517.956.4 On the numerical solution of the inverse problem of heat conduction with radiation

Gribov A. F. (Bauman Moscow State Technical University), Zhidkov E. N. (Bauman Moscow State Technical University), Krasnov I. K. (Bauman Moscow State Technical University)

INVERSE PROBLEM, PARABOLIC EQUATION, APPROXIMATION, TIKHONOV FUNCTIONAL, RANDOM SEARCH


doi: 10.18698/2309-3684-2019-1-4353


The inverse problem of restoring the thermal conductivity coefficient of a nonlinear parabolic equation by the final temperature distribution, which serves as a mathematical model for the problem of determining structural defects, is investigated. An algorithm for numerical solution of the problem is proposed. A numerical example is considered.


[1] Budadin O.N., Kutyurin V.Yu., Kaledin V.O. Diagnostics of the technical con-dition of pressure vessels operating under internal pressure by a thermal (thermal imaging) method. Russian Journal of Nondestructive Testing, 2008, vol. 44, no. 10, pp. 669−675.
[2] Vavilov V.P., Nesteruk D.A., Shiryaev V.V., Ivanov A.I., Swiderski W. Thermal (infrared) tomography: Terminology, principal procedures, and application to nondestructive testing of composite materials. Russian Journal of Nonde-structive Testing, 2010, vol. 46, no. 3, pp. 151−161.
[3] Budadin O.N., Potapov A.I., Kolganov V.I., Troickij−Markov T.E., Ab-ramova E.V. Teplovoj nerazrushayushchij kontrol' izdelij [Thermal non-destructive testing of products]. Moscow, Nauka Publ., 2002, 473 p.
[4] Macevityj Yu.M. Obratnye zadachi teploprovodnosti: v 2 t. [Inverse problems of thermal conductivity]. Kiev, Naukova Dumka Publ., 2002, 408 p.
[5] Macevityj Yu.M., Kostikov A.O. Problemy mashinostroeniya — Problems of mechanical engineering, 2007, vol. 10, no. 3, pp. 27–34
[6] Cheng C.-Y. Shape Identification by Inverse Heat Transfer Method. Journal Heat Transfer, 2003, vol. 125(2), рр. 224–231.
[7] Chun-Yun Wu, Wen-Chang Lin Using genetic algorithms to detect interfacial cracks on the basis of the thermal resistance of multilayer materials. Russian Journal of Nondestructive Testing, 2007, vol. 43, iss. 7, pp. 474–483.
[8] Huang C.H., Shih C.C. Identify the Interfacial Configurations in a Multiple Re-gion Domain Problem. Journal Thermophysics Heat Transfer, 2005, vol. 19, iss. 4, pp. 533–641.
[9] Dimitrienko Yu.I., Nikolaev A.A., Krasnov I.K. Razrabotka avtomatizirovannoy tekhnologii raspoznavaniya trekhmernykh defektov v kompozitnykh elementakh konstruktsiy po teplovizionnym izobrazheniyam. [Development of Computer-Aided Technology of 3D-Defect Identification in Composite Members Using Thermal Images]. Vestnik MGTU im N.E.Baumana. Ser. Estestvennye nauki [Herald of the Bauman Moscow State Technical University. Natural Sciences]. 2010, № 2, pp. 40−49.
[10] Prilepko A.I., Orlovsky D.G., Vasin I.A. Methods for solving inverse problems in Mathematical Physics. New−York, Marcel Dekker, Inc., 1999, 724 p.
[11] Kozhanov A.I. Composite type equations and inverse problems. Utrecht, VSP Publ., 1999, 171 p.
[12] Ivanchov M. Inverse problems for equation of parabolic type. Lviv, WNTL Publ., 2003.
[13] Isakov V. Inverse Problems for Partial Differential Equations. Berlin, Spring-er−Verlag, 1998, 346 p.
[14] Isakov V. The inverse problem of option pricing. Recent Developments in Theo-ry and Numerics. International Conference on Inverse problems, 2002, pp. 47–55.
[15] Goldman, N.L. Doklady akademii nauk — Reports of the Academy of Sciences, 2011, vol. 438, no. 2, pp. 162–167.
[16] Kalitkin N.N. Chislennye metody [Numerical methods] Moscow, Nauka Publ., 1978, 512 p.
[17] Tihonov A.N., Arsenin V.Ya. Metody resheniya nekorrektnyh zadach [Methods for solving incorrect problems]. Moscow, Nauka Publ., 1979, 223 p.
[18] Krasnov I.K., Zubarev K.M., Ivanova T.L. Matematicheskoe modelirovanie i chislennye metody — Mathematical Modeling and Computational Methods, 2018, no. 1, pp. 41–54.
[19] Gribov A.F., Zhidkov E.N., Krasnov I.K. Inzhenernyy zhurnal: nauka i inno-vatsii — Engineering Journal: Science and Innovation, 2013, no. 9 (21). DOI: 10.18698/2308-6033-2013-9-964


Грибов А.Ф., Жидков Е.Н., Краснов И.К. О численном решении обратной зада-чи теплопроводности с излучением. Математическое моделирование и численные методы, 2019, № 1, с. 43–53.



Download article

Количество скачиваний: 81