Multigrid Preconditioning for the Overlap Operator in Lattice QCD
arXiv:1410.7170
Abstract
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.
References in corpus (6)
- Ab-initio Determination of Light Hadron Masses
- Adaptive multigrid algorithm for the lattice Wilson-Dirac operator
- Adaptive Multigrid Algorithm for Lattice QCD
- QCD thermodynamics with dynamical overlap fermions
- Localized eigenmodes of the overlap operator and their impact on the eigenvalue distribution
- Numerical properties of staggered overlap fermions