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A new approximate method for an inverse time-dependent heat source problem using fundamental solutions and RBFs

机译:基于基本解和RBF的逆时变热源问题的一种新的近似方法

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This paper presents a meshless numerical scheme to solve the inverse heat source time dependent problem. Fundamental solutions of heat equations and radial basis functions (RBFs) are used to obtain a numerical solution. Since the coefficient matrix may be ill-conditioned, the Tikhonov regularization (TR) method is employed to solve the resulting system of linear equations. Therefore, the generalized cross-validation (GCV) criterion is applied to choose a regularization parameter. The accuracy and efficiency of the proposed method is illustrated by some numerical examples.
机译:本文提出了一种无网格的数值方案来解决热源逆时变问题。使用热方程和径向基函数(RBF)的基本解来获得数值解。由于系数矩阵可能是病态的,因此采用Tikhonov正则化(TR)方法来求解所得的线性方程组。因此,应用通用交叉验证(GCV)准则选择正则化参数。数值算例说明了该方法的准确性和有效性。

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