### 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 language | English (US) |
---|---|

Pages (from-to) | 463-490 |

Number of pages | 28 |

Journal | Numerische Mathematik |

Volume | 132 |

Issue number | 3 |

DOIs | |

State | Published - Mar 1 2016 |

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### All Science Journal Classification (ASJC) codes

- Computational Mathematics
- Applied Mathematics

### Cite this

*Numerische Mathematik*,

*132*(3), 463-490. https://doi.org/10.1007/s00211-015-0725-6

}

*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.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Multigrid preconditioning for the overlap operator in lattice QCD

AU - Brannick, James Joseph

AU - Frommer, Andreas

AU - Kahl, Karsten

AU - Leder, Björn

AU - Rottmann, Matthias

AU - Strebel, Artur

PY - 2016/3/1

Y1 - 2016/3/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84957849338&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84957849338&partnerID=8YFLogxK

U2 - 10.1007/s00211-015-0725-6

DO - 10.1007/s00211-015-0725-6

M3 - Article

AN - SCOPUS:84957849338

VL - 132

SP - 463

EP - 490

JO - Numerische Mathematik

JF - Numerische Mathematik

SN - 0029-599X

IS - 3

ER -