  We present a new implementation of the Fourier acceleration method for Landau
gauge fixing. By means of a multigrid inversion we are able to avoid the use of
the fast Fourier transform. This makes the method more flexible, and well
suited for vector and parallel machines. We study the performance of this
algorithm on serial and on parallel (APE100) machines for the 4-dimensional
SU(2) case. We find that our method is equivalent to the standard
implementation of Fourier acceleration already on a serial machine, and that it
parallelizes very efficiently: its computational cost shows a linear speedup
with the number of processors. We have also implemented, on the parallel
machines, a version of the method using conjugate gradient instead of
multigrid. This leads to an algorithm that is efficient at intermediate lattice
volumes.
