A parallel-in-time fixed-stress splitting method for Biot's consolidation model
This work addresses the need for faster solvers in coupled flow and geomechanics simulations, but the results are incremental as it extends an existing method to parallel-in-time without reporting concrete speedups or comparisons.
The authors propose a parallel-in-time version of the fixed-stress splitting method for solving Biot's consolidation model, enabling parallelization across the time dimension. They provide a rigorous convergence analysis and demonstrate robust algorithm behavior through numerical experiments.
In this work, we study the parallel-in-time iterative solution of coupled flow and geomechanics in porous media, modelled by a two-field formulation of the Biot's equations. In particular, we propose a new version of the fixed stress splitting method, which has been widely used as solution method of these problems. This new approach forgets about the sequential nature of the temporal variable and considers the time direction as a further direction for parallelization. We present a rigorous convergence analysis of the method and a numerical experiment to demonstrate the robust behaviour of the algorithm.