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The method of fundamental solution for solving multidimensional inverse heat conduction problems

Y.C. Hon1, T. Wei2
Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong emailmaychon@cityu.edu.hk
Department of Mathematics, City University of Hong Kong & Department of Mathematics, Lanzhou University, Lanzhou, Gansu Province 730000, China email: t.wei@student.cityu.edu.hk

Computer Modeling in Engineering & Sciences 2005, 7(2), 119-132. https://doi.org/10.3970/cmes.2005.007.119

Abstract

We propose in this paper an effective meshless and integration-free method for the numerical solution of multidimensional inverse heat conduction problems. Due to the use of fundamental solutions as basis functions, the method leads to a global approximation scheme in both the spatial and time domains. To tackle the ill-conditioning problem of the resultant linear system of equations, we apply the Tikhonov regularization method based on the generalized cross-validation criterion for choosing the regularization parameter to obtain a stable approximation to the solution. The effectiveness of the algorithm is illustrated by several numerical two- and three-dimensional examples.

Keywords

Inverse heat conduction problem, fundamental solution method, Tikhonov regularization

Cite This Article

Hon, Y., Wei, T. (2005). The method of fundamental solution for solving multidimensional inverse heat conduction problems. CMES-Computer Modeling in Engineering & Sciences, 7(2), 119–132.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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