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Application of the method of fundamental solutions and radial basis functions for inverse transient heat source problem

机译：基本解法和径向基函数法在逆热源反问题中的应用

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The paper considers the determination of heat sources in unsteady 2-D heat conduction problem. The determination of the strength of a heat source is achieved by using the boundary condition, initial condition and a known value of temperature in chosen points placed inside the domain. For the solution of the inverse problem of identification of the heat source the θ-method with the method of fundamental solution and radial basis functions is proposed. Due to ill conditioning of the inverse transient heat conduction problem the Tikhonov regularization method based on SVD decomposition was used. In order to determine the optimum value of the regularization parameter the L-curve criterion was used. For testing purposes of the proposed algorithm the 2-D inverse boundary-initial-value problems in square region Ω with the known analytical solutions are considered. The numerical results show that the proposed method is easy to implement and pretty accurate. Moreover the accuracy of the results does not depend on the value of the θ parameter and is greater in the case of the identification of the temperature field than in the case of the identification of the heat sources function.
机译：本文考虑了二维不稳定热传导问题中热源的确定。通过使用边界条件，初始条件和放置在域内部的选定点中的已知温度值来确定热源的强度。为了解决热源识别反问题，提出了采用基本解法和径向基函数的θ法。由于逆向瞬态热传导问题的条件不好，因此使用了基于SVD分解的Tikhonov正则化方法。为了确定正则化参数的最佳值，使用了L曲线准则。为了测试所提出算法的目的，考虑了具有已知解析解的平方区域Ω中的二维逆边界初始值问题。数值结果表明，所提方法易于实现，且精度较高。此外，结果的精度不取决于θ参数的值，并且在识别温度场的情况下比在识别热源功能的情况下更大。

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