Abstract
This paper is intended to provide a numerical algorithm involving the combined use of the Levenberg-Marquardt algorithm and the Galerkin finite element method for estimating the diffusion coefficient in an inverse heat conduction problem (IHCP). In the present study, the functional form of the diffusion coefficient is unknown a priori. The unknown diffusion coefficient is approximated by the polynomial form and the present numerical algorithm is employed to find the solution. Numerical experiments are presented to show the efficiency of the proposed method.
Highlights
The numerical solution of the inverse heat conduction problem (IHCP) requires determining diffusion coefficient from additional information
Inverse heat conduction problems have many applications in various branches of science and engineering; mechanical and chemical engineers, mathematicians, and specialists in many other science branches are interested in inverse problems, each with different application in mind [1–15]
We propose an algorithm for numerical solving of an inverse heat conduction problem
Summary
The numerical solution of the inverse heat conduction problem (IHCP) requires determining diffusion coefficient from additional information. We propose an algorithm for numerical solving of an inverse heat conduction problem. It is assumed that no prior information is available on the functional form of the unknown diffusion coefficient in the present study; it is classified as the function estimation in inverse calculation. Run the numerical algorithm to solve the unknown diffusion coefficient which is approximated by the polynomial form. The LevenbergMarquardt optimization is adopted to modify the estimated values.
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