  We present promising initial results of our adaptive multigrid solver
developed for application directly to the non-Hermitian Wilson-Dirac system in
4 dimensions, as opposed to the solver developed in [1] for the corresponding
normal equations. The key behind the success of this algorithm is the use of an
adaptive projection onto coarse grids that preserves the near null space of the
system matrix. We demonstrate that the resulting algorithm has weak dependence
on the gauge coupling and exhibits extremely mild critical slowing down in the
chiral limit.
