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A method of fundamental solutions for inverse heat conduction problems in an anisotropic medium

机译:各向异性介质中导热反问题的基本解法

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Recently, Hon and Wei proposed a method of fundamental solutions for solving isotropic inverse heat conduction problems (IHCP). It provides an efficient global approximation scheme in both spatial and time domains. In this paper, we try to extend the inherently meshless and integration-free method to solve 2D IHCP in an anisotropic medium. First, we acquire the fundamental solution of the governing equation through variables transformation. Then the truncated singular value decomposition and the L-curve criterion are applied to solve the resulting matrix equation which is highly ill-conditioned. Results for several numerical examples are presented to demonstrate the efficiency of the method proposed. The relationship between the accuracy of the numerical solutions and the value of the parameter T is also investigated. (C) 2006 Published by Elsevier Ltd.
机译:最近,Hon和Wei提出了一种解决各向同性逆热传导问题(IHCP)的基本方法。它在时域和时域均提供了有效的全局逼近方案。在本文中,我们尝试扩展固有的无网格和无积分方法,以解决各向异性介质中的二维IHCP问题。首先,我们通过变量转换获得控制方程的基本解。然后,采用截断的奇异值分解和L曲线准则来求解所产生的病态严重的矩阵方程。给出了几个数值示例的结果,以证明所提出方法的有效性。还研究了数值解的精度与参数T的值之间的关系。 (C)2006由Elsevier Ltd.出版

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