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首页> 外文期刊>International Journal of Heat and Mass Transfer >Iterative algorithms for solving inverse problems of heat conduction in multiply connected domains
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Iterative algorithms for solving inverse problems of heat conduction in multiply connected domains

机译：求解多重连通域中导热反问题的迭代算法

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摘要

The presented paper displays a method of solving the inverse problems of heat transfer in multi-connected regions, consisting in iterative solving of convergent series of the direct problems. For known temperature and flux values at the outer boundary of the region the temperature and flux values at the inner boundaries are sought (the cauchy problem for the Laplace equation). In case of such a formulation of the problem, the solution does not always exist, one of the conditions is met in the mean-square sense, providing the optimization criterion. The idea of the process consists in solving the direct problem in which the boundary condition is subject to iterative changes so as to attain minimum of the optimization criterion (the square functional). Two algorithms have been formulated. In the first of them the heat flux at the inner boundaries of the region, while in the other the temperature were subject to changes. Convergence of both the algorithms have been compared.The numerical calculation has been made for selected examples, for which an analytical solution is known. The effect of random disturbance of the boundary conditions on the solution obtained with iterative algorithms has been checked. Moreover, a function was defined, serving as convergence measure of the solution of the inverse problem solved with the algorithms proposed in the paper. The properties of the function give evidence that it tends to the value exceeding unity.
机译：本文提出了一种解决多连通区域内传热逆问题的方法，其中包括对直接问题的收敛级数的迭代求解。对于该区域的外边界处的已知温度和通量值，寻求内边界处的温度和通量值（拉普拉斯方程的柯西问题）。在提出这样的问题的情况下，解决方案并不总是存在，在均方意义上满足条件之一，提供了优化标准。该过程的思想在于解决直接问题，在该问题中边界条件会发生迭代变化，以使优化准则（平方函数）达到最小值。已经制定了两种算法。在第一个中，区域内边界处的热通量，而在另一个中，温度则发生变化。比较了这两种算法的收敛性。对选定的例子进行了数值计算，对于这些例子，解析解是已知的。已经检查了边界条件的随机干扰对使用迭代算法获得的解的影响。此外，定义了一个函数，作为用本文提出的算法求解反问题的解的收敛度量。函数的性质提供了证据，表明该值趋于超过单一值。

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