Spectrum of the Dirac Operator and Multigrid Algorithm with Dynamical Staggered Fermions

Details Spectrum of the Dirac Operator and Multigrid Algorithm with Dynamical Staggered Fermions Spectrum of the Dirac Operator and Multigrid Algorithm with Dynamical Staggered Fermions

1994-08-17

arxiv.org/abs/hep-lat/9408013v1

Phys.Rev. D51 (1995) 1305-1313

Physics

High Energy Physics

High Energy Physics - Lattice

19 pages, 8 figures, HUB-IEP-94/12 and KL-TH 19/94; comes as a uuencoded tar-compressed .ps-file

Scientific paper

10.1103/PhysRevD.51.1305

Complete spectra of the staggered Dirac operator $\Dirac$ are determined in quenched four-dimensional $SU(2)$ gauge fields, and also in the presence of dynamical fermions. Periodic as well as antiperiodic boundary conditions are used. An attempt is made to relate the performance of multigrid (MG) and conjugate gradient (CG) algorithms for propagators with the distribution of the eigenvalues of~$\Dirac$. The convergence of the CG algorithm is determined only by the condition number~$\kappa$ and by the lattice size. Since~$\kappa$'s do not vary significantly when quarks become dynamic, CG convergence in unquenched fields can be predicted from quenched simulations. On the other hand, MG convergence is not affected by~$\kappa$ but depends on the spectrum in a more subtle way.

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