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ARTICLE

Stable Boundary and Internal Data Reconstruction in Two-Dimensional Anisotropic Heat Conduction Cauchy Problems Using Relaxation Procedures for an Iterative MFS Algorithm

Liviu Marin¹

1 Institute of Solid Mechanics, Romanian Academy, 15 Constantin Mille, P.O. Box 1-863, 010141Bucharest, Romania. Tel./Fax: +40-(0)21-312 6736. E-mails: marin.liviu@gmail.com; liviu@imsar.bu.edu.ro

Computers, Materials & Continua 2010, 17(3), 233-274. https://doi.org/10.3970/cmc.2010.017.233

Abstract

We investigate two algorithms involving the relaxation of either the given boundary temperatures (Dirichlet data) or the prescribed normal heat fluxes (Neumann data) on the over-specified boundary in the case of the iterative algorithm of Kozlov91 applied to Cauchy problems for two-dimensional steady-state anisotropic heat conduction (the Laplace-Beltrami equation). The two mixed, well-posed and direct problems corresponding to every iteration of the numerical procedure 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. The iterative MFS algorithms with relaxation are tested for over-, equally and under-determined Cauchy problems associated with the steady-state anisotropic heat conduction in various two-dimensional geometries to confirm the numerical convergence, stability, accuracy and computational efficiency of the method.

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Keywords

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