The method of fundamental solutions for problems in static thermo-elasticity with incomplete boundary data

Liviu Marin, A Karageorghis, Daniel Lesnic, B. Tomas Johansson

Research output: Contribution to journalArticle

Abstract

An inverse problem in static thermo-elasticity is investigated. The aim is to reconstruct the unspecified boundary data, as well as the temperature and displacement inside a body from over-specified boundary data measured on an accessible portion of its boundary. The problem is linear but ill-posed. The uniqueness of the solution is established but the continuous dependence on the input data is violated. In order to reconstruct a stable and accurate solution, the method of fundamental solutions is combined with Tikhonov regularization where the regularization parameter is selected based on the L-curve criterion. Numerical results are presented in both two and three dimensions showing the feasibility and ease of implementation of the proposed technique.
Original languageEnglish
Pages (from-to)652-673
JournalInverse Problems in Science and Engineering
Volume25
Issue number5
Early online date7 Jun 2016
DOIs
Publication statusE-pub ahead of print - 7 Jun 2016

Keywords

  • Thermo-elasticity
  • method of fundamental solutions
  • inverse problem

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