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. 
@article{MM_2019_31_4_a0,
     author = {O. V. Osipov and A. G. Brusentsev},
     title = {Optimal location of heat sources inside areas of complex geometric forms},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {3--16},
     publisher = {mathdoc},
     volume = {31},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2019_31_4_a0/}
}
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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/