  This work addresses uncertainty quantification of electromagnetic devices
determined by the eddy current problem. The multilevel Monte Carlo (MLMC)
method is used for the treatment of uncertain parameters while the devices are
discretized in space by the finite element method. Both methods yield numerical
approximations such that the total errors is split into stochastic and spatial
contributions. We propose a particular implementation where the spatial error
is controlled based on a Richardson-extrapolation-based error indicator. The
stochastic error in turn is efficiently reduced in the MLMC approach by
distributing the samples on multiple grids. The method is applied to a toy
problem with closed-form solution and a permanent magnet synchronous machine
with uncertainties. The uncertainties under consideration are related to the
material properties in the stator and the magnets in the rotor. The examples
show that the error indicator works reliably, the meshes used for the different
levels do not have to be nested and, most importantly, MLMC reduces the
computational cost by at least one order of magnitude compared to standard
Monte Carlo.
