Uncertainty Quantification for Porous Media Flow Using Multilevel Monte Carlo

Uncertainty quantification (UQ) for porous media flow is of great importance for many societal, environmental and industrial problems. An obstacle for progress in this area is the extreme computational effort needed for solving realistic problems. It is expected that exa-scale computers will open the door for a significant progress in this area. We demonstrate how new features of the Distributed and Unified Numerics Environment DUNE [1] address these challenges. In the frame of the DFG funded project EXA-DUNE the software has been extended by multiscale finite element methods (MsFEM) and by a parallel framework for the multilevel Monte Carlo (MLMC) approach. This is a general concept for computing expected values of simulation results depending on random fields, e.g. the permeability of porous media. It belongs to the class of variance reduction methods and overcomes the slow convergence of classical Monte Carlo by combining cheap/inexact and expensive/accurate solutions in an optimal ratio.