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

Fingerprint

Method of Fundamental Solutions
Thermoelasticity
Inverse problems
Elasticity
L-curve
Tikhonov Regularization
Continuous Dependence
Regularization Parameter
Temperature
Three-dimension
Two Dimensions
Inverse Problem
Uniqueness
Numerical Results

Keywords

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

Cite this

Marin, Liviu ; Karageorghis, A ; Lesnic, Daniel ; Johansson, B. Tomas. / The method of fundamental solutions for problems in static thermo-elasticity with incomplete boundary data. In: Inverse Problems in Science and Engineering. 2016 ; Vol. 25, No. 5. pp. 652-673.
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The method of fundamental solutions for problems in static thermo-elasticity with incomplete boundary data. / Marin, Liviu; Karageorghis, A; Lesnic, Daniel; Johansson, B. Tomas.

In: Inverse Problems in Science and Engineering, Vol. 25, No. 5, 07.06.2016, p. 652-673.

Research output: Contribution to journalArticle

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