Geodesic
Optimal location of heat sources inside areas of complex geometric forms
Matematičeskoe modelirovanie, Tome 31 (2019) no. 4, pp. 3-16.

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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/

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