The method of fundamental solutions for the backward heat conduction problem
The method of fundamental solutions for the backward heat conduction problem
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DOI：
10.1080/10682760410001710141
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发表时间：
2005-01
影响因子：
1.3
通讯作者：
N. S. Mera *
中科院分区：
文献类型：
--
作者：
N. S. Mera *
本文提出了一种求解反向热传导问题的无网格数值格式。以热传导方程的基本解为基函数，得到了数值解。采用标准的Tikhonov正则化技术和L曲线方法求解所得的病态线性代数方程组。通过一个严格的算例，研究了该方法的收敛性和稳定性，从而揭示了该方法的计算性能和局限性。给出了一维和二维反向热传导问题的数值结果。
In this article a meshless numerical scheme for solving the backward heat conduction problem (BHCP) is proposed. The numerical solution is developed by using the fundamental solution of the heat equation as a basis function. The standard Tikhonov regularization technique and the L-curve method are adopted for solving the resultant ill-conditioned system of linear algebraic equations. The convergence and the stability of the method are investigated for a severe test example, hence revealing the computational performance and limitations of the method proposed. Numerical results are presented for bo th the one-dimensional and the two-dimensional backward heat conduction problems.