Method of removing the domain to identify the position of the heat source by the inverse method

Abstract

This research work is a numerical study which conducted a spatiotemporal identification of a thermal source inside a domain using inverse method. Temperatures are simulated by means of resolving direct problem with finite differences method. The authors suggested heat source identification in diffusive medium. The studied problem has two distinctive aspects: (1) source location research; (2) identifying source amplitude in terms of time. Direct simulation: The authors achieved a leveled scale on the studied source over the total duration of the study time interval. Step responses, at measuring points, are saved (for matrix building). After that, the authors computed source value at every step time. In order to characterize inverse quality, the authors have introduced mean square deviations corresponding to inverse process, we notice that we have a good result for the location, whilst the intensity of the source volume we have a worse outcome, because we identified a point source is equivalent to an approximate solution.