An Alternating Iterative MFS Algorithm for the Cauchy Problem in Two-Dimensional Anisotropic Heat Conduction
Liviu Marin;

doi:10.3970/cmc.2009.012.071
Source CMC: Computers, Materials, & Continua, Vol. 12, No. 1, pp. 71-100, 2009
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Keywords Anisotropic Heat Conduction; Inverse Problem; Cauchy Problem; Iterative Method of Fundamental Solutions (MFS); Regularization.
Abstract In this paper, the alternating iterative algorithm originally proposed by ` 12 `
12 `$12 `&12 `#12 `^12 `_12 `%12 `~12 *Kozlov91 is numerically implemented for the Cauchy problem in anisotropic heat conduction using a meshless method. Every iteration of the numerical procedure consists of two mixed, well-posed and direct problems which are solved using the method of fundamental solutions (MFS), in conjunction with the Tikhonov regularization method. For each direct problem considered, the optimal value of the regularization parameter is chosen according to the generalized cross-validation (GCV) criterion. An efficient regularizing stopping criterion which ceases the iterative procedure at the point where the accumulation of noise becomes dominant and the errors in predicting the exact solutions increase, is also presented. The iterative MFS algorithm is tested for Cauchy problems related to heat conduction in two-dimensional anisotropic solids to confirm the numerical convergence, stability and accuracy of the method.
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