Inverse problem of simultaneously estimating the thermal conductivity and boundary shape

Farzad Mohebbi, Mathieu Sellier, Timon Rabczuk

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


An inverse analysis is used to simultaneously estimate the thermal conductivity and the boundary shape in steady-state heat conduction problems. The numerical scheme consists of a body-fitted grid generation technique to mesh the heat conducting body and solve the heat conduction equation–a novel, efficient, and easy to implement sensitivity analysis scheme to compute the sensitivity coefficients, and the conjugate gradient method as an optimization method to minimize the mismatch between the computed temperature distribution on some part of the body boundary and the measured temperatures. Using the proposed scheme, all sensitivity coefficients can be obtained in one solution of the direct heat conduction problem, irrespective of the large number of unknown parameters for the boundary shape. The obtained results reveal the accuracy, efficiency, and robustness of the proposed algorithm.

Original languageEnglish
Pages (from-to)166-181
Number of pages16
JournalInternational Journal of Computational Methods in Engineering Science and Mechanics
Issue number2-3
Publication statusPublished - 2017 May 4
Externally publishedYes


  • Inverse heat transfer
  • conjugate gradient method
  • elliptic grid generation
  • finite difference method
  • sensitivity analysis

ASJC Scopus subject areas

  • Computational Mechanics
  • Computational Mathematics


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