Open Access

ARTICLE

Reconstruction of Boundary Data in Two-Dimensional Isotropic Linear Elasticity from Cauchy Data Using an Iterative MFS Algorithm

Liviu Marin¹

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

Computer Modeling in Engineering & Sciences 2010, 60(3), 221-246. https://doi.org/10.3970/cmes.2010.060.221

Abstract

We investigate the implementation of the method of fundamental solutions (MFS), in an iterative manner, for the algorithm of Kozlov, Maz'ya and Fomin (1991) in the case of the Cauchy problem in two-dimensional isotropic linear elasticity. At every iteration, two mixed well-posed and direct problems are solved using the Tikhonov regularization method, while the optimal value of the regularization parameter is chosen according to the generalized cross-validation (GCV) criterion. An efficient regularizing stopping criterion is also presented. The iterative MFS algorithm is tested for Cauchy problems for isotropic linear elastic materials to confirm the numerical convergence, stability and accuracy of the method.

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Keywords

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