A FETI-based multi-time-step coupling method for Newmark schemes in structural dynamics

We present an efficient and accurate multi-time-step coupling method using FETI domain decomposition for structural dynamics. Using this method one can divide a large structural mesh into a number of smaller subdomains, solve the individual subdomains separately and couple the solutions together to obtain the solution to the original problem. The various subdomains can be integrated in time using different time steps and/or different Newmark schemes. This approach will be most effective for very large-scale simulations on complex geometries. Our coupling method builds upon a method previously proposed by Gravouil and Combescure (GC method). We show that for the simplest case when the same time step is used in all subdomains of the mesh our method reduces to the GC method and is unconditionally stable and energy preserving. In addition, we show that our method possesses these desirable properties for general multi-time-step cases too unlike the GC method which is dissipative. Greater computational efficiency is also achieved through our method by limiting the computation of interface forces to the largest time step as opposed to the smallest time step in the GC method.