Green`s function approach to optimal arrangement of heat sources in a heat conductor
Green`s function approach to optimal arrangement of heat sources in a heat conductor
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热导体中热源优化布置的格林函数方法
DOI：
10.1299/kikaib.61.1762
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发表时间：
1996
期刊：
影响因子：
--
通讯作者：
H. Kimoto
中科院分区：
文献类型：
--
作者：
K. Momose;H. Kimoto
提出了一种分析和数值方法相结合的方法，用于优化n个热源的布置，以在m个位置实现所需的温度。根据点源近似下绿色函数的特点，通过对热传导方程进行n + 1或m + 1次数值模拟，可以非迭代地确定最佳热源强度.利用m + 1次数值模拟的结果，无需进行额外的数值模拟，也可以通过传统的基于梯度的优化策略获得最优热源位置。此外，这些数值模拟与热源的存在和期望的温度无关。因此，即使热源的数量和期望温度改变，也不需要进一步的数值模拟。
A combined approach of analytical and numerical methods is proposed for the optimal arrangement of n heat sources to achieve the desired temperatures at m locations. From the characteristics of Green`s function under a point-source approximation, it is shown that the optimal heat-source intensities can be determined noniteratively by executing n + 1 or m + 1 numerical simulations of the heat-conduction equations. By using the results of m + 1 numerical simulations, the optimal heat-source locations can also be obtained by the conventional gradient-based optimization strategy without additional numerical simulations. Moreover, these numerical simulations are independent of the existence of heat sources and of the desired temperatures. Therefore further numerical simulations are not required even if the number of heat sources and the desired temperatures are changed.