A shape identification problem in estimating the unknown interfacial surface for a multiple region domain

A thermal tomography problem, i.e. the shape identification problem or inverse geometry problem, in estimating the interfacial geometry for a three-dimensional multiple region domains is examined in this study based on the Conjugate Gradient Method (CGM). The accuracy of this thermal tomography analysis is examined using the simulated temperatures measured by an imaginary infrared scanner. Different temperature measurement positions and errors are considered in the numerical experiments to justify the validity of the present algorithm in solving the three-dimensional thermal tomography problem. Finally it is concluded that the reliable interfacial configurations can be estimated by the CGM.