A Mixed-Time Explicit-Implicit Generalized Finite Element Method for Multi-Scale Field Problems

Mixed-time explicit-implicit time-integration schemes are developed for the Generalized Finite Element Method (GFEM) for the simulation of transient multi-scale problems exhibiting highly-localized and non-stationary phenomena. The spatial domain is partitioned into implicit and explicit subdomains, enabling tailored time-steps and integration schemes for each subdomain. Individual subdomains are coupled together through the assembly of finite elements, inherently maintaining continuity without the need for complex interface coupling techniques. These characteristics result in a method that is highly amenable to parallelization and straightforward to implement, making it well-suited for large-scale computations. The temporal accuracy, convergence, and stability of the mixed-time explicit-implicit GFEM (mE-I GFEM) are assessed in the context of heat transfer problems experiencing thermal loads with sharp temporal and spatial gradients. The results demonstrate that the proposed mE-I GFEM is robust and efficient, yielding time-accurate solutions with improved stability criterion at a significantly reduced computational cost compared to G/FEM approaches using standard time-stepping schemes with uniform time-steps.