Multi-time-step domain decomposition and coupling methods for nonlinear parabolic problems

In this paper we propose and examine a multi-time-step algorithm using a FETI-based domain decomposition method for nonlinear parabolic problems. The computational domain is divided into a set of smaller subdomains that may be integrated concurrently with their own time steps. The continuity condition at the interface is ensured employing local Lagrange multipliers. The equation of continuity of primary unknowns at the interface is written only at the so-called system time step. The subdomain problems are coupled together by requiring the Lagrange multipliers on the interface at the intermediate time steps to match a suitable interpolation of the values at the system time steps. This allows each subdomain to be solved with its own time step. The rigorous nonlinear stability is performed via the energy method. Several numerical examples will be solved to illustrate the overall performance of the proposed coupling method.