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

Abstract

We investigate the implementation of the method of fundamental so- lutions (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 lin- ear 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 elas- tic materials to confirm the numerical convergence, stability and accuracy of the method.