Flow, transport and diffusion in random geometries I: a MLMC algorithm

Handle URI:
http://hdl.handle.net/10754/624050
Title:
Flow, transport and diffusion in random geometries I: a MLMC algorithm
Authors:
Canuto, Claudio; Hoel, Haakon; Icardi, Matteo ( 0000-0003-3924-3117 ) ; Quadrio, Nathan; Tempone, Raul ( 0000-0003-1967-4446 )
Abstract:
Multilevel Monte Carlo (MLMC) is an efficient and flexible solution for the propagation of uncertainties in complex models, where an explicit parametrization 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 geoemtry and with random parameters. 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 discretization 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.
KAUST Department:
Computer, Electrical and Mathematical Sciences & Engineering (CEMSE)
Conference/Event name:
Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)
Issue Date:
7-Jan-2015
Type:
Poster
Appears in Collections:
Posters; Conference on Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)

Full metadata record

DC FieldValue Language
dc.contributor.authorCanuto, Claudioen
dc.contributor.authorHoel, Haakonen
dc.contributor.authorIcardi, Matteoen
dc.contributor.authorQuadrio, Nathanen
dc.contributor.authorTempone, Raulen
dc.date.accessioned2017-06-05T08:35:46Z-
dc.date.available2017-06-05T08:35:46Z-
dc.date.issued2015-01-07-
dc.identifier.urihttp://hdl.handle.net/10754/624050-
dc.description.abstractMultilevel Monte Carlo (MLMC) is an efficient and flexible solution for the propagation of uncertainties in complex models, where an explicit parametrization 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 geoemtry and with random parameters. 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 discretization 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.en
dc.titleFlow, transport and diffusion in random geometries I: a MLMC algorithmen
dc.typePosteren
dc.contributor.departmentComputer, Electrical and Mathematical Sciences & Engineering (CEMSE)en
dc.conference.dateJanuary 6-9, 2015en
dc.conference.nameAdvances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)en
dc.conference.locationKAUSTen
dc.contributor.institutionUniversity of Osloen
dc.contributor.institutionPolitecnico di Torinoen
kaust.authorIcardi, Matteoen
kaust.authorQuadrio, Nathanen
kaust.authorTempone, Raulen
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