  The overlap operator is a lattice discretization of the Dirac operator of
quantum chromodynamics, the fundamental physical theory of the strong
interaction between the quarks. As opposed to other discretizations it
preserves the important physical property of chiral symmetry, at the expense of
requiring much more effort when solving systems with this operator. We present
a preconditioning technique based on another lattice discretization, the
Wilson-Dirac operator. The mathematical analysis precisely describes the effect
of this preconditioning in the case that the Wilson-Dirac operator is normal.
Although this is not exactly the case in realistic settings, we show that
current smearing techniques indeed drive the Wilson-Dirac operator towards
normality, thus providing a motivation why our preconditioner works well in
computational practice. Results of numerical experiments in physically relevant
settings show that our preconditioning yields accelerations of up to one order
of magnitude.
