Open Access

ARTICLE

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

by

1 Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong emailmaychon@cityu.edu.hk
2 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.

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