Uncertainty Quantification for Porous Media Flow Using Multilevel Monte Carlo
- 616 Downloads
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  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.
KeywordsUncertainty quantification Multilevel Monte Carlo Multiscale finite elements Porous media Random permeability Exa-scale DUNE
This research was funded by the DFG SPP 1648 Software for Exascale Computing.
- 6.Ngo, A.Q.: Discontinuous Galerkin based geostatistical inversion of stationary flow and transport processes in groundwater. Dissertation, University of Heidelberg (2015)Google Scholar
- 7.Milk, R., Mohring, J.: DUNE mlmc, March 2015. http://dx.doi.org/10.5281/zenodo.16562
- 9.Efendiev, Y., Hou, T.Y.: Multiscale Finite Element Methods: Theory and Applications. Surveys and Tutorials in the Applied Mathematical Sciences, vol. 4. Springer, New York (2009)Google Scholar
- 13.Schindler, F., Milk, R.: DUNE Generic Discretization Toolbox, March 2015. http://dx.doi.org/10.5281/zenodo.16563
- 14.Milk, R., Schindler, F.: DUNE Stuff, March 2015. http://dx.doi.org/10.5281/zenodo.16564
- 15.Milk, R., Kaulmann, S.: DUNE Multiscale, March 2015. http://dx.doi.org/10.5281/zenodo.16560
- 16.Bastian, P., et al.: EXA-DUNE: flexible PDE solvers, numerical methods and applications. In: Lopes, L., et al. (eds.) Euro-Par 2014, Part II. LNCS, vol. 8806, pp. 530–541. Springer, Heidelberg (2014) Google Scholar