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 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. The method is partially parallel-in-time. We present a rigorous convergence analysis of the method and numerical experiments to demonstrate the robust behaviour of the algorithm.

Biot's model, Convergence analysis, Finite elements, Iterative fixed-stress splitting scheme, Parallel-in-time, Poromechanics
dx.doi.org/10.1016/j.camwa.2018.09.005
Computers & Mathematics with Applications
Centrum Wiskunde & Informatica, Amsterdam, The Netherlands

Borregales, M, Kumar, K, Radu, F.A, Rodrigo, C, & Gaspar, F.J. (2018). A partially parallel-in-time fixed-stress splitting method for Biot's consolidation model. Computers & Mathematics with Applications. doi:10.1016/j.camwa.2018.09.005