COMPARISON OF SENSITIVITY EQUATION AND ADJOINT EQUATION METHODS FOR PARAMETER IDENTIFICATION PROBLEMS

This paper deals with the inverse analysis of a thermal conduction problem, in which the thermal conductivity is identi ed as an unknown parameter, which is determined so as to minimize the cost function represented by the square of the di erence 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 di erentiating the governing equation directly. The sensitivity coe cient 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 coe cient 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 e ciency points of view