Multigrid preconditioning for the overlap operator in lattice QCD

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

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

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
Volume132
Issue number3
DOIs
StatePublished - Mar 1 2016

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Dirac Operator
Preconditioning
Overlap
Physical properties
Discretization
Operator
Experiments
Preconditioning Techniques
Chiral Symmetry
Mathematical Analysis
Physical property
Preconditioner
Normality
Quarks
Numerical Experiment
Interaction

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

Cite this

Brannick, James Joseph ; Frommer, Andreas ; Kahl, Karsten ; Leder, Björn ; Rottmann, Matthias ; Strebel, Artur. / Multigrid preconditioning for the overlap operator in lattice QCD. In: Numerische Mathematik. 2016 ; Vol. 132, No. 3. pp. 463-490.
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Brannick, JJ, Frommer, A, Kahl, K, Leder, B, Rottmann, M & Strebel, A 2016, 'Multigrid preconditioning for the overlap operator in lattice QCD', Numerische Mathematik, vol. 132, no. 3, pp. 463-490. https://doi.org/10.1007/s00211-015-0725-6

Multigrid preconditioning for the overlap operator in lattice QCD. / Brannick, James Joseph; Frommer, Andreas; Kahl, Karsten; Leder, Björn; Rottmann, Matthias; Strebel, Artur.

In: Numerische Mathematik, Vol. 132, No. 3, 01.03.2016, p. 463-490.

Research output: Contribution to journalArticle

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