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European Union’s Horizon 2020 research and
innovation programme
Marie Sklodowska-Curie grant agreement NO
705402, POROSOS
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MULTILEVEL MONTE CARLO METHODS FOR UNCERTAINTY QUANTIFICATION FOR POROUS
MEDIA FLOWS
We have proposed a multilevel Monte Carlo
method for Uncertainty Quantification of advection-dominated contaminant
transport in a coupled Darcy-Stokes flow system. We focus on high-dimensional
epistemic uncertainty due to an unknown permeability field in the Darcy domain
that is modeled as a lognormal random field.
We also propose a cell-centered multigrid
method for the robust and efficient solution of partial differential equations
with random coefficients. The excellent convergence of the method is supported
by a non-standard local Fourier analysis, which is capable of accurately
predicting the multigrid convergence for problems with random coefficients. Moreover,
the information provided by this analysis helps us to estimate a-priori the
time needed for solving uncertainty quantification problems by means of a
multigrid multilevel Monte Carlo method.
PUBLICATIONS:
A multigrid multilevel Monte Carlo method for transport in the
Darcy-Stokes system.
P. Kumar, P. Luo, F.J. Gaspar, C.W. Oosterlee. Journal of Computational Physics
(2018) : LINK
On cell-centered multigrid methods and Local
Fourier Analysis for PDEs with random coefficients. P. Kumar, C. Rodrigo, F .J. Gaspar, C.W. Oosterlee. LINK