Algorithm for geometry boundary identification of heat conduction problem based on boundary element discretization

A boundary identification problem, i.e., inverse geometry problem of two-dimensional heat conduction was solved by using boundary element method (BEM) and conjugate gradient method (CGM)-based inverse algorithm. The direct problem was solved by BEM, while the inverse solution was obtained through minimizing the object function using CGM based on the direct problem. When the unknown boundaries were eccentric cycle, sinusoidal curve, ellipse and so on, the identification cases were considered. The effects of the initial guesses, the measured errors and the number of measured points etc. upon the accuracy of inverse solutions were discussed. The results show that the proposed method can identify different kind of irregular boundaries, and is not sensitivity to initial guesses or measured errors. The accuracy of inverse solutions is not affected largely when the number of measured points is reduced moderately, and is higher when the measured points are more near the unknown boundary.