Data Assimilation Meetings at Reading

Date Meeting type Speakers
23 May 2013 Invited Speaker Aretha Tuckentrup (University of Bath)
Multilevel Monte Carlo methods for uncertainty quantification in subsurface flow (pdf)
The quantification of uncertainty in groundwater flow plays a central role in the safety assessment of radioactive waste disposal and of CO2 capture and storage underground. Stochastic modelling of data uncertainties in the rock permeabilities lead to elliptic PDEs with random coefficients. Typical models used for the random coefficients, such as log-normal random fields with exponential covariance, are unbounded and have only limited spatial regularity, making practical computations very expensive and the rigorous numerical analysis challenging. To overcome the problem of the prohibitively large computational cost of standard Monte Carlo methods, we introduce a multilevel Monte Carlo algorithm, based on a hierarchy of spatial levels/grids. We will demonstrate on a typical model problem the significant gains with respect to conventional Monte Carlo that are possible with this new approach. We will also discuss the extension of the multilevel idea to the case of Markov chain Monte Carlo.

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