  In Lattice QCD computations a substantial amount of work is spent in solving
the Dirac equation. In the recent past it has been observed that conventional
Krylov solvers tend to critically slow down for large lattices and small quark
masses. We present a Schwarz alternating procedure (SAP) multilevel method as a
solver for the Clover improved Wilson discretization of the Dirac equation.
This approach combines two components (SAP and algebraic multigrid) that have
separately been used in lattice QCD before. In combination with a bootstrap
setup procedure we show that considerable speed-up over conventional Krylov
subspace methods for realistic configurations can be achieved.
