Reconstruction of time-dependent coefficients from heat moments

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• 作者：M.J. Huntul^a ; ^b ; ^{mmmjmh@leeds.ac.uk} ; D. Lesnic ; ^a ; ^{amt5ld@maths.leeds.ac.uk} ; ^{dnlpiticu@yahoo.co.uk} ; M.S. Hussein^a ; ^c ; ^{mmmsh@leeds.ac.uk}
• 关键词：Inverse problem ; Tikhonov&rsquo ; s regularization ; Heat transfer ; Heat moments
• 刊名：Applied Mathematics and Computation
• 出版年：2017
• 出版时间：15 May 2017
• 年：2017
• 卷：301
• 期：Complete
• 页码：233-253
• 全文大小：1118 K
• 卷排序：301

文摘

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.