Empirical reduction of modes for the shape identification problems of heat conduction systems

The Karhunen–Loeve Galerkin procedure is a type of Galerkin method that employs as basis functions the empirical eigenfunctions of the Karhunen–Loeve decomposition, and proved to be a powerful tool for reducing the degree of freedom of partial differential equations [Int. J. Numer. Methods Engrg. 41 (1998) 1131; Comput. Methods Appl. Mech. Engrg. 188 (2000) 165]. In the present investigation, we extend the applicability of the Karhunen–Loeve Galerkin procedure to systems of variable domains and apply it to the shape identification problems of heat conduction systems, where the unknown boundary shape is estimated from temperature measurements on the other boundary. The efficiency and accuracy of the present technique are assessed as compared to the traditional technique employing the original partial differential equation.