Identification of phase change interface using imaginary heat sources

This paper presents a methodology for time-independent and time-dependent shape identification problems. The problem considered is that of determining the phase-change interface from several observed temperatures. In the present method, imaginary heat sources arranged in an imaginary domain are introduced. Then the phase-change interface is identified as the isothermal surface at the melting temperature by controlling the imaginary heat source intensities. Using the delta-function type imaginary heat sources, their corresponding Green's functions can numerically be calculated before the identification. As a result, the imaginary heat source intensities can explicitly be obtained by the least squares method. Some numerical examples are presented.