A globally convergent numerical method for coefficient inverse problems for thermal tomography

Natee Pantong, Aubrey Rhoden, Shao Hua Yang, Sandra Boetcher, Hanli Liu, Jianzhong Su

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

In our terminology 'globally convergent numerical method' means a numerical method, whose convergence to a good approximation for the correct solution is independent of the initial approximation. A new numerical imaging algorithm has been proposed to solve a coefficient inverse problem for an elliptic equation with the data generated by computer simulation. A rigorous convergence analysis shows that this method converges globally. A heuristic approach for approximating the 'new tail-function', which is a crucial part (assuming the smallness of the tail-function) of our problem, has been utilized and verified in numerical experiments, so as the global convergence. Applications to both optical and thermal tomography are discussed. Numerical experiments in the 2D thermal property reconstruction are presented.

Original languageEnglish
Pages (from-to)1573-1594
Number of pages22
JournalApplicable Analysis
Volume90
Issue number10
DOIs
StatePublished - 1 Oct 2011

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Tomography
Inverse problems
Tail
Numerical methods
Inverse Problem
Numerical Methods
Numerical Experiment
Thermal Properties
Coefficient
Terminology
Approximation
Convergence Analysis
Global Convergence
Elliptic Equations
Computer Simulation
Thermodynamic properties
Experiments
Imaging
Heuristics
Converge

Keywords

  • Globally convergent method
  • Inverse problems
  • Thermal tomography

Cite this

Pantong, Natee ; Rhoden, Aubrey ; Yang, Shao Hua ; Boetcher, Sandra ; Liu, Hanli ; Su, Jianzhong. / A globally convergent numerical method for coefficient inverse problems for thermal tomography. In: Applicable Analysis. 2011 ; Vol. 90, No. 10. pp. 1573-1594.
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A globally convergent numerical method for coefficient inverse problems for thermal tomography. / Pantong, Natee; Rhoden, Aubrey; Yang, Shao Hua; Boetcher, Sandra; Liu, Hanli; Su, Jianzhong.

In: Applicable Analysis, Vol. 90, No. 10, 01.10.2011, p. 1573-1594.

Research output: Contribution to journalArticle

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