European Union’s Horizon 2020 research and innovation programme

Marie Sklodowska-Curie grant agreement NO 705402, POROSOS

FAST SOLVERS FOR POROELASTICITY PROBLEMS

The fixed-stress split method has been widely used as solution method in the coupling of flow and geomechanics. We have analyzed the behavior of an inexact version of this algorithm as smoother within a geometric multigrid method, in order to obtain an efficient monolithic solver for Biot’s problem. This solver combines the advantages of being a fully coupled method, with the benefit of decoupling the flow and the mechanics part in the smoothing algorithm. Moreover, the fixed-stress split smoother is based on the physics of the problem, and therefore all parameters involved in the relaxation are based on the physical properties of the medium and are given a priori. A local Fourier analysis is applied to study the convergence of the multigrid method and to support the good convergence results obtained.

Besides, we have proposed a new version of the fixed stress splitting method. 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.

PUBLICATIONS:

On the fixed-stress scheme as smoother in multigrid methods for coupling flow and geomechanics. F.J. Gaspar, C. Rodrigo. Computer Methods in Applied Mechanics and Engineering (2017) : LINK

A partially parallel-in-time fixed-stress splitting method for Biot’s consolidation model. M. Borregales, K. Kumar, F. Radu, C. Rodrigo, F .J. Gaspar, Computers & Mathematics with Applications (2018). LINK

On an Uzawa smoother in multigrid for poroelasticity equations. P. Luo, C. Rodrigo, F.J. Gaspar, C.W. Oosterlee. Numerical Linear Algebra with Applications (2017) : LINK