Reconstruction of time-dependent coefficients from heat moments

M.J. Huntul, D. Lesnic and M.S. Hussein

Applied Mathematics and Computation, 2017, vol. 301, issue C, 233-253

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.

Keywords: Inverse problem; Tikhonov’s regularization; Heat transfer; Heat moments (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:301:y:2017:i:c:p:233-253

DOI: 10.1016/j.amc.2016.12.028

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