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

doi:10.3970/cmes.2010.060.221
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 60, No. 3, pp. 221-246, 2010
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Keywords Inverse Problem; Cauchy Problem; Isotropic Linear Elasticity; Iterative Method of Fundamental Solutions (MFS); Regularization.
Abstract We investigate the implementation of the method of fundamental solutions (MFS), in an iterative manner, for the algorithm of ` 12 `
12 `$12 `&12 `#12 `^12 `_12 `%12 `~12 *Kozlov91 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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