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Reconstruction of time-dependent coefficients from heat moments

Author

Listed:
  • Huntul, M.J.
  • Lesnic, D.
  • Hussein, M.S.

Abstract

This paper investigates the inverse problems of simultaneous reconstruction of time-dependent thermal conductivity, convection or absorption coefficients in the parabolic heat equation governing transient heat and bio-heat thermal processes. Using initial and boundary conditions, as well as heat moments as over-determination conditions ensure that these inverse problems have a unique solution. However, the problems are still ill-posed since small errors in the input data cause large errors in the output solution. To overcome this instability we employ the Tikhonov regularization. A discussion of the choice of multiple regularization parameters is provided. The finite-difference method with the Crank–Nicolson scheme is employed as a direct solver. The resulting inverse problems are recast as nonlinear minimization problems and are solved using the lsqnonlin routine from the MATLAB toolbox. Numerical results are presented and discussed.

Suggested Citation

  • Huntul, M.J. & Lesnic, D. & Hussein, M.S., 2017. "Reconstruction of time-dependent coefficients from heat moments," Applied Mathematics and Computation, Elsevier, vol. 301(C), pages 233-253.
    • Handle: RePEc:eee:apmaco:v:301:y:2017:i:c:p:233-253
    DOI: 10.1016/j.amc.2016.12.028
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