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.
@article{arxiv.1802.00949,
title = {A parallel-in-time fixed-stress splitting method for Biot's consolidation model},
author = {Manuel Borregales and Kundan Kumar and Florin Adrian Radu and Carmen Rodrigo and Francisco José Gaspar},
journal= {arXiv preprint arXiv:1802.00949},
year = {2018}
}