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Computational Thermal Sciences: An International Journal
ESCI SJR: 0.249 SNIP: 0.434 CiteScore™: 0.7

ISSN Imprimer: 1940-2503
ISSN En ligne: 1940-2554

Computational Thermal Sciences: An International Journal

DOI: 10.1615/ComputThermalScien.2011001776
pages 187-201

Comprehensive investigation of an inverse geometry problem in heat conduction via adjoint-based optimization method

Hamid Fazeli
K. N. Toosi University of Technology, Tehran, ‎Iran
P. Forooghi
Department of Mechanical Engineering, University of Queensland, Brisbane

RÉSUMÉ

An inverse geometry problem in heat conduction is solved using different versions of an iterative regularization method. The algorithm consists of direct and inverse problems, which aims to modification of geometry. The direct problem is solved using a finite element method(FEM). The employed iterative regularization method is constructed using the adjoint and sensitivity equations that are used to calculate the gradient of the objective function and the optimal step size, respectively. Results shown that the Powel-Beale version has the best convergence rate compared to the Fletcher-Reeves and Polak-Ribiere versions of the conjugate gradient method (CGM). Effects of geometric parameters, location and number of sensors, heat flux value, error of sensors, and size of meshes are studied. Results show that as the sensors get closer to the unknown boundary, both accuracy and convergence rate of the algorithm improve. Increasing the number of sensors has a positive effect on accuracy and convergence rate, only when it is smaller than a certain number. Presence of a measurement error leads to inaccurate estimation of the geometry shape. A proper size of mesh has the best convergence and accuracy in shape identification problem.


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