  We present a multi-level algorithm for the solution of five dimensional
chiral fermion formulations, including domain wall and Mobius Fermions. The
algorithm operates on the red-black preconditioned Hermitian operator, and
directly accelerates conjugate gradients on the normal equations. The coarse
grid representation of this matrix is next-to-next-to-next-to-nearest neighbour
and multiple algorithmic advances are introduced, which help minimise the
overhead of the coarse grid. The treatment of the coarse grids is purely four
dimensional, and the bulk of the coarse grid operations are nearest neighbour.
The intrinsic cost of most of the coarse grid operations is therefore
comparable to those for the Wilson case. We also document the implementation of
this algorithm in the BAGEL/Bfm software package and report on the measured
performance gains the algorithm brings to simulations at the physical point on
IBM BlueGene/Q hardware.
