Advances on the domain decomposition solution of large scale porous media problems

In this paper, a family of state-of-the-art parallel domain decomposition methods that combine the advantages of both direct and iterative solvers are investigated for the monolithic solution of the u–p formulation of the porous media problem. Moreover, a new family of parallel domain decomposition methods, specifically tailored for the above problem formulation is presented which outperforms the current state-of-the-art parallel domain decomposition solvers. The power of this family of solvers is demonstrated in two large scale porous media problems.