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Improved Monte Carlo methods for computing failure probabilities of porous media flow systems
Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, LUVAL.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, LUVAL.
2015 (English)Report (Other academic)
Place, publisher, year, edition, pages
2015.
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2015-025
National Category
Computational Mathematics Oceanography, Hydrology, Water Resources
Identifiers
URN: urn:nbn:se:uu:diva-261005OAI: oai:DiVA.org:uu-261005DiVA: diva2:849281
Available from: 2015-08-31 Created: 2015-08-27 Last updated: 2016-07-05Bibliographically approved
In thesis
1. Multiscale and multilevel methods for porous media flow problems
Open this publication in new window or tab >>Multiscale and multilevel methods for porous media flow problems
2015 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

We consider two problems encountered in simulation of fluid flow through porous media. In macroscopic models based on Darcy's law, the permeability field appears as data.

The first problem is that the permeability field generally is not entirely known. We consider forward propagation of uncertainty from the permeability field to a quantity of interest. We focus on computing p-quantiles and failure probabilities of the quantity of interest. We propose and analyze improved standard and multilevel Monte Carlo methods that use computable error bounds for the quantity of interest. We show that substantial reductions in computational costs are possible by the proposed approaches.

The second problem is fine scale variations of the permeability field. The permeability often varies on a scale much smaller than that of the computational domain. For standard discretization methods, these fine scale variations need to be resolved by the mesh for the methods to yield accurate solutions. We analyze and prove convergence of a multiscale method based on the Raviart–Thomas finite element. In this approach, a low-dimensional multiscale space based on a coarse mesh is constructed from a set of independent fine scale patch problems. The low-dimensional space can be used to yield accurate solutions without resolving the fine scale.

Place, publisher, year, edition, pages
Uppsala University, 2015
Series
Information technology licentiate theses: Licentiate theses from the Department of Information Technology, ISSN 1404-5117 ; 2015-003
National Category
Computational Mathematics
Research subject
Scientific Computing with specialization in Numerical Analysis
Identifiers
urn:nbn:se:uu:diva-262276 (URN)
Supervisors
Available from: 2015-09-09 Created: 2015-09-11 Last updated: 2017-08-31Bibliographically approved

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Fagerlund, FritjofHellman, FredrikMålqvist, AxelNiemi, Auli

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