Multigrid algorithm for staggered lattice fermions
Critical slowing down in Krylov methods for the Dirac operator presents a major obstacle to further advances in lattice field theory as it approaches the continuum solution. Here we formulate a multigrid algorithm for the KogutSusskind (or staggered) fermion discretization which has proven difficult relative to Wilson multigrid due to its firstorder antiHermitian structure. The solution is to introduce a novel spectral transformation by the KählerDirac spin structure prior to the Galerkin projection. As a result, we present numerical results for the twodimensional, twoflavor Schwinger model; however, the general formalism is agnostic to dimension and is directly applicable to fourdimensional lattice QCD.
 Authors:

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^{[2]};
^{[3]}
 Boston Univ., Boston, MA (United States)
 NVIDIA Corp., Santa Clara, CA (United States)
 Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
 Publication Date:
 Report Number(s):
 FERMILABPUB18073CD; arXiv:1801.07823
Journal ID: ISSN 24700010; PRVDAQ; 1650136
 Grant/Contract Number:
 AC0207CH11359; SC0015845
 Type:
 Published Article
 Journal Name:
 Physical Review D
 Additional Journal Information:
 Journal Volume: 97; Journal Issue: 11; Journal ID: ISSN 24700010
 Publisher:
 American Physical Society (APS)
 Research Org:
 Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
 Sponsoring Org:
 USDOE National Nuclear Security Administration (NNSA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
 OSTI Identifier:
 1457586
 Alternate Identifier(s):
 OSTI ID: 1437400
Brower, Richard C., Weinberg, Evan, Clark, M. A., and Strelchenko, Alexei. Multigrid algorithm for staggered lattice fermions. United States: N. p.,
Web. doi:10.1103/PhysRevD.97.114513.
Brower, Richard C., Weinberg, Evan, Clark, M. A., & Strelchenko, Alexei. Multigrid algorithm for staggered lattice fermions. United States. doi:10.1103/PhysRevD.97.114513.
Brower, Richard C., Weinberg, Evan, Clark, M. A., and Strelchenko, Alexei. 2018.
"Multigrid algorithm for staggered lattice fermions". United States.
doi:10.1103/PhysRevD.97.114513.
@article{osti_1457586,
title = {Multigrid algorithm for staggered lattice fermions},
author = {Brower, Richard C. and Weinberg, Evan and Clark, M. A. and Strelchenko, Alexei},
abstractNote = {Critical slowing down in Krylov methods for the Dirac operator presents a major obstacle to further advances in lattice field theory as it approaches the continuum solution. Here we formulate a multigrid algorithm for the KogutSusskind (or staggered) fermion discretization which has proven difficult relative to Wilson multigrid due to its firstorder antiHermitian structure. The solution is to introduce a novel spectral transformation by the KählerDirac spin structure prior to the Galerkin projection. As a result, we present numerical results for the twodimensional, twoflavor Schwinger model; however, the general formalism is agnostic to dimension and is directly applicable to fourdimensional lattice QCD.},
doi = {10.1103/PhysRevD.97.114513},
journal = {Physical Review D},
number = 11,
volume = 97,
place = {United States},
year = {2018},
month = {6}
}