Abstract

Algorithms of 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, as well as 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.

中文翻译：

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具有复杂几何形状的区域内热源的最佳位置

摘要

考虑了在复杂几何形状的区域内具有大量热量释放的热源的最佳布置算法。找到的分布具有最小的总功率，并提供给定温度范围内的温度。原始问题的有限维近似以线性规划问题的形式构造。给出了一种用于构造求解热方程的有限差分方案的方法，并简要介绍了已开发的用于构建网格和求解方程的软件模块。使用开发的程序已进行了几次计算机实验。