Improved Inverse Explicit Method for Three-Dimensional Source Term Estimation With the Classical Integral Transform Technique

This work presents an explicit methodology for estimating source terms in the diffusion equation based on the classical integral transform technique (CITT), employing eigenfunction expansions. This work extends the application of a recently developed methodology to more general three-dimensional cases. Given the high computational costs associated with these calculations, the study introduces essential enhancements for solving the related inverse problems more efficiently and proposes an automatic criterion for selecting the truncation order in the inverse problem solution, aiming at regularization based on the discrepancy principle. The results, based on simulated measurements for transient three-dimensional diffusion problems, demonstrate the effective improvements achieved, yielding consistently good results across the tested scenarios, including varying noise levels and different functional forms of the sought source terms. Accurate source term detection via an explicit computationally fast approach. Three-dimensional transient source terms are successfully handled. Selection of expansion truncation order for regularization is handled automatically. Computational efficiency is achieved through automatic truncation.