Localized Fourier collocation method for 2D transient heat conduction problems

The localized Fourier collocation method (LFCM) is a newly developed meshless approach for solving certain types of partial differential equations (PDEs). The main idea of this method is to break down the problem domain into a series of overlapping small regions, where the solution within each sub-domain is approximated using Fourier series expansions. The rapid convergence and high computational accuracy make the method particularly effective for handing complex geometries and boundary conditions. This paper presents the first application of LFCM to transient heat conduction problems. The Houbolt method is employed for the time discretization. Several benchmark examples with complex geometries and diverse initial/boundary conditions are well-studied to illustrate the flexibility and accuracy of the new method.