A relaxation method of an alternating iterative algorithm for the Cauchy problem in linear isotropic elasticity

Liviu Marin, B. Tomas Johansson

Research output: Contribution to journalArticlepeer-review

Abstract

We propose two algorithms involving the relaxation of either the given Dirichlet data (boundary displacements) or the prescribed Neumann data (boundary tractions) on the over-specified boundary in the case of the alternating iterative algorithm of Kozlov et al. [16] applied to Cauchy problems in linear elasticity. A convergence proof of these relaxation methods is given, along with a stopping criterion. The numerical results obtained using these procedures, in conjunction with the boundary element method (BEM), show the numerical stability, convergence, consistency and computational efficiency of the proposed method.
Original languageEnglish
Pages (from-to)3179-3196
Number of pages18
JournalComputer Methods in Applied Mechanics and Engineering
Volume199
Issue number49-52
DOIs
Publication statusPublished - 15 Dec 2010

Keywords

  • alternating iterative algorithm;
  • linear elasticity
  • inverse problem
  • Cauchy problem
  • relaxation procedures
  • boundary element method

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