  3D non-LTE radiative transfer problems are computationally demanding, and
this sets limits on the size of the problems that can be solved. So far
Multilevel Accelerated Lambda Iteration (MALI) has been to the method of choice
to perform high-resolution computations in multidimensional problems. The
disadvantage of MALI is that its computing time scales as $\mathcal{O}(n^2)$,
with $n$ the number of grid points. When the grid gets finer, the computational
cost increases quadratically. We aim to develop a 3D non-LTE radiative transfer
code that is more efficient than MALI. We implement a non-linear multigrid,
fast approximation storage scheme, into the existing Multi3D radiative transfer
code. We verify our multigrid implementation by comparing with MALI
computations. We show that multigrid can be employed in realistic problems with
snapshots from 3D radiative-MHD simulations as input atmospheres. With
multigrid, we obtain a factor 3.3-4.5 speedup compared to MALI. With
full-multigrid the speed-up increases to a factor 6. The speedup is expected to
increase for input atmospheres with more grid points and finer grid spacing.
Solving 3D non-LTE radiative transfer problems using non-linear multigrid
methods can be applied to realistic atmospheres with a substantial speed-up.
