A non-iterative meshless method for heat source identification in steady and unsteady problems

This paper presents a novel non-iterative method for solving a challenging class of partial differential equations (PDEs) named as Inverse Heat Source Problems (IHPs). The solution technique employs Pascal polynomials within a collocation framework to obtain numerical solution of the IHPs containing either unknown time-dependent heat source, unknown space-dependent heat source or unknown space-and-time-dependent heat source alongside unknown temperature field. The main emphasis is on the non-iterative approach, which has the capability to re-construct the unknown inverse heat source and the unknown inverse point heat source from the limited available data. Pascal polynomials are coupled with the implicit finite-difference method in the case of unsteady heat source. To validate the method, various two-dimensional benchmark tests are conducted on regular and irregular geometries. In some cases, regularized solutions are also obtained using simple Tikhonov and TSVD-based Tikhonov regularizations. Performance comparison with and without regularization is provided. Numerical experiments on regular and irregular geometries including point heat source are conducted to demonstrate wider applicability, accuracy, efficiency and computational stability of the proposed method.