NUMERICAL SOLUTION OF THE NON-STATIONARY PROBLEM OF CHOOSING THE OPTIMAL PLACEMENT OF HEAT SOURCES IN A PARALLELEPIPED
Keywords:non-stationary problems, density, optimal choice, heat sources, implicit schemes, finite-dimensional approximation
In this paper, we study the problem of ensuring the temperature inside the field within the specified limits by choosing the optimal location of the heat sources in the parallelepiped. In this case, the optimal placement of heat sources on the area should be such that the total power of the consumed heat sources is minimal, so that the temperature is within the specified limits. By approximating the original problem, we obtain a difference equation. The construction of implicit difference schemes for the heat equation is given. From the difference equation it is reduced to a system of linear algebraic equations. The problem was solved using the M-method. In the parallelepiped, a new approach is proposed based on the numerical solution of the non-stationary problem of the optimal choice of the location of heat sources. Algorithms and software were developed for the numerical solution of the problem. A brief description of the software is provided. The results of a computational experiment are visualized.
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