Reconstruction of the heat transfer coefficient in the inverse Stefan problem

摘要

In the paper we will present the method of finding the heat transfer coefficient in the inverse problem of pure metal solidification. In the considered model the shrinkage of metal and the air-gap between material and mold will be taken into account. The method is based on the algorithm for solution of the direct problem and on the Artificial Bee Colony algorithm. In the algorithm for solving the direct problem we use the finite element method supplemented by the procedure allowing to define the position of the moving interface and the change of material size associated with the shrinkage. To solve the inverse problem, a fimctional defining the error of approximate solution must be minimized. To minimize this functional we use the Artificial Bee Colony algorithm. Then we present the computational example illustrating precision and stability of the presented method.