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Uncertainty Quantification for Porous Media Flow Using Multilevel Monte Carlo

  • Jan Mohring
  • René Milk
  • Adrian Ngo
  • Ole Klein
  • Oleg Iliev
  • Mario Ohlberger
  • Peter Bastian
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9374)

Abstract

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.

Keywords

Uncertainty quantification Multilevel Monte Carlo Multiscale finite elements Porous media Random permeability Exa-scale DUNE 

Notes

Acknowledgements

This research was funded by the DFG SPP 1648 Software for Exascale Computing.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Jan Mohring
    • 1
  • René Milk
    • 2
  • Adrian Ngo
    • 3
  • Ole Klein
    • 3
  • Oleg Iliev
    • 1
  • Mario Ohlberger
    • 2
  • Peter Bastian
    • 3
  1. 1.Fraunhofer ITWMKaiserslauternGermany
  2. 2.Institute for Computational and Applied MathematicsUniversity of MünsterMünsterGermany
  3. 3.Interdisciplinary Center for Scientific ComputingUniversity of HeidelbergHeidelbergGermany

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