On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics

Francisco J. Gaspar, Carmen Rodrigo
2017 Computer Methods in Applied Mechanics and Engineering  
The fixed-stress split method has been widely used as solution method in the coupling of flow and geomechanics. In this work, we analyze the behaviour of an inexact version of this algorithm as smoother within a geometric multigrid method, in order to obtain an efficient monolithic solver for the 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
more » ... 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. The proposed geometric multigrid algorithm is used to solve several tests in semi-structured triangular grids, in order to show the good behaviour of the method and its practical utility.
doi:10.1016/j.cma.2017.08.025 fatcat:7o6hxgvi3rdj5dhg2rps3e6nre