Int. J. of Applied Mathematics, Computational Science and Systems Engineering

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Solving Inverse Heat Conduction Problems by Using Tikhonov Regularization in Combination with the Genetic Algorithm

Author(s): Mohammad Reza Shahnazari, Alireza RoohiShali, Ali Saberi

Abstract: It is well-known that inverse heat conduction problems (IHCPs) are severely lll-posed, which means that small perturbations in data may cause extremely large errors in the solution. This paper introduces an accurate method for solving inverse problems, as solution procedure, we use Tikhonov regularization in combination with the genetic algorithm. Finding the regularization parameter as the decisive parameter is modeled by this method, a few sample problems were solved to investigate the efficiency and accuracy of the method. A linear sum of fundamental solutions with unknown constant coefficients assumed as an approximated solution to the sample IHCP problem and collocation method is used to minimize residues in the collocation points. In this contribution, we use Morozov’s discrepancy principle and Quasi-Optimality criterion for defining the objective function, which must be minimized to yield the value of the optimum regularization parameter.

Keywords: Inverse Heat Transfer, Tikhonov regularization, Genetic algorithms, III-Posed Problems, Morozov’s discrepancy principle.

Pages: 60-66

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