European Union’s Horizon 2020 research and innovation programme

Marie Sklodowska-Curie grant agreement NO 705402, POROSOS

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