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 Matem. Mod., 2019, Volume 31, Number 4, Pages 3–16 (Mi mm4061)

Optimal location of heat sources inside areas of complex geometric forms

O. V. Osipov, A. G. Brusentsev

Shukhov Belgorod State Technological University

Abstract: 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.

 Funding Agency The article was prepared within a development program of the Base V.G. Shukhov University on the basis of BSTU.

DOI: https://doi.org/10.1134/S0234087919040014

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Revised: 21.05.2018
Accepted:10.09.2018

Citation: O. V. Osipov, A. G. Brusentsev, “Optimal location of heat sources inside areas of complex geometric forms”, Matem. Mod., 31:4 (2019), 3–16

Citation in format AMSBIB
\Bibitem{OsiBru19} \by O.~V.~Osipov, A.~G.~Brusentsev \paper Optimal location of heat sources inside areas of complex geometric forms \jour Matem. Mod. \yr 2019 \vol 31 \issue 4 \pages 3--16 \mathnet{http://mi.mathnet.ru/mm4061} \crossref{https://doi.org/10.1134/S0234087919040014} \elib{https://elibrary.ru/item.asp?id=37242381}