  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 enforce the continuity of velocities 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. We also discuss the
conditions under which the proposed method will be energy preserving, and the
conditions under which the method will be energy conserving. 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 similar methods available in the literature.
