Multigrid preconditioning for the overlap operator in lattice QCD

James Brannick, Andreas Frommer, Karsten Kahl, Björn Leder, Matthias Rottmann, Artur Strebel

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


The overlap operator is a lattice discretization of the Dirac operator of quantum chromodynamics (QCD), 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 posed 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 strategy 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 motivation for why our preconditioner works well in practice. Results of numerical experiments in physically relevant settings show that our preconditioning yields accelerations of more than an order of magnitude compared to unpreconditioned solvers.

Original languageEnglish (US)
Pages (from-to)463-490
Number of pages28
JournalNumerische Mathematik
Issue number3
StatePublished - Mar 1 2016

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics


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