Identify the interfacial configurations in a multiple region domain problem

A two-dimensional inverse geometry problem, that is, a shape identification problem, of estimating the interfacial geometry in a multiple region domain, is solved in this study based on the conjugate gradient and boundary element methods. It is assumed that no prior information is available on the functional form of the unknown interfacial geometry in this work; thus, it is classified as the function estimation in the inverse calculation. The accuracy of the inverse analysis is examined using simulated temperature measurements. This approach can be applied to many applications, such as interfacial geometry identification for phase change (Stefan) problems. Numerical experiments using different numbers of sensors, measurement errors, and positions are performed to justify the validity of the present algorithm in solving the shape identification problem. Finally it is concluded that the conjugate gradient method can estimate the reliable interfacial configuration.