On multi-time-step monolithic coupling algorithms for elastodynamics

We present a way of constructing multi-time-step monolithic coupling methods for elastodynamics. The governing equations for constrained multiple subdomains are written in dual Schur form and the continuity of velocities is enforced at system time levels. The resulting equations will be in the form of differential–algebraic equations. To crystallize the ideas we shall employ Newmark family of time-stepping schemes. The proposed method can handle multiple subdomains, and allows different time-steps as well as different time stepping schemes from the Newmark family in different subdomains. We shall use the energy method to assess the numerical stability, and quantify the influence of perturbations under the proposed coupling method. Two different notions of energy preservation are introduced and employed to assess the performance of the proposed method. Several numerical examples are presented to illustrate the accuracy and stability properties of the proposed method. We shall also compare the proposed multi-time-step coupling method with some other methods available in the literature.