A FETI-based mixed explicit-implicit multi-time-step method for parabolic problems

Nonstationary partial differential equations are numerically solved by discretizing in space and then integrating over time using discrete solvers. In this paper we propose and examine a mixed subcycling time stepping strategy using FETI domain decomposition for parabolic problems (e.g. transient heat conduction). The computational domain is divided into a set of smaller subdomains that may be integrated sequentially with its own time steps and generalized trapezoidal α-methods. The continuity condition at the interface is ensured using a dual Schur complement formulation. The rigorous stability analysis of the proposed algorithm is performed via the energy method. It was proved that the method is unconditionally stable provided αk≥1∕2 in all subdomains Ωk. Moreover, the same analysis indicates that the mixed explicit/implicit Euler method is conditionally stable. Some example problems are presented to examine the rate of convergence, stability as well as accuracy of the mixed multi-time step algorithm.