Relaxation procedures for an iterative MFS algorithm for the stable reconstruction of elastic fields from Cauchy data in two-dimensional isotropic linear elasticity

Liviu Marin, B. Tomas Johansson

Research output: Contribution to journalArticle

Abstract

We investigate two numerical procedures for the Cauchy problem in linear elasticity, involving the relaxation of either the given boundary displacements (Dirichlet data) or the prescribed boundary tractions (Neumann data) on the over-specified boundary, in the alternating iterative algorithm of Kozlov et al. (1991). The two mixed direct (well-posed) problems associated with each iteration are solved using the method of fundamental solutions (MFS), in conjunction with the Tikhonov regularization method, while the optimal value of the regularization parameter is chosen via 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 MFS-based iterative algorithms with relaxation are tested for Cauchy problems for isotropic linear elastic materials in various geometries to confirm the numerical convergence, stability, accuracy and computational efficiency of the proposed method.
Original languageEnglish
Pages (from-to)3462–3479
Number of pages17
JournalInternational Journal of Solids and Structures
Volume47
Issue number25-26
Early online date31 Aug 2010
DOIs
Publication statusPublished - 15 Dec 2010

Keywords

  • inverse problem
  • boundary data reconstruction
  • isotropic linear elasticity
  • iterative method of fundamental solutions (MFS)
  • relaxation procedures
  • regularization

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