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The overlap operator is a lattice discretization of the Dirac operator ofquantum chromodynamics, the fundamental physical theory of the stronginteraction between the quarks. As opposed to other discretizations itpreserves the important physical property of chiral symmetry, at the expense ofrequiring much more effort when solving systems with this operator. We presenta preconditioning technique based on another lattice discretization, theWilson-Dirac operator. The mathematical analysis precisely describes the effectof this preconditioning in the case that the Wilson-Dirac operator is normal.Although this is not exactly the case in realistic settings, we show thatcurrent smearing techniques indeed drive the Wilson-Dirac operator towardsnormality, thus providing a motivation why our preconditioner works well incomputational practice. Results of numerical experiments in physically relevantsettings show that our preconditioning yields accelerations of up to one orderof magnitude.

Multigrid Preconditioning for the Overlap Operator in Lattice QCD