A Time Spectral Generalized Finite Difference Method for Three‐Dimensional Transient Heat Conduction Analysis in Functionally Graded Materials With Space–Time Coefficients

ABSTRACT This paper presents a time spectral generalized finite difference method (TS‐GFDM) for three‐dimensional (3D) transient heat conduction in functionally graded materials (FGMs) with space–time dependent coefficients. The time derivative of temperature in the governing equation is approximated as a linear combination of temperatures at Gaussian points within each time step, achieved via the inverse transform of spectral integration. Space derivatives of temperature are evaluated as linear combinations of nodal temperatures, constructed using Taylor series expansion in conjunction with the moving least squares (MLS) approximation. The proposed method allows for large time steps in the temporal direction while ensuring stability over long‐time simulations. In the spatial domain, it eliminates the need for mesh generation, making it particularly well suited for heat conduction analysis in complex structures. The numerical results obtained using the TS‐GFDM are compared with those from existing methods and the analytical solution, demonstrating the higher computational efficiency of the proposed approach.