A Parallel-in-time Method Based on Preconditioner for Biot's Model

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.