  We proposed a parallel-in-time method based on preconditioner for Biot's
consolidation model in poroelasticity. In order to achieve a fast and stable
convergence for the matrix system of the Biot's model, we design two
preconditioners with approximations of the Schur complement. The
parallel-in-time method employs an inverted time-stepping scheme that iterates
to solve the preconditioned linear system in the outer loop and advances the
time step in the inner loop. This allows us to parallelize the iterations with
a theoretical parallel efficiency that approaches 1 as the number of time steps
and spatial steps grows. We demonstrate the stability, accuracy, and linear
speedup of our method on HPC platform through numerical experiments.
