10 mmd11 applied mathematics - jan 2011

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We investigated the applicability and efficiency of the MLMC approach to the Henry-like problem with uncertain porosity, permeability and recharge. These uncertain parameters were modelled by random fields with three independent random variables. Permeability is a function of porosity. Both functions are time-dependent, have multi-scale behaviour and are defined for two layers. The numerical solution for each random realisation was obtained using the well-known ug4 parallel multigrid solver. The number of random samples required at each level was estimated by calculating the decay of the variances and the computational cost for each level. The MLMC method was used to compute the expected value and variance of several QoIs, such as the solution at a few preselected points $(t,\bx)$, the solution integrated over a small subdomain, and the time evolution of the freshwater integral. We have found that some QoIs require only 2-3 mesh levels and samples from finer meshes would not significantly improve the result. Other QoIs require more grid levels.

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