Abstract
This paper deals with the inverse analysis of a thermal conduction problem, in which the thermal conductivity is identified as an unknown parameter, which is determined so as to minimize the cost function represented by the square of the difference between the computed and observed temperatures at pre-assigned observation points. To minimize the cost function, both sensitivity equation and adjoint equation methods can be adopted. The sensitivity equation can be introduced by differentiating the governing equation directly. The sensitivity coefficient is obtained by the sensitivity equation. The adjoint equation is introduced via a variational approach using a Lagrange multiplier. The Lagrange multiplier is solution to an adjoint equation. Both sensitivity coefficient and Lagrange multiplier are used to calculate the gradient of the cost function. The purpose of this paper is to compare the sensitivity equation and adjoint equation methods from the convergence and computational efficiency points of view. © 1997 by John Wiley & Sons, Ltd.
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