat-conduction problem

S. I. Kabanikhina, A. Kh. Khasanovb, A. V. Penenkoa

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Applied Mathematical Sciences Research, Center Kocaeli University
Full-text PDF (307 kB) Citations (34)
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Abstract: An iterative gradient descent method has been applied to the inverse coefficient heat-conduction problem with overdetermined boundary conditions. Some theoretical estimates have been obtained for variation of the target functional with respect to the variation of the coefficient. Using these estimates, an approximated gradient of the target functional has been constructed. In the numerical experiments, the iteration convergence rates for different gradient descent parameters were compared.
Key words: coefficient identification, inverse heat conduction problem, gradient, adjoint problem, gradient descent parameter.
Received: 23.11.2006
Revised: 08.02.2007
English version:
Numerical Analysis and Applications, 2008, Volume 1, Issue 1, Pages 34–45
DOI: https://doi.org/10.1007/s12258-008-1004-x
UDC: 519.6
Language: Russian
Citation: S. I. Kabanikhin, A. Kh. Khasanov, A. V. Penenko, “The gradient-based method for solving the inverse coefficient heat-conduction problem”, Sib. Zh. Vychisl. Mat., 11:1 (2008), 41–51; Num. Anal. Appl., 1:1 (2008), 34–45
Citation in format AMSBIB
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\by S.~I.~Kabanikhin, A.~Kh.~Khasanov, A.~V.~Penenko
\paper The gradient-based method for solving the inverse coefficient heat-conduction problem
\jour Sib. Zh. Vychisl. Mat.
\yr 2008
\vol 11
\issue 1
\pages 41--51
\mathnet{http://mi.mathnet.ru/sjvm32}
\transl
\jour Num. Anal. Appl.
\yr 2008
\vol 1
\issue 1
\pages 34--45
\crossref{https://doi.org/10.1007/s12258-008-1004-x}
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    • This publication is cited in the following 34 articles:
    1. H.K. Al-Mahdawi, Farah Hatem Khorsheed, Ali Subhi Alhumaima, Ali J. Ramadhan, Kilan M Hussien, Hussein Alkattan, N. Aldahan, A.J. Ramadhan, “Intelligent Particle Swarm Optimization Method for Parameter Selecting in Regularization Method for Integral Equation”, BIO Web Conf., 97 (2024), 00039  crossref
    2. Deng Xiaomao, Jiang Jiahua, Yuan Jinglan, Liao Ziju, “A parallel domain decomposition method for identifying the space-time dependent diffusion coefficients of 3D parabolic problems”, Sci. Sin.-Math., 53:11 (2023), 1487  crossref
    3. Rostislav D. Nedin, Sergei A. Nesterov, Alexander O. Vatulyan, Advanced Structured Materials, 185, Solid Mechanics, Theory of Elasticity and Creep, 2023, 247  crossref
    4. Bashar Talib Al-Nuaimi, H.K. Al-Mahdawi, Zainalabideen Albadran, Hussein Alkattan, Mostafa Abotaleb, El-Sayed M. El-kenawy, “Solving of the Inverse Boundary Value Problem for the Heat Conduction Equation in Two Intervals of Time”, Algorithms, 16:1 (2023), 33  crossref
    5. Salam Abdulkhaleq Noaman, H.K. Al-Mahdawi, Bashar Talib Al-Nuaimi, A.I. Sidikova, “Iterative method for solving linear operator equation of the first kind”, MethodsX, 10 (2023), 102210  crossref
    6. Hassan K. Ibrahim Al-Mahdawi, Mostafa Abotaleb, Hussein Alkattan, Al-Mahdawi Zena Tareq, Amr Badr, Ammar Kadi, “Multigrid Method for Solving Inverse Problems for Heat Equation”, Mathematics, 10:15 (2022), 2802  crossref
    7. H.K. Al-Mahdawi, A. I Sidikova, Hussein Alkattan, Mostafa Abotaleb, Ammar Kadi, El-Sayed M El-kenawy, “Parallel multigrid method for solving inverse problems”, MethodsX, 9 (2022), 101887  crossref
    8. Hassan K. Ibrahim Al-Mahdawi, Hussein Alkattan, Mostafa Abotaleb, Ammar Kadi, El-Sayed M. El-kenawy, “Updating the Landweber Iteration Method for Solving Inverse Problems”, Mathematics, 10:15 (2022), 2798  crossref
    9. I. V. Boykov, V. A. Ryazantsev, “An approximate method for solving the inverse coefficient problem for the heat equation”, J. Appl. Industr. Math., 15:2 (2021), 175–189  mathnet  crossref  crossref  elib
    10. S. B. Sorokin, “Direct method for solving the inverse coefficient problem for elliptic equation with piecewise constant coefficients”, J. Appl. Industr. Math., 15:2 (2021), 331–342  mathnet  crossref  crossref  elib
    11. Zhao Zh.-X., Guo B.-Zh., Han Zh.-J., “Boundary Control and Observation to Inverse Coefficient Problem For Heat Equation With Unknown Source and Initial Value”, IEEE Trans. Autom. Control, 66:12 (2021), 6003–6010  crossref  mathscinet  isi  scopus
    12. Vatulyan A.O., Nesterov S.A., “On Determination of the Thermomechanical Characteristics of a Functionally Graded Finite Cylinder”, Mech. Sol., 56:7 (2021), 1429–1438  crossref  mathscinet  isi  scopus
    13. Kabanikhin S., Krivorotko O., Takuadina A., Andornaya D., Zhang Sh., “Geo-Information System of Tuberculosis Spread Based on Inversion and Prediction”, J. Inverse Ill-Posed Probl., 29:1 (2021), 65–79  crossref  mathscinet  isi  scopus
    14. Vatulyan A.O., Nesterov S.A., “On the Identification Problem of the Thermomechanical Characteristics of the Finite Functionally Graded Cylinder”, Izv. Sarat. Univ. Novaya Ser.-Mat. Mekhan. Inform., 21:1 (2021), 35–47  mathnet  crossref  mathscinet  isi  scopus
    15. A. O. Vatulyan, S. A. Nesterov, Trends in Mathematics, Operator Theory and Differential Equations, 2021, 303  crossref
    16. Gorozhankina A.S., Orlov I D., Belousova D.A., Iv International Scientific and Technical Conference Mechanical Science and Technology Update (Mstu-2020), Journal of Physics Conference Series, 1546, IOP Publishing Ltd, 2020  crossref  isi  scopus
    17. A. I. Sidikova, “The study of an inverse boundary problem for the heat conduction equation”, Num. Anal. Appl., 12:1 (2019), 70–86  mathnet  crossref  crossref  isi  elib
    18. I. V. Boikov, V. A. Ryazantsev, “Ob odnom priblizhennom metode opredeleniya koeffitsienta teploprovodnosti”, Zhurnal SVMO, 21:2 (2019), 149–163  mathnet  crossref  elib
    19. Berger J., Busser T., Dutykh D., Mendes N., “An Efficient Method to Estimate Sorption Isotherm Curve Coefficients”, Inverse Probl. Sci. Eng., 27:6 (2019), 735–772  crossref  mathscinet  isi  scopus
    20. Vatulyan A.O., Nesterov S.A., “On the Peculiarities of Solving the Coefficient Inverse Problem of Heat Conduction For a Two-Part Layer”, Izv. Sarat. Univ. Novaya Ser.-Mat. Mekhan. Inform., 19:4 (2019), 409–423  mathnet  crossref  mathscinet  isi
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