dc.contributor.author Liu, Yang dc.contributor.author Li, Jingfa dc.contributor.author Sun, Shuyu dc.contributor.author Yu, Bo dc.date.accessioned 2019-12-18T06:02:11Z dc.date.available 2019-12-18T06:02:11Z dc.date.issued 2019-10-10 dc.identifier.uri http://hdl.handle.net/10754/660649 dc.description.abstract The subsurface flow is usually subject to uncertain porous media structures. In most cases, however, we only have partial knowledge about the porous media properties. A common approach is to model the uncertain parameters of porous media as random fields, then the statistical moments (e.g. expectation) of the Quantity of Interest(QoI) can be evaluated by the Monte Carlo method. In this study, we develop a full multigrid-multilevel Monte Carlo (FMG-MLMC) method to speed up the evaluation of random parameters effects on single-phase porous flows. In general, MLMC method applies a series of discretization with increasing resolution and computes the QoI on each of them. The effective variance reduction is the success of the method. We exploit the similar hierarchies of MLMC and multigrid methods and obtain the solution on coarse mesh $Q^c_l$ as a byproduct of the full multigrid solution on fine mesh $Q^f_l$ on each level $l$. In the cases considered in this work, the computational saving due to the coarse mesh samples saving is $20\%$ asymptotically. Besides, a comparison of Monte Carlo and Quasi-Monte Carlo (QMC) methods reveals a smaller estimator variance and a faster convergence rate of the latter approach in this study. dc.description.sponsorship The authors gratefully acknowledge the support from the National Natural Science Foundation of China (Nos. 51874262, 51904031) and the Research Funding from King Abdullah University of Science and Technology (KAUST) through the grants BAS/1/1351-01-01. dc.publisher arXiv dc.relation.url https://arxiv.org/pdf/1910.04727 dc.rights Archived with thanks to arXiv dc.title A full multigrid multilevel Monte Carlo method for the single phase subsurface flow with random coefficients dc.type Preprint dc.contributor.department Computational Transport Phenomena Lab dc.contributor.department Computational Transport Phenomena Laboratory, Division of Physical Science and Engineering, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia dc.contributor.department Earth Science and Engineering Program dc.contributor.department Physical Science and Engineering (PSE) Division dc.eprint.version Pre-print dc.contributor.institution School of Mechanical Engineering, Beijing Key Laboratory of Pipeline Critical Technology and Equipment for Deepwater Oil & Gas Development, Beijing Institute of Petrochemical Technology, Beijing 102617, China dc.identifier.arxivid 1910.04727 kaust.person Liu, Yang kaust.person Li, Jingfa kaust.person Sun, Shuyu kaust.grant.number BAS/1/1351-01-01 refterms.dateFOA 2019-12-18T06:02:48Z
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