  We develop a multirate timestepper for semi-implicit solutions of the
unsteady incompressible Navier-Stokes equations (INSE) based on a
recently-developed multidomain spectral element method (SEM). For {\em
incompressible} flows, multirate timestepping (MTS) is particularly challenging
because of the tight coupling implied by the incompressibility constraint,
which manifests as an elliptic subproblem for the pressure at each timestep.
The novelty of our approach stems from the development of a stable overlapping
Schwarz method applied directly to the Navier-Stokes equations, rather than to
the convective, viscous, and pressure substeps that are at the heart of most
INSE solvers. Our MTS approach is based on a predictor-corrector (PC) strategy
that preserves the temporal convergence of the underlying semi-implicit
timestepper. We present numerical results demonstrating that this approach
scales to an arbitrary number of overlapping grids, accurately models complex
turbulent flow phenomenon, and improves computational efficiency in comparison
to singlerate timestepping-based calculations.
