Improved Computational Techniques for Heat Sources Localization

This paper addresses the inverse heat source problem, which involves determining the location and intensity of heat sources from observed temperature distributions. Through the use of the Green function, the heat conduction problem is transformed into a Volterra integral equation of the first kind. An iterative approach, combined with numerical quadrature and Tikhonov regularization, is employed to stabilize and solve the system. Numerical experiments, conducted in a simulated environment with varying grid sources configurations, demonstrate the method’s accuracy and robustness in identifying multiple heat sources.