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Uncertainty Quantification for Porous Media Flow Using Multilevel Monte Carlo

Jan Mohring, Rene Milk, Adrian Ngo, Ole Klein, Oleg Iliev, Mario Ohlberger, Peter Bastian
Large-Scale Scientific Computing. 10th International Conference, LSSC 2015, Sozopol, Bulgaria, June 8-12, 2015. , Volume 9374 , page 145--152 - 2015
Uncertainty quanti cation (UQ) for porous media flow is of great importance for many societal, environmental and industrial prob- lems. 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 signi cant progress in this area. We demonstrate how new features of the Distributed and Uni ed Numerics Environment DUNE address these challenges. In the frame of the DFG funded project EXA-DUNE the software has been extended by multi- scale nite element methods (MsFEM) and by a parallel framework for the multilevel Monte Carlo approach (MLMC). This is a general concept for computing expected values of simulation results depending on random elds, e.g. the permeability of porous media. It belongs to the class of variance reduction methods and overcomes the slow convergence of clas- sical Monte Carlo by combining cheap/inexact and expensive/accurate solutions in an optimal ratio.

Références BibTex

@InProceedings{MMNKIOB15,
  author       = {Mohring, J. and Milk, R. and Ngo, A. and Klein, O. and Iliev, O. and Ohlberger, M. and Bastian, P.},
  title        = {Uncertainty Quantification for Porous Media Flow Using Multilevel Monte Carlo},
  booktitle    = {Large-Scale Scientific Computing. 10th International Conference, LSSC 2015, Sozopol, Bulgaria, June 8-12, 2015. },
  series       = {Lecture Notes in Computer Science   },
  volume       = {9374 },
  pages        = {145--152},
  year         = {2015},
  editor       = {I. Lirkov, S. D. Margenov, J. Wasniewski},
  publisher    = {Springer International Publishing},
  issn         = {0302-9743},
  doi          = {10.1007/978-3-319-26520-9_15},
  url          = \{/2015/MMNKIOB15},
}

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