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Uncertainty Quantification for Porous Media Flow Using Multilevel Monte Carlo

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Large-Scale Scientific Computing (LSSC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 9374))

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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.

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Notes

  1. 1.

    https://github.com/wwu-numerik/DUNE-Multiscale/, BSD-2 licensed.

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Acknowledgements

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

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Authors and Affiliations

  1. Fraunhofer ITWM, Fraunhofer-Platz 1, 67663, Kaiserslautern, Germany

    Jan Mohring & Oleg Iliev

  2. Institute for Computational and Applied Mathematics, University of Münster, Orleans-Ring 10, 48149, Münster, Germany

    René Milk & Mario Ohlberger

  3. Interdisciplinary Center for Scientific Computing, University of Heidelberg, Im Neuenheimer Feld 368, 69120, Heidelberg, Germany

    Adrian Ngo, Ole Klein & Peter Bastian

Authors
  1. Jan Mohring
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  2. René Milk
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  3. Adrian Ngo
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  4. Ole Klein
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  5. Oleg Iliev
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  6. Mario Ohlberger
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  7. Peter Bastian
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Corresponding author

Correspondence to Jan Mohring .

Editor information

Editors and Affiliations

  1. Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Lirkov

  2. Inst. of Inform. & Communication, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Svetozar D. Margenov

  3. Informatics and Mathematical Modell, Technical University of Denmark, Kongens Lyngby, Denmark

    Jerzy Waśniewski

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Mohring, J. et al. (2015). Uncertainty Quantification for Porous Media Flow Using Multilevel Monte Carlo. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2015. Lecture Notes in Computer Science(), vol 9374. Springer, Cham. https://doi.org/10.1007/978-3-319-26520-9_15

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  • DOI: https://doi.org/10.1007/978-3-319-26520-9_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-26519-3

  • Online ISBN: 978-3-319-26520-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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