Optimization based approach for solving inverse geometrical phase change problems

Inverse geometrical problem in which the geometry of the system is not fully blown and is the aim of the solution. The considered example refers to a two-dimensional inverse phase change problem. We identify the location of a molten pool as well as we estimate the temperature distribution within a workpiece during plasma arc welding. The inverse problem is stated as an optimization problem. Several optimization methods in conjunction with a control volume method (for discretization) and a least square method (for improving the accuracy and stability of the results) are proposed to solve the inverse problem. The physical problem is governed by a linear or a nonlinear two-dimensional advection-diffusion equation including phase change process. The effect of the error in the data, number of sensors and their location and thermal properties on the solution is studied.