Geodesic
Optimal location of heat sources inside areas of complex geometric forms
Matematičeskoe modelirovanie, Tome 31 (2019) no. 4, pp. 3-16 Cet article a éte moissonné depuis la source Math-Net.Ru

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Algorithms for the optimal arrangement of heat sources with volumetric heat release within regions of a complex geometric shape are considered. The distribution found has the minimum total power and provides the temperature in the given temperature corridor. Finite-dimensional approximations of the original problem are constructed in the form of a linear programming problem. A method is given for constructing a finite-difference scheme for solving the heat equation, a brief description of the developed software modules for constructing grids and solving equations. Several computer experiments have been carried out using the developed programs.
Keywords: inverse heat conduction problem, density of heat sources, optimal control problem for elliptic boundary value problems, finite-dimensional approximation, heat balance, simplex method, computational grid. 
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O. V. Osipov; A. G. Brusentsev. Optimal location of heat sources inside areas of complex geometric forms. Matematičeskoe modelirovanie, Tome 31 (2019) no. 4, pp. 3-16. http://geodesic.mathdoc.fr/item/MM_2019_31_4_a0/

[1] Lions J.-L., Controle.optimal de systemes gouvernes par des equations aux derivees partielles, Dunod, Paris, 1968 | MR | Zbl

[2] Mirskaia S. Iu., Sidelnikov V. I., “Ekonomichnyi obogrev pomeshcheniia kak zadacha optimalnogo upravleniia”, Tekhniko-tekhnologicheskie problemy servisa, 2014, no. 4(30), 75–78

[3] Akhmetzianov A. V., Kulibanov V. N., “Optimalnoe razmeshchenie istochnikov dlia statsionarnykh skaliarnykh polei”, Avtomatika i telemekhanika, 1999, no. 6, 50–58

[4] Fedorenko R. P., Priblizhennoe reshenie zadach optimalnogo upravleniia, Nauka, M., 1978, 497 pp.

[5] Butkovskii A. G., Teoriia optimalnogo upravleniia sistemami s raspredelennymi parametrami, Nauka, M., 1965, 474 pp.

[6] Tabak D., Kuo V. S., Optimal control and mathematical programming, Prentice Hall, 1971 | MR

[7] O. M. Alifanov, Inverse heat transfer problems, Springer-Verlag, Berlin–New York, 1994 | Zbl

[8] Sabdenov K. O., Baitasov T. M., “Optimalnoe (energoeffektivnoe) teplosnabzhenie zdaniia v sisteme tsentralnogo otopleniia”, Izvestiia Tomskogo politekhnicheskogo universiteta. Inzhiniring georesursov, 326:8 (2015), 53–60

[9] Brusentsev A. G., Osipov O. V., “Priblizhennoe reshenie zadachi ob optimalnom vybore istochnikov tepla”, Nauchnye vedomosti Belgorodskogo gosudarstvennogo universiteta, 5(124):26 (2012), 60–69 | Zbl

[10] Osipov O. V., “Optimalnoe raspolozhenie istochnikov tepla v neodnorodnoi srede”, Vestnik Belgorodskogo gosudarstvennogo tekhnologicheskogo universiteta im. V.G. Shukhova, 2013, no. 1, 154–158

[11] Brusentsev A. G., Osipov O. V., “Optimalnyi vybor istochnikov tepla pri nalichii konvektsii”, Nauchnye vedomosti BelGU. Matematika. Fizika, 26(169):33 (2013), 64–82

[12] Vabishchevich P. N., Samarskii A. A., “Raznostnye skhemy dlia zadach konvektsii-diffuzii na nereguliarnykh setkakh”, Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki, 40:5 (2000), 726–739 | Zbl

[13] Shangareeva G. R., Mustafina S. A., “Rasparallelivanie metoda sopriazhennykh gradientov s ispolzovaniem tekhnologii Nvidia CUDA”, Nauchnyi vestnik, 2014, no. 2(2), 154–161

[14] Chernyshenko A. Iu., “Postroenie setok tipa vosmerichnoe derevo so skolotymi iacheikami v neodnorodnykh oblastiakh”, Vychislitelnye metody i programmirovanie, 14 (2013), 229–245