Generalized finite element method with time-independent enrichment functions for 3D transient heat diffusion problems

Abstract

An enriched generalized finite element method (GFEM) is proposed for the efficient solution of three-dimensional (3D) transient heat diffusion problems. The proposed GFEM formulation is shown to produce results with better accuracy and less degrees of freedoms (DOFs) as compared to the standard FEM with linear basis functions. For GFEM, the solution space is enriched with an approximate solution describing the heat diffusion decay. Multiple enrichment functions that mimic the solution behaviour are used to capture the high temperature gradients. The enrichment functions are independent of time; the spatial and time varying decay of the solution is embedded in the formulation of the enrichment functions. The resultant formulation significantly reduces the computational cost as compared to the enrichment functions with only spatial approximations. In the current formulation, the system matrix is assembled only at the first time step and retained for subsequent time steps. Different numerical examples in 3D spatial domains are considered to analyze the performance of the proposed method. Depending on the nature of the problem, two different enrichment functions; exponential enrichment functions and hyperbolic enrichment functions are used in the computations. It is shown that the proposed approach is more simple and efficient than the conventional h-refinement to increase the accuracy of the finite element method.