Solution of Large-Scale Porous Media Problems

Porous media are encountered in many fields of applications such as chemical and geotechnical engineering. A porous media problem formulation of special interest is the u-p formulation where the displacements u of the solid skeleton and the pressures p of the pore fluid(s) are the main variables. The optimum solution method for such coupled problems is still an open issue. The monolithic approach is the most reliable but also the most expensive one for solving field equations simultaneously. Accelerating the solution procedure in parallel computer environment has been unsuccessfully attempted in the past. In this work 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.