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In the framework of uncertainty quantification, we consider a quantity ofinterest which depends non-smoothly on the high-dimensional parameterrepresenting the uncertainty. We show that, in this situation, the multilevelMonte Carlo algorithm is a valid option to compute moments of the quantity ofinterest (here we focus on the expectation), as it allows to bypass the preciselocation of discontinuities in the parameter space. We illustrate how such lackof smoothness occurs for the point evaluation of the solution to a (Helmholtz)transmission problem with uncertain interface, if the point can be crossed bythe interface for some realizations. For this case, we provide a spaceregularity analysis for the solution, in order to state converge results in theL1-norm for the finite element discretization. The latter are then used todetermine the optimal distribution of samples among the Monte Carlo levels.Particular emphasis is given on the robustness of our estimates with respect tothe dimension of the parameter space.

Multilevel Monte Carlo on a high-dimensional parameter space for transmission problems with geometric uncertainties