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A meshless method based on the method of fundamental solution for solving the steady-state heat conduction problems

机译：基于基本解法的无网格法求解稳态导热问题

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Motivated by the incompleteness of the method of fundamental solution (MFS) for the interior problem, we give another meshless method both theoretically and numerically for recovering the temperature and the heat flux based on the normal derivative of the fundamental solution in this paper. Although the problems under investigation are well-posed, we should note that the method presented here results in an ill-conditioned system and this is a feature of the numerical method employed in the present approach. The ill-posedness of this system is given by the potential function. In order to overcome the ill-posedness of the system, the Tikhonov regularization method, as well as Morozov's discrepancy principle for selecting an appropriate regularization parameter, are used to increase the stability of this method. Then three kinds of boundary value problems are presented to show the effectiveness of this method with some examples, whilst the comparisons with the MFS is presented. The numerical convergence and stability of this method are also analyzed.
机译：由于内在问题的基本解法（MFS）的不完备性，本文基于基本解的正态导数，在理论上和数值上给出了另一种无网格方法来恢复温度和热通量。尽管所研究的问题是适当的，但我们应注意，此处介绍的方法会导致系统状况不佳，这是本方法中采用的数值方法的特征。该系统的不适状态由势函数给出。为了克服系统的不适定性，Tikhonov正则化方法以及Morozov的用于选择适当正则化参数的差异原理被用来提高该方法的稳定性。然后以三种边值问题为例，通过实例说明了该方法的有效性，并与MFS进行了比较。还分析了该方法的数值收敛性和稳定性。

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