Handle URI:
http://hdl.handle.net/10754/624838
Title:
Flow in Random Microstructures: a Multilevel Monte Carlo Approach
Authors:
Icardi, Matteo; Tempone, Raul ( 0000-0003-1967-4446 )
Abstract:
In this work we are interested in the fast estimation of effective parameters of random heterogeneous materials using Multilevel Monte Carlo (MLMC). MLMC is an efficient and flexible solution for the propagation of uncertainties in complex models, where an explicit parametrisation of the input randomness is not available or too expensive. We propose a general-purpose algorithm and computational code for the solution of Partial Differential Equations (PDEs) on random heterogeneous materials. We make use of the key idea of MLMC, based on different discretization levels, extending it in a more general context, making use of a hierarchy of physical resolution scales, solvers, models and other numerical/geometrical discretisation parameters. Modifications of the classical MLMC estimators are proposed to further reduce variance in cases where analytical convergence rates and asymptotic regimes are not available. Spheres, ellipsoids and general convex-shaped grains are placed randomly in the domain with different placing/packing algorithms and the effective properties of the heterogeneous medium are computed. These are, for example, effective diffusivities, conductivities, and reaction rates. The implementation of the Monte-Carlo estimators, the statistical samples and each single solver is done efficiently in parallel. The method is tested and applied for pore-scale simulations of random sphere packings.
KAUST Department:
Computer, Electrical and Mathematical Sciences & Engineering (CEMSE)
Conference/Event name:
Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2016)
Issue Date:
6-Jan-2016
Type:
Poster
Appears in Collections:
Posters; Conference on Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2016)

Full metadata record

DC FieldValue Language
dc.contributor.authorIcardi, Matteoen
dc.contributor.authorTempone, Raulen
dc.date.accessioned2017-06-08T06:32:29Z-
dc.date.available2017-06-08T06:32:29Z-
dc.date.issued2016-01-06-
dc.identifier.urihttp://hdl.handle.net/10754/624838-
dc.description.abstractIn this work we are interested in the fast estimation of effective parameters of random heterogeneous materials using Multilevel Monte Carlo (MLMC). MLMC is an efficient and flexible solution for the propagation of uncertainties in complex models, where an explicit parametrisation of the input randomness is not available or too expensive. We propose a general-purpose algorithm and computational code for the solution of Partial Differential Equations (PDEs) on random heterogeneous materials. We make use of the key idea of MLMC, based on different discretization levels, extending it in a more general context, making use of a hierarchy of physical resolution scales, solvers, models and other numerical/geometrical discretisation parameters. Modifications of the classical MLMC estimators are proposed to further reduce variance in cases where analytical convergence rates and asymptotic regimes are not available. Spheres, ellipsoids and general convex-shaped grains are placed randomly in the domain with different placing/packing algorithms and the effective properties of the heterogeneous medium are computed. These are, for example, effective diffusivities, conductivities, and reaction rates. The implementation of the Monte-Carlo estimators, the statistical samples and each single solver is done efficiently in parallel. The method is tested and applied for pore-scale simulations of random sphere packings.en
dc.titleFlow in Random Microstructures: a Multilevel Monte Carlo Approachen
dc.typePosteren
dc.contributor.departmentComputer, Electrical and Mathematical Sciences & Engineering (CEMSE)en
dc.conference.dateJanuary 5-10, 2016en
dc.conference.nameAdvances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2016)en
dc.conference.locationKAUSTen
dc.contributor.institutionUniversity of Warwicken
kaust.authorTempone, Raulen
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