Uncertainty Quantification for Porous Media Flow Using Multilevel Monte Carlo

Mohring Jan, Milk Rene, Ngo Adrian, Klein Ole, Iliev Oleg, Ohlberger Mario, Bastian Peter

Research article in edited proceedings (conference) | Peer reviewed

Abstract

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 classical Monte Carlo by combining cheap/inexact and expensive/accurate solutions in an optimal ratio.

Details about the publication

PublisherLirkov I., Margenov S. D. , Wasniewski J.
Book titleProceedings of 10th International Conference on Large-Scale Scientific Computations, Sozopol 2015
Page range145-152
Publishing companySpringer International Publishing
Title of seriesLecture Notes in Computational Science
Volume of series9374
StatusPublished
Release year2015
Language in which the publication is writtenEnglish
Conference10th International Conference on Large-Scale Scientific Computations, Sozopol, undefined
DOI10.1007/978-3-319-26520-9_15

Authors from the University of Münster

Fritze, René
Professorship of Applied Mathematics, especially Numerics (Prof. Ohlberger)
Ohlberger, Mario
Professorship of Applied Mathematics, especially Numerics (Prof. Ohlberger)
Center for Nonlinear Science
Center for Multiscale Theory and Computation