Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multilevel Monte Carlo on a high-dimensional parameter space for
  transmission problems with geometric uncertainties   In the framework of uncertainty quantification, we consider a quantity of
interest which depends non-smoothly on the high-dimensional parameter
representing the uncertainty. We show that, in this situation, the multilevel
Monte Carlo algorithm is a valid option to compute moments of the quantity of
interest (here we focus on the expectation), as it allows to bypass the precise
location of discontinuities in the parameter space. We illustrate how such lack
of smoothness occurs for the point evaluation of the solution to a (Helmholtz)
transmission problem with uncertain interface, if the point can be crossed by
the interface for some realizations. For this case, we provide a space
regularity analysis for the solution, in order to state converge results in the
L1-norm for the finite element discretization. The latter are then used to
determine the optimal distribution of samples among the Monte Carlo levels.
Particular emphasis is given on the robustness of our estimates with respect to
the dimension of the parameter space.

1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph