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Spectrum of the Dirac operator and multigrid algorithm with dynamical staggered fermions

Technical Report:

Abstract

Complete spectra of the staggered Dirac operator D 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 D. The convergence of the CG algorithm is determined only by the condition number k and by the lattice size. Since k`s do not vary signigicantly 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 k but depends on the spectrum in a more subtle way. (orig.)
Authors:
Kalkreuter, T [1] 
  1. Kaiserslautern Univ. (Germany). Fachbereich Physik
Publication Date:
Aug 01, 1994
Product Type:
Technical Report
Report Number:
DESY-94-150; HUB-IEP-94/12; KL-TH-19/94
Reference Number:
SCA: 662110; PA: DEN-94:0FM113; EDB-95:017826; SN: 95001304898
Resource Relation:
Other Information: PBD: Aug 1994
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; UNIFIED GAUGE MODELS; LATTICE FIELD THEORY; DIRAC OPERATORS; ALGORITHMS; BOUNDARY CONDITIONS; DIRAC EQUATION; EIGENVALUES; FERMIONS; FOUR-DIMENSIONAL CALCULATIONS; PROPAGATOR; SU-2 GROUPS; SPECTRA; FLUCTUATIONS; SPECTRAL DENSITY; CONVERGENCE; COMPUTERIZED SIMULATION; NUMERICAL SOLUTION; ITERATIVE METHODS; 662110; THEORY OF FIELDS AND STRINGS
Sponsoring Organizations:
Deutsche Forschungsgemeinschaft, Bonn (Germany)
OSTI ID:
10105081
Research Organizations:
Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
Country of Origin:
Germany
Language:
English
Other Identifying Numbers:
Journal ID: ISSN 0418-9833; Other: ON: DE95725566; TRN: DE94FM113
Availability:
OSTI; NTIS (US Sales Only); INIS
Submitting Site:
DEN
Size:
21 p.
Announcement Date:
Jun 30, 2005

Technical Report:

Citation Formats

Kalkreuter, T. Spectrum of the Dirac operator and multigrid algorithm with dynamical staggered fermions. Germany: N. p., 1994. Web.
Kalkreuter, T. Spectrum of the Dirac operator and multigrid algorithm with dynamical staggered fermions. Germany.
Kalkreuter, T. 1994. "Spectrum of the Dirac operator and multigrid algorithm with dynamical staggered fermions." Germany.
@misc{etde_10105081,
title = {Spectrum of the Dirac operator and multigrid algorithm with dynamical staggered fermions}
author = {Kalkreuter, T}
abstractNote = {Complete spectra of the staggered Dirac operator D 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 D. The convergence of the CG algorithm is determined only by the condition number k and by the lattice size. Since k`s do not vary signigicantly 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 k but depends on the spectrum in a more subtle way. (orig.)}
place = {Germany}
year = {1994}
month = {Aug}
}