This paper is concerned with an inverse problem for the conduction of heat in a two-dimensional domain. It seeks to recover the subsurface conductivity profile based on the measurements obtained at the boundary. The method considers a temporal interval for which time-dependent measurements are provided. It formulates an optimal estimation problem which seeks to minimize the error difference between the given data and the response from the system. It uses a combination of the zeroth-order and the first-order Tikhonov regularization to stabilize the inversion. The method leads to an iterative algorithm which, at every iteration, requires the solution to a two-point boundary value problem. A number of numerical results are presented which indicate that a close estimate of the thermal conductivity function can be obtained based on the boundary measurements only. [S0022-1481(00)00902-6]
Evaluation of a Two-Dimensional Conductivity Function Based on Boundary Measurements
Contributed by the Heat Transfer Division for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received by the Heat Transfer Division, May 15, 1999; revision received, December 9, 1999. Associate Technical Editor: T. Avedisian.
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Tadi , M. (December 9, 1999). "Evaluation of a Two-Dimensional Conductivity Function Based on Boundary Measurements ." ASME. J. Heat Transfer. May 2000; 122(2): 367–371. https://doi.org/10.1115/1.521473
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